Generated using version 3.0 of the official AMS LATEX template

Shear and shear-driven diapycnal mixing at the base of the1

oceanic mixed layer2

Liam Brannigan ∗

Atmospheric, Oceanic & Planetary Physics, University of Oxford, Oxford, UK

3

Yueng-Djern Lenn and Tom P. Rippeth

School of Ocean Sciences, Bangor University, Menai Bridge, Wales, UK

4

Elaine McDonagh

National Oceanography Centre, Southampton, UK

5

Teresa K. Chereskin and Janet Sprintall

Scripps Institution of Oceanography, University of California in San Diego, USA

6

∗Corresponding author address: Liam Brannigan, Atmospheric, Oceanic & Planetary Physics, University

of Oxford, Oxford, United Kingdom.

E-mail: brannigan@atm.ox.ac.uk

1

ABSTRACT7

Observational data have been used to evaluate a simple theoretical model for the generation8

of shear spikes at the base of the oceanic mixed layer. The model predicts that large changes9

in shear squared are due to the alignment and magnitude of the wind and shear vectors.10

The observational data from a high resolution cruise in Drake Passage have shown that the11

model is most effective at predicting changes in shear when shear is driven by near-inertial12

wind-driven currents. It is also more effective as stratification approaches typical open ocean13

values. Richardson number analysis confirms that much of the shear spiking is adequate to14

drive diapycnal mixing across the base of the mixed layer well in excess of background levels.15

Rotary spectral and statistical analysis of an additional 242 Drake Passage transects from16

1999 to 2011 reveals the prevalence of shear-spiking throughout the year, with the highest17

associated diapycnal mixing potential occurring in northern Drake Passage during winter.18

1

1. Introduction19

High shear characterises the water column just below the surface mixed layer in observa-20

tions throughout the global ocean (Johnston and Rudnick 2009). The key driving force for21

this shear is thought to be the wind stress applied locally at the ocean surface (Grant and22

Belcher 2011). Observations from shelf-sea locations, however, have shown that periods of23

high shear are very intermittent and are not always directly correlated with the magnitude24

of the wind forcing (Rippeth et al. 2009).25

The high near-surface shear has a number of important consequences for the general26

circulation of the ocean and the fluxes of properties such as heat and nutrients. Intermittent27

spikes in shear can be sufficiently strong to generate Kelvin-Helmholtz instabilities. These28

instabilities can generate diapycnal mixing which changes the properties of the water masses29

in the ocean above the thermocline (Dohan and Davis 2011). However, the instabilities also30

dissipate a significant portion of the kinetic energy flux into the ocean arising from the wind31

work at the surface (Plueddemann and Farrar 2006), leaving a reduced amount of kinetic32

energy available to drive the large-scale geostrophic circulation (von Storch et al. 2007) and a33

deep overturning circulation driven by abyssal diapycnal mixing (Munk and Wunsch 1998).34

The mixing at the base of the surface layer is also thought to control the supply of primary35

production-limiting nutrients to the euphotic zone (Law et al. 2003; Rippeth et al. 2009) and36

could explain the presence of sub-surface chlorophyll maxima (Parslow et al. 2001). Hence,37

diapycnal mixing helps drive the biological pump which draws down atmospheric CO2 and38

can also affect the subduction of surface layer fluids, both of which have been implicated in39

the deep export of CO2 (Karleskind et al. 2011) to the abyssal ocean.40

2

The observed intermittent shear spikes lead to two significant oceanographic challenges.41

Firstly, they are difficult to observe in situ (they require finescale observations) and are42

also invisible to satellites. Secondly, they occur at a sub-grid scale for General Circulation43

Models (GCMs) and so must be parameterized. Clearly, the problem of adequately observing44

the mixing processes limits our ability to parameterize them. Dalan et al. (2005) noted that45

diapycnal diffusivity is among the least known parameters in the current generation of GCMs46

while the sensitivity of model outputs to it is high.47

A recent theoretical advance by Burchard and Rippeth (2009) (hereafter BR09) has48

shed light on the dynamical process leading to generation of shear spikes first observed in49

continental shelf seas (Rippeth et al. 2009). BR09 showed that spikes in the shear magnitude50

can be caused by an interaction between the shear and the surface wind stress. Observations51

from the northern North Sea (BR09) and the Arctic Laptev Sea (Lenn et al. 2011) lend52

further support to this theory. Furthermore, these studies highlighted that when the water53

column is of marginal stability (Ri ≈ 1, where Ri is the Richardson number) shear spiking54

incidents were associated with dissipation of turbulent kinetic energy orders of magnitude55

higher than background levels.56

In this study, we examine Southern Ocean data to investigate whether a similar process57

is effective in the open ocean. High winds, the transformation of key overturning water58

masses that outcrop within the surface mixed layer, and high primary production leading59

to the Southern Ocean’s reputation as an overall carbon sink make it an ideal location for60

this study. The data used here include two transects of the Drake Passage region made by61

the RRS James Cook (hereafter Cook) in February 2009 and 242 transects of Drake Passage62

made by the ARSV Laurence M. Gould (LMG) between 1999 and 2011 (Fig. 1). The63

3

primary aims of this research are to: (1) identify mechanisms leading to the generation of64

shear spikes in the open ocean surface boundary layer; (2) estimate the seasonal and spatial65

variability of shear and (3) evaluate the potential of shear spikes to drive diapycnal mixing66

across the seasonal thermocline. The analytical model for the production of shear squared67

(S2) in an open ocean environment is derived in Section 2. The datasets are described in68

Section 3. The overall structure of the water column and the observed shear are set out in69

Section 4 while the effectiveness of the model is evaluated in Section 5. The potential for70

shear spikes to drive mixing is considered in Section 6 before concluding with a summary71

and discussion in Section 7.72

2. Shear production model73

The central idea of this model is that the production or destruction of shear across the74

base of the surface mixed layer can be driven by interaction between the shear and the75

surface wind stress.76

BR09 based their continental shelf sea model for shear production on a one-dimensional77

momentum balance between linear and Coriolis acceleration, the surface wind stress and78

friction. For the open ocean, following Pollard and Millard (1970), we can express the79

vertically-averaged momentum balance in the mixed layer as:80

du

dt− fv =

τxw − τxiρH

(1a)81

82

dv

dt+ fu =

τ yw − τyi

ρH(1b)83

where ddt

is the (non-advective) time derivative, u and v are the zonal and meridional compo-84

4

nents of velocity in the mixed layer, t is time, f is the Coriolis parameter, τw is the relative85

wind stress (with superscripts indicating the directional component), τi is the interfacial86

frictional stress, ρ is the layer average potential density and H is the mixed layer depth87

(MLD). Note that surface stress is taken to be the relative wind stress, that is the velocity88

of the wind relative to the surface ocean current. Hereafter, the body forces due to wind89

and interfacial friction are denoted as Tw and Ti respectively, where these are the stresses90

divided by ρ.91

The momentum balance can be adapted into shear form with the further assumption that92

the layer below the mixed layer is quiescent i.e. that the acceleration due to wind forcing93

is restricted to the surface mixed layer. In practice, the model does not require zero flow94

below the mixed layer, only that any background flow (e.g. mesoscale eddy or geostrophic95

flow) is more lightly sheared across the base of the mixed layer than the flow driven by the96

local wind. The relationship between velocity and shear is as follows:97

Su =u− ulhs

(2a)98

99

Sv =v − vlhs

(2b)100

where hs is the distance between the centers of mass of the upper layer (above the mixed101

layer base) and lower layer (below the mixed layer base), which are assumed to be constant102

in time and ul and vl are the lower layer velocity components. Following the approach of103

BR09, we can substitute equation (2) into equation (1) by dividing all terms in equation (1)104

by hs:105

dSudt− fSv =

T xw − T xihsH

(3a)106

107

dSvdt

+ fSu =T yw − T

yi

hsH(3b)108

5

These equations are then multiplied by Su and Sv respectively:109

1

2

dS2u

dt− fSuSv =

SuTxw − SuT xihsH

(4a)110

111

1

2

dS2v

dt+ fSuSv =

SvTyw − SvT

yi

hsH(4b)112

Adding these equations leads to the Coriolis terms cancelling and a dot product relationship113

emerges on the RHS:114

dS2

dt= 2(

S

hs· TwH− S

hs· TiH

) (5)115

or:116

dS2

dt= P (S2)−D(S2) (6)117

where P (S2) denotes the production/destruction of S2 (dependent on relative alignment of118

the wind and shear vectors) and D(S2) denotes the destruction of S2 by interfacial friction.119

Finally, the interfacial friction body force Ti can be parameterized using a quadratic120

friction law (following BR09) as:121

T xi = ci(u− ul)[(u− ul)2 + (v − vl)2]12 = cih

2sSu|S| (7a)122

123

T yi = ci(v − vl)[(u− ul)2 + (v − vl)2]12 = cih

2sSv|S| (7b)124

where ci is the drag coefficient. This allows equation (5) to be restated as:125

dS2

dt= 2(

S

hs· TwH− ci

hsHS3) (8)126

127

This simple theoretical model predicts that alignment of wind and shear produces the128

maximum value for the production of S2. Note, however, that if the shear vector is rotating129

inertially S2 continues to increase after the point of alignment and only reaches its maximum130

6

value where equation (5) is zero i.e. when wind and shear are 90◦ out of phase. The model131

addresses changes in S2 at timescales of hours or less, at which timescales the MLD generally132

varies much less than the other terms and so is held constant in the model. However, the133

variations in MLD at monthly timescales are comparable to the variations in the other factors134

and so are considered for the observations of the annual cycle in Section 4 (c). This simple135

momentum balance does not take into account pressure gradients, advection, shear due to136

surface or internal waves or mixing. The effectiveness of the model given these assumptions137

is considered further in Section 5.138

3. Data139

Two Drake Passage datasets are used for this analysis. The densely-sampled hydrographic140

surveys from the Cook provide long (≥ 5 day) pseudo time-series data used to evaluate the141

model for specific conditions at high temporal resolution. The comparatively fast (∼ 2 day)142

repeat transects spanning the 12 years of the LMG dataset are used to evaluate the model143

with lower temporal resolution but covering the full range of conditions experienced through144

the annual cycle. As the focus here is on open ocean processes, data gathered in continental145

shelf and slope areas (i.e. bathymetry < 1500 m depth) are excluded from the analysis. As146

Drake Passage sections encompass only two wind decorrelation lengthscales (≈ 500 km), it147

is reasonable to treat each transect as a virtual time-series, while two degrees of freedom are148

assumed when conducting spectral analysis across a whole transect.149

The Cook observations consist of two hydrographic surveys of the Drake Passage region150

gathered on the JC31 cruise in February 2009 (McDonagh et al. 2009). This was a dedi-151

7

cated oceanographic cruise with frequent stops to perform full-depth hydrographic casts with152

a conductivity-temperature-depth (CTD) instrument and both lowered and ship-mounted153

acoustic Doppler current profilers (ADCP). It took place from 3rd February to 3rd March154

2009, in the late austral summer. The first survey was conducted southbound from South155

America towards the West Antarctic Peninsula (SB, Fig. 1) and the other survey was156

conducted northbound from the West Antarctic Peninsula towards the eastern edge of the157

Patagonian Shelf and the Falkland Islands (NB, Fig. 1).158

The LMG dataset consists of underway observations from 242 crossings of Drake Passage159

made between 1999 and 2011. Upper ocean currents were measured by the LMG ship-160

mounted ADCP during year-round crossings of the Passage as part of regular resupply trips161

to Palmer Station on Anvers Island off the West Antarctic Peninsula or for specialist scientific162

cruises in the region. The hydrographic data came from the deployment of expendable163

bathythermograph (XBT) and expendable conductivity-temperature-depth (XCTD) probes.164

The LMG transects lay primarily between the two Cook surveys and fan out from Cape165

Horn towards the south, with some clustering along the directly-southbound transect at the166

western end of the domain (Fig. 1). The LMG ADCP surveys used in this study were167

conducted between September 1999 and April 2011, while the 96 XBT/XCTD surveys were168

conducted between September 1996 and February 2011. There are ADCP and XBT/XCTD169

data from all months with fewer transects in July and August.170

The velocity data used in this study were sampled using 153.6 kHz RDI ADCPs. On the171

Cook, the ADCP was mounted on the portside retractable drop keel. When the keel was172

extended, transducer depth was approximately 9.6 m and only these data are used here. The173

LMG ADCP is located in a special anti-freeze filled sonar pod that sits below bubbles in174

8

order to minimise data noise in the surface boundary layer. The speed of sound through the175

anti-freeze is measured independently and the ADCP data were adjusted accordingly (see176

Lenn et al. (2007) for further detail). Both the Cook and LMG ADCP data were collected177

with a vertical bin length of 8 m. These data were gridded to an 8 m grid with a first depth178

of 23.5 m for the Cook data and 26 m for the LMG data. The temporal averaging was179

five-minute ensembles for the Cook dataset and 15-minute ensembles for the LMG dataset180

During the Cook cruise, 47 full-depth CTD profiles were collected on the southbound181

transect and 30 profiles on the northbound transect. These were typically deployed at182

separations of 30 km. The instrument used was a Seabird 911Plus that had a 300 kHz183

RD Instruments Workhorse ADCP unit attached with an altimeter pinger to ascertain the184

bottom depth at the point of each CTD deployment. The LMG hydrographic profiles were185

made using Sippican Deep Blue XBT and TSK Sippican Digital XCTD probes. The XBTs186

record temperature data with 2 m vertical resolution and 6-15 km along-track resolution.187

These observations were objectively mapped to a grid with 10 m vertical resolution and 0.1◦188

latitudinal resolution. Since 2001 XCTDs have also recorded both temperature and salinity189

data with a vertical resolution of less than 1 m. The XCTDs have been deployed more190

sparsely than the XBTs with an along-track resolution of 25-100 km. Salinity is inferred191

from a historical climatology using a position-dependent T-S-z relation adjusted for salinity192

anomalies observed by the XCTDs when available (see Sprintall (2003) for more detail). The193

adjusted salinities were objectively mapped to the same 10 m vertical resolution and 0.1◦194

latitudinal resolution as the XBT data. Density was then calculated using the objectively195

mapped temperature and inferred salinity fields.196

Wind data were recorded by onboard meteorological data systems and averaged into197

9

one minute ensembles. Cook wind speed and direction were recorded by a Gill Windsonic198

anemometer located on a foremast at a height of 16 m above the waterline, while LMG wind199

speed and direction were recorded by port and starboard RM Young 5106 anemometers200

located on the ship′s main mast at a height of 30 m above the waterline.201

These winds were then used to estimate the 10 m wind components using the boundary202

layer profile of Large and Pond (1981). The relative wind speed was then calculated by203

subtracting the surface ocean current (using the shallowest ADCP depth bins as a proxy)204

from the calculated 10 m wind before using the Large and Pond (1981) parameterization205

to calculate the relative wind stress. This parameterization assumes the atmosphere is of206

neutral stability and the air density was taken as 1.25 kg m−3 throughout. Large and Pond207

(1981) note that there is an error in the calculated stress of less than 10% in converting208

the wind speed from the observed wind to the 10 m wind and this error decreases with209

wind speed. If the magnitude of the atmospheric stability parameter (the Monin-Obukhov210

length) is of the order of the observation height this can introduce a further 20% error in211

the calculated stress. We assume however, that these errors are bounded in the evaluation212

of the model below as stronger winds tend to induce neutral stability in the atmospheric213

boundary layer and, furthermore, these errors do not affect the direction of the wind stress214

which is the most critical part of our analysis below. For the Cook dataset there were no215

observations of wind speed greater than the 25 m s−1 upper limit for which the Large and216

Pond (1981) parameterization is defined and less than 0.3% of the observations in the LMG217

dataset exceeded this limit. Observations below the 4 m s−1 lower limit are not important218

for the analysis below as the model aims to describe periods of significant wind stress.219

Data are analyzed by season to observe temporal patterns. Here summer is taken to220

10

be January, February and March, fall is April, May and June, winter is July, August and221

September and spring is October, November and December.222

4. Characteristics of stratification and shear223

Stratification determines where the mixed-layer base is located and can also impact the224

near-inertial shear that is the focus of this study. In this section, we describe the seasonal225

variability of Drake Passage upper ocean stratification, and the definitions and characteristics226

of the mixed-layer depth and the bulk shear used to test our theoretical model.227

a. Stratification228

The temperature and salinity profiles from the Cook transects in Fig. 2 (a,b) show a229

warm surface mixed layer (above 100 m depth) overlying the main thermocline, and a surface230

temperature gradient with colder water polewards. Latitudinal gradients in density due to231

different water masses are also present below the mixed layer. In the north of Drake Passage232

the surface layer is not homogeneously mixed but instead is more weakly stratified than the233

thermocline below (Fig. 2 (e,f)). The water column to the south has a well-defined mixed234

layer with a uniform density profile near the surface above a sharp transition layer (Fig. 2235

(e,f)). The upper ocean departs from stable thermal stratification south of 59◦ S between 50236

m and 250 m depth (Fig. 2 (a)), the location of a temperature minimum in the upper ocean.237

The overall static stability is maintained by the strong salinity gradient in this region. The238

steeply sloping isopycnals of the Polar Front (PF) (Fig. 2 (c,d)) mark the transition between239

11

a water mass to the south with thermal and haline stratification and a water mass to the240

north with thermal stratification but no vertical salinity gradient in the upper ocean.241

The buoyancy frequency squared (N2) was calculated as242

N2 = − g

ρ0

(ρu − ρl)hs

(9)243

where g is gravitational acceleration, ρ0 is the mean density of the two layers, ρu and ρl are244

the densities in the upper and lower layers respectively and hs is the distance between the245

centers of mass of the two layers.246

Seasonal variability in the water column structure characterises the calculated LMG247

monthly-mean N2 sections (Fig. 3). Beginning in the austral spring (October-November),248

surface layer stratification develops above 150 m depth. This intensifies and shoals through-249

out the austral summer and peaks in March when the MLD is at ∼40 m depth. As fall sets in250

this stratification weakens and is substantially eroded by late winter (August). Latitudinal251

variations in water mass properties observed in the Cook cruise are evident throughout the252

year (Fig. 3). In the late austral summer (February-March in Fig. 3), for example, strat-253

ification is twice as intense in the south of the Passage as in the north, and even in winter254

(July-August) the water column in the north remains more weakly stratified north of the255

PF than to the south. These latitudinal differences are due to the different vertical salinity256

gradients near the surface (e.g. Fig. 2 (a,b)). In particular, the weak haline stratification in257

the north of the Passage leads to greater thermal control of water column structure.258

The effect of Drake Passage stratification on shear-driven diapycnal mixing is non-trivial259

to diagnose. More shear is expected to be generated in the south of Drake Passage where the260

higher stratification at the base of the mixed layer inhibits downwards momentum transfer,261

12

but the formation of shear instabilities may be inhibited by the high stratification. In262

the north of Drake Passage, the lower density gradients result in weaker shear which may263

be sufficient to overcome the stabilising effect of the stratification. However, any shear-264

instabilities that occur in the north may lead to less water mass transformation and energy265

dissipation than similar instabilities in the south given the smaller vertical density gradient.266

These features are investigated below.267

b. Defining the bulk shear268

In order to estimate the near-inertial shear, we define a bulk shear from the difference269

between the current averaged over the upper layer (above the mixed layer base) and the lower270

layer (below the mixed layer base), divided by the distance between the centers of mass of271

these two layers. First, the MLD was defined for the Cook data (following the definition of272

the Dong et al. (2008) Southern Ocean MLD climatology) as the shallowest depth where the273

potential density is 0.03 kg m−3 greater than at the surface. The thickness of the layers and274

the size of the gap between them is based on a conservative estimate for the thickness of the275

high shear layer from Johnston and Rudnick (2009). As such, the upper layer defined for276

the Cook bulk shear extended from the ADCP depth bin centered at 31.5 m depth (having277

excluded the shallowest layer centered at 23.5 m due to occasional missing observations) to278

the depth closest to the MLD. The lower layer was 32 m thick. There is a gap between the279

two layers of 24 m (the portion of the water column with the highest density gradient). The280

MLD for the LMG bulk shear layers were given by the Dong et al. (2008) 1◦×1◦ climatology.281

The LMG upper layer extended from the first gridded depth at 26 m to the depth closest to282

13

the MLD. The LMG lower layer was up to 50 m thick where the data were available, with283

a 24 m gap between the two layers.284

The bulk shear time series below are presented without interpolation, with details of any285

filters used noted in the relevant captions. When the bulk shear are used in Fourier spectral286

analysis, linear interpolation within transects is used to fill in missing data. When the LMG287

data are used, the Fourier components are computed transect by transect and then averaged288

to produce the spectra, with each transect providing two degrees of freedom.289

c. Annual cycle of shear290

A comparison of the monthly-mean stratification (Fig. 3) and shear (Fig. 4) shows that291

they covary positively over the annual cycle. However, this covariance does not occur in292

a uniform spatial manner. South of the PF, the peak shear depth is generally coincident293

with the MLD (Figs. 3 and 4), but north of the PF the correspondence between MLD and294

peak shear depth is weaker. In August, for example, the shear maximum at 57◦ S is located295

around 180 m depth when the MLD is almost 100 m deeper (Fig. 4). This is likely a function296

of the difference in stratification north and south of the PF. The sharp transition layer south297

of the PF provides a greater density gradient across which the currents are more sheared298

than occurs across the diffuse thermocline north of the PF. This can result in shear up to an299

order of magnitude higher south of PF. These results illustrate the importance of buoyancy300

forcing in pre-conditioning the shear field. While the model proposed in Section 2 assumes301

that the MLD is constant over a short time scale and shear production then scales with the302

wind stress (depending on alignment of the wind and shear vectors), seasonal changes in the303

14

buoyancy profile appear to influence MLD and thus shear magnitudes.304

Firing et al. (2011) observed that the vertical shear in Drake Passage (both mean and305

time-varying) is small throughout the upper 1000 m below the mixed layer, which implies306

there is no high shear layer below that observed here.307

d. Bulk shear statistics and rotary properties308

The probability distribution functions (PDF) of S2 (Fig. 5) show that it has a non-309

Gaussian distribution with a distinctly leptokurtic profile in all seasons. This property is310

confirmed by taking the kurtosis of the distribution (Table 1), where kurtosis values of 17311

or greater are found in all seasons (versus a value of three for a Gaussian distribution).312

The highest mean values of S2 are found in summer, fall and spring (Table 1). The mean313

values in winter are somewhat lower, despite this being the season of highest wind stress and314

wind stress variance in Drake Passage (Thompson et al. 2007). The (normalised) standard315

deviations show that the degree of variation is relatively uniform throughout the year. These316

statistics confirm that enhancement of shear is an intermittent process, with bursts of high317

shear interspersed among longer intervals of much lower shear.318

Rotary spectral analysis of bulk shear provides insight to the forces affecting it in Drake319

Passage (Fig. 6 (a-c)). The inertial frequency in Drake Passage ranges from 0.070 cycles320

per hour (cph) (14.25 hour period) in the north to 0.075 cph (13.25 hours) in the south.321

The rotary spectra of the southbound Cook bulk shear peaks at an anti-cyclonic rotation322

of 0.072 cph, very close to the mean inertial frequency of 0.073 cph. There is much less323

shear variance rotating cyclonically. In the northbound transect there is a much broader324

15

anti-cyclonic spectrum peak (Fig. 6 (b)), stretching between 0.03-0.08 cph, with the peak325

located between 0.04-0.05 cph (20-25 hours), and a second smaller peak at ∼0.14 cph. The326

95% confidence intervals are, however, relatively large due to the few degrees of freedom in327

these individual transects with only the largest peaks significantly different from zero.328

The cause behind shear variance rotating close to the inertial period is wind-driven near-329

inertial oscillations in the surface layer. Bulk shear variance at lower frequencies on the330

northbound transect (Fig. 6 (b)) must have other origins. On the Cook cruise, the typical331

ship speed was 4.6 knots (∼ 8.5 km per hour). This implies that features with a 20 - 30 hour332

observed rotation period would have a spatial scale of 170 - 270 km. These values correspond333

to the observed length scales of mesoscale eddies in Drake Passage (Lenn et al. 2007) and334

suggest that, at least during the northbound Cook transect, the eddy field may contribute335

to shear at the base of the surface mixed layer. There is no evidence in the spectrum of a336

significant tidal influence.337

The magnitude of the LMG bulk shear variance differs between seasons (Fig. 6 (c)) in338

line with the means shown in Table 1. The spectra in spring and fall have a similar shape339

with a peak close to the inertial frequency and the variance falling off more slowly at lower340

frequencies. In summer and winter the peak shear variance occurs at 0.045 cph (22 hours),341

with the remainder spread broadly around this (Fig. 6 (c)). On account of the much higher342

degrees of freedom in this calculation the shear variance is shown to be significantly different343

from zero in all seasons at frequencies less than approximately 0.15 cph (6.7 hours).344

The lack of a wintertime peak at the inertial period is surprising, given that this is the345

season of greatest wind stress variance, while the winds slacken in summer (Thompson et al.346

2007). This is also the season of highest kurtosis of S2 (Table 1) and may indicate that a347

16

different regime applies in winter. This could have consequences for the range of applicability348

of the model and is considered further below. As for the Cook transects, the anti-cyclonic349

rotation of the LMG data is greater than the cyclonic rotation with 95% confidence, the350

latter of which has very low variance and is indistinguishable by season except in summer351

(Fig. 6 (c)). Taken together, the analysis here suggests that shear results from a variety of352

forcing mechanisms and the background buoyancy field.353

One factor that can be investigated in the shear generation process is interfacial friction.354

Again following BR09, the interfacial drag term can be parameterized as follows:355

cih2sS

2 = KmSif (10)356

where Km is the interfacial eddy viscosity and Sif is the interfacial shear. With Sif = 5×10−3357

s−1(±4× 10−5 s−1) taken as the mean of shear between successive ADCP depth bins in the358

high shear layer during the Cook cruise, hs = 40 m and an assumption of Km = 10−5 m2s−1359

as a typical open ocean diapycnal mixing value (Moum and Rippeth 2009). This gives an360

interfacial drag coefficient of 10−4. Furthermore, if we assume the following scale values:361

S = 10−3 s−1, Tw = 10−1 N m−2, T = 102 s, hs = 40 m and H = 100 m, then the shear362

production term P(S2) is O(10−8) while the dissipation term D(S2) is O(10−14). This scale363

analysis leads to the conclusion that interfacial shear can be neglected and suggests that the364

alignment of the relative surface wind and shear vectors is the key driver of changes in S2.365

17

5. Model evaluation366

Here, we employ a dual approach to evaluating the proposed open-ocean shear spike gen-367

eration model with the Drake Passage observations. First, we perform a detailed comparison368

of dtS2 (with the subscript denoting differentiation) and predicted shear squared production369

(P(S2)) for the two Cook transects as set out in equation (5). Second, we expand our model370

evaluation over all seasons using the LMG data to provide a statistical test of model skill.371

The Cook dtS2 series are noisy and therefore a five-hour moving average filter has been372

applied (Fig. 7 (e,f)). The dissipation of S2 by interfacial friction was shown to be in-373

significant with respect to the production of S2 in Section 4 (d) and so is omitted from the374

comparison. The southbound transect data run from hour 0900 in 2009 (12.00h Universal375

Time on 7th February 2009) and continued for nine days. The northbound transect began376

at hour 1215 in 2009 (15.00h on 20th February) and continued for five days.377

At the start of the southbound transect (in northern Drake Passage between hours 0900378

and 0975) S2 is lower compared to later in the transect (Fig. 7 (c)) and the P (S2) term379

is smaller than dtS2 (Fig. 7 (e)). From hour 0960 the magnitude of P (S2) and dtS

2 both380

increase and the model and data remain well correlated until approximately hour 1000 when381

the wind stress drops below 0.05 N m−2 resulting in model output P (S2) close to zero.382

When the wind stress picks up again from hour 1025 to hour 1100, peaks in dtS2 and P (S2)383

align and the model cycles are more pronounced (Fig. 7(e)). For example, there are near-384

coincident peaks in dtS2 and P (S2) at hours 1032, 1046 and 1090.385

The model also predicts the development of shear spikes in the northbound transect,386

despite differences in the bulk shear relative to the southbound transect highlighted by the387

18

rotary spectrum (Fig. 6 (b)). The model predicts shear production due to wind and shear388

alignment at the points of shear spiking near hours 1230, 1261 and 1323, albeit with a smaller389

magnitude than dtS2. However, the model worked best in the southbound transect. This390

is because the shear in this case was dominated by wind-forced near-inertial rotations, as391

can be seen by the shear vector rotating at the inertial frequency for much of the transect392

(Fig. 7 (g)). In the northbound transect the shear vector rotation is much more variable393

with frequent changes of direction and a number of frequencies present (Fig. 7 (h)).394

In the southbound transect the model proved a better predictor of the magnitude of395

dtS2 in the southern part of the Passage (hours 1025-1125). This is because the model396

assumes that wind accelerations are confined to the surface layer. As the stratification397

became stronger south of the PF this assumption is better justified, as it gave rise to shear398

concentrated at the base of the mixed layer where the calculation is performed. If the water399

column is lightly and continually stratified, inertial currents and shear will be distributed400

over a thicker layer, as compared to a water column that has a layer of relatively uniform401

density but with a distinct jump in density at the base of the surface layer.402

This simple model does not provide a complete prognostic description for the generation403

of shear at the base of the mixed layer and there is evidence of other processes. For example,404

the sub-inertial period shear generated near hour 1010 of the southbound Cook transect405

(Fig. 7 (c)) is due to stronger velocities in the layer below the mixed layer base (not shown),406

whereas other shear spikes at times of surface wind forcing arise from stronger velocities in407

the surface layer. This may be from the propagation of near-inertial internal waves generated408

further south. The shear variance spectra in Section 4 (d) also highlighted the role of longer409

period rotations in both directions, which may indicate shearing of mesoscale eddies or410

19

geostrophic features in all seasons in Drake Passage.411

Bathymetry may account for differences between the shear fields of the two Cook tran-412

sects. Although both transects take place in open ocean conditions the northbound transect413

was downstream of the Shackleton Fracture Zone and overlies rougher topography at depth.414

This leaves open the possibility that the large scale flow may be generating additional ver-415

tically propagating internal waves in the northbound transect.416

Given the intermittent nature of shear spikes, it is instructive to consider a statistical417

measure of the model skill using the larger LMG dataset (Fig. 6 (d)). We estimated and418

compared the magnitude-squared coherence (hereafter coherence) between (1) shear-squared419

and relative surface stress, (2) the time derivatives of the aforementioned and (3) dtS2 and420

predicted P (S2). All of the estimated coherences differed significantly from zero at 95%421

confidence. Coherence was highest between the shear-squared and relative surface stress at422

low frequencies, suggesting that longer periods of forcing will generate more shear, which is423

consistent with previous findings (Grant and Belcher 2011). However, the coherence drops424

markedly at super–inertial frequencies. Notably, the coherence between dtS2 and predicted425

P (S2) exceeded the other estimates with 95% confidence over most of the super-inertial426

frequencies resolved. In fact, the peak in the dtS2 and P (S2) coherence between 0.2 cph and427

0.3 cph corresponds to the duration of a typical shear-spike. This implies that our simple428

theoretical model can predict the intermittency of the shear spikes better than wind stress429

alone because it is at the higher frequencies where the alignment of wind and shear captured430

by the model becomes crucial.431

20

6. Diapycnal mixing potential432

The diapycnal mixing potential of shear-driven instabilities can be estimated for both433

the Cook transects by calculating Ri and then applying a statistical parameterization to434

estimate the mixing level. The Richardson number was estimated for the Cook transects435

using the MLD shear (calculated from successive ADCP depth bins, rather than the bulk436

shear). Each Ri calculation was made by dividing N2 for each profile by the maximum437

value of S2 observed closest to that station. The higher resolution (2 m) density data are438

averaged vertically to give N2 at the same (8 m) vertical resolution as the velocity data.439

The maximum value of S2 is used due to the non-linear dependence of turbulent mixing on440

high values of shear. As such, the calculation gives an upper bound to diapycnal mixing.441

The short-term variability of S2 is markedly higher than N2 (Fig. 8 (a,b)). The overall442

trend was for Ri to increase polewards with consistently low values (< 0.5) in the northern443

part of both transects (between hours 0910 and 1000 southbound and 1290 to 1320 north-444

bound, Fig. 8 (c,d)). This is notable as the value of S2 also increases polewards and shows445

that the increase in stratification polewards more than offsets the more intense shear in the446

Ri calculation and so reduces the potential for mixing.447

A statistical solution to the problem of estimating diapycnal mixing from shear and buoy-448

ancy observations of limited vertical resolution was proposed by Polzin (1996). It requires449

an assumption of a higher Ric (the critical threshold below which mixing is assumed to take450

place) to account for the upward bias in observed Ri due to the limited temporal and spatial451

resolution in the observations. Polzin (1996) examined a model proposed by Kunze et al.452

(1990) that set out the following parameterization for ε, the rate of dissipation of turbulent453

21

kinetic energy to heat:454

ε =frδz2

96〈N3(

1

Ri− 1

Ric)(

1√Ri− 1√

Ric)〉 (11)455

Here fr is the fraction of time that the water column is unstable, δz is the vertical resolution456

of the observations and angle brackets denote temporal averaging over an event. The values457

of fr have been derived empirically by Polzin (1996). Ric must be chosen to reflect the458

limited vertical resolution available and is, in general, greater than the theoretical critical459

value of 0.25. In the analysis which follows, Ric is chosen to be 0.5. This is the largest460

value for which the statistical analysis is defined. Polzin (1996) notes that the range of461

applicability of the model is where 〈S2〉\N2 (where the overbar indicates the background462

buoyancy frequency squared is used) is greater than one, which is satisfied here. The value463

of dissipation calculated can then be used to estimate the diapycnal mixing according to the464

standard parameterization:465

κρ = ΓεN−2 (12)466

where Γ is a mixing efficiency, estimated as 0.2 by Osborn (1980). This approach has been467

the most commonly used to estimate diapycnal mixing (e.g. Thompson et al. (2007)), but468

there remain significant caveats. Ivey et al. (2008) note that the mixing efficiency Γ is not469

a universal constant and becomes smaller as the turbulence becomes more intense. As such,470

this estimate is often taken as an upper bound to diffusivity (Lenn et al. 2011).471

This approach was applied to the Cook data where Ri < 0.5 to derive an upper bound on472

diffusivity (Fig. 8 (e,f)). In the intervening periods it is likely to be closer to some background473

level, presumably higher than the value of 10−5 m2s−1 often thought to be typical of the ocean474

interior (Moum and Rippeth 2009). The highest values of κρ are O(10−4) m2s−1 and are475

22

found in the northern part of the Cook transects near 58◦ S in the southbound transect (i.e.476

between hours 0940 and 1020) and near 57◦ S in the northbound transect (between hours477

1260 and 1300).478

A broader perspective is provided by a Ri analysis using the LMG data set. To account479

for the intermittent nature of the spikes in S2, the Ri are computed from each LMG transect480

and then sorted by season. The percentage of Ri from each season that fall below Ri = 1 is481

calculated per 0.1◦ latitude box (Fig. 9). This calculation is approximate due to the inferred482

salinity relationship.483

While there are some isolated high percentages of low Ri observed in the winter months,484

a clear overall pattern is present (Fig. 9). The latitude band between 58◦ and 56◦ S has the485

greatest percentage of low Ri values, with winter characterised by more low Ri than summer.486

Our results imply that while both stratification and shear are weak north of the PF, the487

observed Ri are closer to the critical threshold for instabilities to grow and mixing to occur.488

It is clear that the non-linear dependence of mixing on Ri is a crucial step in understanding489

mixing rates.490

7. Discussion491

A simple theoretical model for the generation of shear spikes in open ocean conditions492

has been derived. There is evidence that the model provides a useful prognostic tool for493

predicting the generation of shear spikes where the shear arises due to local wind forcing.494

Spikes in the production of shear were observed to be nearly coincident with the alignment495

of wind stress and shear. The model predicts that shear is generated intermittently and496

23

statistics of shear indicate that this is how it behaves year-round. The shear spikes generated497

in line with the model prediction have been shown to produce mixing much higher than498

background levels. The higher level of stratification in the near-surface layer in the south499

of Drake Passage is more typical of mid-latitude oceans than that in the north of Drake500

Passage. As the simple model proved a better predictor of shear production in the south of501

the Passage, this is encouraging for its wider applicability.502

As mesoscale eddies dominate Southern Ocean dynamics, they are also likely to influence503

the shear field, particularly in the eddy-rich north of Drake Passage (Lenn et al. 2007). Zhai504

et al. (2005), for example, showed that inertial oscillations can interact with eddies rotating505

in the same direction and thereby channel energy down into the abyssal ocean. While the506

implications of this for the shear field are not yet clear, such interactions could account for507

the significant shear variance at periods longer than the inertial period, especially if resonant508

wave-wave interactions lead to shear variance rotating at the inertial frequency being spread509

to different frequencies.510

Thompson et al. (2007) also found that the region near 57-58◦ S was where the highest511

diapycnal mixing between 100-200 m depth occurs in Drake Passage from an analysis of512

observed density overturns in the XCTD portion of the LMG dataset. This provides some513

support for the argument that shear-driven mixing is at its highest in this part of the Passage514

and therefore parameterizations based on Ri should generate the right pattern of mixing in515

Drake Passage.516

The bulk shear statistics illustrate that the large values of shear crucial for generating517

mixing are intermittent in time and the seasonal probability density distributions of shear518

display high kurtosis. This presents a challenge for modelling efforts with resolution coarser519

24

than O(10) m, as any time or space averaging is likely to reduce the value of S2 below520

the threshold for instabilities to grow. Although shear-driven mixing is a feature of widely-521

used parameterizations of upper ocean mixing such as the KPP scheme (Large et al. 1994)522

or the PWP scheme (Price et al. 1986), horizontal grid spacings on the order of tens or523

hundreds of kilometres are likely too large to capture the effect detailed here. BR09 observed524

diapycnal mixing scaling positively with S3. Furthermore, Lenn et al. (2011) found that525

intermittent mixing events had rates of energy dissipation up to three orders of magnitude526

greater than background levels. While weaker Drake Passage stratification would result in527

different scalings, it is likely that the spikes that arise from wind-shear alignment would528

drive levels of energy dissipation higher than predicted by the parameterizations, though529

this must be confirmed by direct observations.530

Acknowledgments.531

The work of Liam Brannigan was supported by an NERC MSc. Studentship and NERC532

OSMOSIS grant DCRUHN0. Yueng-Djern Lenn is an NERC Postdoctoral Fellow (NE/H016007/1)533

and the JC31 cruise to the Southern Ocean was supported by the NERC Oceans2025534

programme. The LMG time series measurements are supported by the National Science535

Foundation′s Office of Polar Programs grants ANT-9816226/0338103/0838750 (ADCP) and536

ANT-0003618/0337998/0943818 (XBT/XCTD). We thank those responsible for gathering537

the data used here: the scientific team, captain and crew of the RRS James Cook cruise to538

Drake Passage in February 2009; and all those involved in the National Science Foundation539

data-gathering program in Drake Passage and the captain and crew of the ARSV Laurence540

25

M. Gould. Ben Lincoln, Drs. Ben Moat, Shane Elipot, Louise Darroch, Chris Old and Prof.541

David Marshall also provided invaluable assistance during the course of the research.542

26

543

REFERENCES544

Burchard, H. and T. Rippeth, 2009: Generation of bulk shear spikes in shallow stratified545

tidal seas. Journal of Physical Oceanography, 39, 969–985.546

Dalan, F., P. Stone, I. Kamenkovich, and J. Scott, 2005: Sensitivity of the ocean’s climate547

to diapycnal diffusivity in an EMIC. Part I: Equilibrium state. Journal of Climate, 18,548

2460–2496.549

Dohan, K. and R. Davis, 2011: Mixing in the transition layer during two storm events.550

Journal of Physical Oceanography, 41, 42–66.551

Dong, S., J. Sprintall, S. Gille, and L. Talley, 2008: Southern Ocean mixed-layer552

depth from Argo float profiles. Journal of Geophysical Research, 113, C06 013,553

doi:10.1029/2006JC004051.554

Firing, Y., T. Chereskin, and M. Mazloff, 2011: Vertical structure and transport of the555

Antarctic Circumpolar Current in Drake Passage from direct velocity observations. Journal556

of Geophysical Research, 116, C08 015, doi:10.1029/2011JC006999.557

Grant, A. and S. Belcher, 2011: Wind-driven mixing below the oceanic mixed layer. Journal558

of Physical Oceanography, 41, 1556–1575.559

Ivey, G., K. Winters, and J. Koseff, 2008: Density stratification, turbulence, but how much560

mixing? Annual Review of Fluid Mechanics, 40, 169–184.561

27

Johnston, T. and D. Rudnick, 2009: Observations of the transition layer. Journal of Physical562

Oceanography, 39, 780–797.563

Karleskind, P., M. Levy, and L. Memery, 2011: Subduction of carbon, nitrogen, and564

oxygen in the northeast Atlantic. Journal of Geophysical Research, 116, C02025,565

doi:10.1029/2010JC006446.566

Kunze, E., A. Williams, and M. Briscoe, 1990: Observations of shear and vertical stability567

from a neutrally buoyant float. Journal of Geophysical Research, 95, 18,127–18,142.568

Large, W. and S. Pond, 1981: Open ocean momentum flux measurements in moderate to569

strong winds. Journal of Physical Oceanography, 11, 324–336.570

Large, W. G., J. McWilliams, and S. Doney, 1994: Oceanic vertical mixing: Review and571

a model with a nonlocal boundary layer parameterization. Reviews of Geophysics, 32,572

363–403.573

Law, C., E. Abraham, A. Watson, and Liddicoat, 2003: Vertical eddy diffusion and nutri-574

ent supply to the surface mixed layer of the Antarctic Circumpolar Current. Journal of575

Geophysical Research, 108, 3272, doi:10.1029/2002JC001604.576

Lenn, Y.-D., T. Chereskin, J. Sprintall, and E. Firing, 2007: Mean jets, mesoscale variability577

and eddy momentum fluxes in the surface layer of the Antarctic Circumpolar Current in578

Drake Passage. Journal of Marine Research, 65, 27–58.579

Lenn, Y.-D., T. Rippeth, C. Old, S. Bacon, I. Polyakov, V. Ivanov, and J. Hoelemann,580

2011: Intermittent intense turbulent mixing under ice in the Laptev Sea continental shelf.581

Journal of Physical Oceanography, 41, 531–547.582

28

McDonagh, E., D. Hamersley, and E. McDonagh, (eds.) 2009: RRS James Cook583

Cruise JC031, 03 Feb-03 Mar 2009. Hydrographic sections of Drake Passage.584

〈http://eprints.soton.ac.uk/69897/〉 Southampton, UK, National Oceanography Centre585

Southampton, 170pp. (National Oceanography Centre Southampton Cruise Report,(39)).586

Moum, J. and T. Rippeth, 2009: Do observations adequately resolve the natural variability587

of oceanic turbulence? Journal of Marine Systems, 77, 409–417.588

Munk, W. and C. Wunsch, 1998: Abyssal recipes II: Energetics of tidal and wind mixing.589

Deep-Sea Research Part I-Oceanographic Research Papers, 45, 1977–2010.590

Osborn, T., 1980: Estimates of the local-rate of vertical diffusion from dissipation measure-591

ments. Journal of Physical Oceanography, 10, 83–89.592

Parslow, J., P. Boyd, S. Rintoul, and F. Griffiths, 2001: A persistent subsurface chlorophyll593

maximum in the Interpolar Frontal Zone south of Australia: Seasonal progression and im-594

plications for phytoplankton-light-nutrient interactions. Journal of Geophysical Research,595

106, 31543–31557.596

Plueddemann, A. and J. Farrar, 2006: Observations and models of the energy flux from597

the wind to mixed-layer inertial currents. Deep-Sea Research Part II-Topical Studies in598

Oceanography, 53, 5–30.599

Pollard, R. and R. Millard, 1970: Comparison between observed and simulated wind-600

generated inertial oscillations. Deep-Sea Research, 17, 813–821.601

Polzin, K., 1996: Statistics of the Richardson number: Mixing models and fine-structure.602

Journal of Physical Oceanography, 26, 1409–1425.603

29

Price, J., R. Weller, and R. Pinkel, 1986: Diurnal cycling: Observations and models of the604

upper ocean response to diurnal heating, cooling, and wind mixing. Journal of Geophysical605

Research, 91, 84118427.606

Rippeth, T., P. Wiles, M. Palmer, J. Sharples and J. Tweddle, 2009: The diapycnal nutrient607

flux and shear-induced diapycnal mixing in the seasonally stratified western Irish Sea.608

Continental Shelf Research, 29, 1580–1587.609

Sprintall, J., 2003: Seasonal to interannual upper-ocean variability in the Drake Passage.610

Journal of Marine Research, 61, 27–57.611

Thompson, A., S. Gille, J. MacKinnon, and J. Sprintall, 2007: Spatial and temporal patterns612

of small-scale mixing in Drake Passage. Journal of Physical Oceanography, 37, 572–592.613

von Storch, J.-S., H. Sasaki and J. Marotzke, 2007: Wind-Generated Power Input to the614

Deep Ocean: An Estimate Using a 1/10◦ General Circulation Model. Journal of Physical615

Oceanography, 37, 657–672.616

Zhai, X., R. J. Greatbatch, and J. Zhao, 2005: Enhanced vertical propagation of storm-617

induced near-inertial energy in an eddying ocean channel model. Geophysical Research618

Letters, 32, L18602, doi:10.1029/2005GL023643.619

30

List of Tables620

1 Statistics of S2 for the Laurence M. Gould data. The standard deviation has621

been normalised by dividing by the respective mean values. The statistics are622

calculated for the 208 transects for which corresponding hydrographic data623

were available. 32624

31

Table 1. Statistics of S2 for the Laurence M. Gould data. The standard deviation has beennormalised by dividing by the respective mean values. The statistics are calculated for the208 transects for which corresponding hydrographic data were available.

Statistic Summer Fall Winter SpringMean (s−2) 3.7× 10−6 1.8× 10−6 0.6× 10−6 1.2× 10−6

Standard deviation 1.3 1.6 1.8 1.5Kurtosis 17.2 48.2 163.3 34.4No. of transects 45 60 40 63

32

List of Figures625

1 Map of Drake Passage with bathymetry in grayscale and contour lines at626

1500 m, 3000 m and 4500 m. The two solid lines show the location of the high627

resolution James Cook transects (with the southbound transect marked as628

‘SB’ and the northbound transect as ‘NB’), while the crosses mark locations629

on the Laurence M. Gould crossings. 36630

2 Hydrographic profiles of the southbound (left panels) and northbound (right631

panels) James Cook transects. (a,b) The potential temperature profiles with632

0.1 PSU salinity contours overlain showing the contrast between the thermally633

stratified region to the north of Drake Passage and the salinity stratified region634

to the south. (c,d) The potential density profiles with contour lines every 0.1635

kg m−3. The steeper isopycnal slopes in the north of the Passage show the636

weaker stratification there. (e,f) The potential density profiles from a selection637

of individual CTD casts showing that the mixed layers are more defined in638

the south of the Passage than the north. 37639

3 Log10N2 in Drake Passage as observed on the Laurence M. Gould transects.640

N2 is calculated for each transect separately and then averaged by month.641

Values of N2 less than zero in any profile are excluded. The Dong et al.642

(2008) mixed layer depth climatology is marked by black dots. The data643

show the tendency for stratification to be stronger in the south of the Passage644

than the north and stronger in summer than winter. 38645

33

4 Log10S2 in Drake Passage showing that monthly-mean shear tends to be higher646

and more spatially concentrated in the south of the Passage and in summer.647

Shear has been calculated here between successive ADCP depth bins rather648

than as a bulk shear. The Dong et al. (2008) mixed layer depth climatology649

has been marked by black dots to illustrate the broad positive covariance650

between the shear and mixed layer depth. The mixed layer depth of 275 m at651

57◦ S in July is off the scale shown here. 39652

5 Probability distribution functions of S2 in Drake Passage where (a) shows the653

PDFs for standard deviations less than 3 and (b) extends this by showing the654

PDFs for the tail with a re-scaled y-axis. A Gaussian distribution has been655

included for comparison. These PDFs have been calculated for each season656

individually with respect to the standard deviation of that season. 40657

6 Rotary spectral analysis of the bulk shear vector in the (a) southbound, (b)658

northbound James Cook transects (where the top of the error bar is out of659

range) and (c) Laurence M. Gould seasonal bulk shear; 95% χ2 confidence660

intervals are shown. Anti-cyclonic spectra are plotted as solid lines; cyclonic661

spectra are plotted as dashed lines. (d) The spectral coherence between S2662

& |τ | (red), dtS2 & P (S2) (blue), dtS

2 & dtτ (green) is shown with 95%663

confidence intervals assuming 2 degrees of freedom for each of 161 transects664

included here. Gray shading in (a-d) indicates the range of inertial frequencies665

of Drake Passage. 41666

34

7 Observations of the wind, shear and model output in the James Cook south-667

bound (left panels) and northbound (right panels) transects: (a,b) wind stress,668

(c,d) bulk S2, (e,f) a comparison of dtS2 and P(S2) and (g,h) the direction of669

the wind (green stars) and shear (blue circles) vectors with black lines showing670

rotation at the local inertial frequency included for comparison. The direction671

is calculated relative to due north with rotation positive in a clockwise sense.672

A five hour moving average filter has been applied to the dtS2 time series in673

(e,f) and a one hour moving average filter has been applied to the shear vector674

in (g,h). Time is given in hours from midnight on 1 January 2009. 42675

8 An estimate of diapycnal mixing for the southbound (left-hand panels) and676

northbound (right-hand panels) James Cook transects: (a,b) N2 (s−2) and S2677

(s−2); (c,d) the Richardson number, with critical values Ric = 0.5 (solid line)678

and Ri = 1 (dashed). Observations where Ri < Ric and so the diffusivity679

estimate can be made have been circled; and (e,f) the estimate of κρ at points680

where it is defined by the Polzin (1996) parameterization. 43681

9 The percentage of the observed values with Ri < 1 in each 0.1◦ latitude box,682

showing that the northern part of Drake Passage in winter is most suscepti-683

ble to shear-driven instabilities. S2 has been calculated with respect to the684

Dong et al. (2008) mixed layer depth climatology, and a moving average has685

been applied over 10 km to match the 10 km interval between hydrographic686

observations. 44687

35

−1500

−3000

72oW 68

oW 64oW 60

oW 56o

W 52oW

68oS

64oS

60oS

56oS

52oS

SB

NB

Longitude

La

titu

de

Ele

va

tio

n a

bo

ve

me

an

se

a le

ve

l (m

)

−6000

−5000

−4000

−3000

−2000

−1000

0

Fig. 1. Map of Drake Passage with bathymetry in grayscale and contour lines at 1500 m,3000 m and 4500 m. The two solid lines show the location of the high resolution JamesCook transects (with the southbound transect marked as ‘SB’ and the northbound transectas ‘NB’), while the crosses mark locations on the Laurence M. Gould crossings.

36

Fig. 2. Hydrographic profiles of the southbound (left panels) and northbound (right pan-els) James Cook transects. (a,b) The potential temperature profiles with 0.1 PSU salinitycontours overlain showing the contrast between the thermally stratified region to the northof Drake Passage and the salinity stratified region to the south. (c,d) The potential densityprofiles with contour lines every 0.1 kg m−3. The steeper isopycnal slopes in the north ofthe Passage show the weaker stratification there. (e,f) The potential density profiles froma selection of individual CTD casts showing that the mixed layers are more defined in thesouth of the Passage than the north.

37

Fig. 3. Log10N2 in Drake Passage as observed on the Laurence M. Gould transects. N2 is

calculated for each transect separately and then averaged by month. Values of N2 less thanzero in any profile are excluded. The Dong et al. (2008) mixed layer depth climatology ismarked by black dots. The data show the tendency for stratification to be stronger in thesouth of the Passage than the north and stronger in summer than winter.

38

Fig. 4. Log10S2 in Drake Passage showing that monthly-mean shear tends to be higher and

more spatially concentrated in the south of the Passage and in summer. Shear has beencalculated here between successive ADCP depth bins rather than as a bulk shear. The Donget al. (2008) mixed layer depth climatology has been marked by black dots to illustrate thebroad positive covariance between the shear and mixed layer depth. The mixed layer depthof 275 m at 57◦ S in July is off the scale shown here.

39

0 0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8P

roba

bilit

y de

nsity

PDF

(a)

SummerFallWinterSpringNormal

3 4 5 6 7 80

1

2

3

4

5

6

7x 10−3

PDF tail(b)

Standard deviations

Fig. 5. Probability distribution functions of S2 in Drake Passage where (a) shows the PDFsfor standard deviations less than 3 and (b) extends this by showing the PDFs for the tail witha re-scaled y-axis. A Gaussian distribution has been included for comparison. These PDFshave been calculated for each season individually with respect to the standard deviation ofthat season.

40

Fig. 6. Rotary spectral analysis of the bulk shear vector in the (a) southbound, (b) north-bound James Cook transects (where the top of the error bar is out of range) and (c) LaurenceM. Gould seasonal bulk shear; 95% χ2 confidence intervals are shown. Anti-cyclonic spectraare plotted as solid lines; cyclonic spectra are plotted as dashed lines. (d) The spectralcoherence between S2 & |τ | (red), dtS

2 & P (S2) (blue), dtS2 & dtτ (green) is shown with

95% confidence intervals assuming 2 degrees of freedom for each of 161 transects includedhere. Gray shading in (a-d) indicates the range of inertial frequencies of Drake Passage.

41

0

0.5

1τ

(N m

−2)

(a) Southbound

0

0.20.40.60.8

1x 10

−4

S2 (

s−2)

(c)

−6

−4

−2

0

2

4

6x 10

−9

s−3

(e)

900 925 950 975 1000 1025 1050 1075 1100 1125−180

−90

0

90

180

Dire

ctio

n °

(g)

Time (hours in 2009)

Northbound

(b)

Wind stress

(d)

Bulk shear squared

(f)

dtS2

P(S2)

1215 1240 1265 1290 1315Time (hours in 2009)

(h)

Wind directionShear direction

Fig. 7. Observations of the wind, shear and model output in the James Cook southbound(left panels) and northbound (right panels) transects: (a,b) wind stress, (c,d) bulk S2, (e,f)a comparison of dtS

2 and P(S2) and (g,h) the direction of the wind (green stars) and shear(blue circles) vectors with black lines showing rotation at the local inertial frequency includedfor comparison. The direction is calculated relative to due north with rotation positive in aclockwise sense. A five hour moving average filter has been applied to the dtS

2 time seriesin (e,f) and a one hour moving average filter has been applied to the shear vector in (g,h).Time is given in hours from midnight on 1 January 2009.

42

00.5

1

2

3

Ri

(c)0

2.5

5x 10−4 Southbound transect

s−2

(a)

N2 S2

900 950 1000 1050 11000

2.5

5x 10−4

Time (hours in 2009)

k ρ (m

2 s−1)

(e)

(d)

Northbound transect(b)

1220 1240 1260 1280 1300 1320Time (hours in 2009)

(f)

Fig. 8. An estimate of diapycnal mixing for the southbound (left-hand panels) and north-bound (right-hand panels) James Cook transects: (a,b) N2 (s−2) and S2 (s−2); (c,d) theRichardson number, with critical values Ric = 0.5 (solid line) and Ri = 1 (dashed). Obser-vations where Ri < Ric and so the diffusivity estimate can be made have been circled; and(e,f) the estimate of κρ at points where it is defined by the Polzin (1996) parameterization.

43

-63 -62 -61 -60 -59 -58 -57 -56 -55 -540

5

10

15

20

25

latitude

pe

rce

nt

Ri <

= 1

summer

fall

winter

spring

Fig. 9. The percentage of the observed values with Ri < 1 in each 0.1◦ latitude box,showing that the northern part of Drake Passage in winter is most susceptible to shear-driven instabilities. S2 has been calculated with respect to the Dong et al. (2008) mixedlayer depth climatology, and a moving average has been applied over 10 km to match the 10km interval between hydrographic observations.

44