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Transcript of Turbulence generation by mountain wave breaking in flows ... · PDF file3D plots showing every...
Turbulence generation by mountain wave breaking in flows with
directional wind shear*
1
Maria Vittoria Guarino, Miguel Teixeira, Maarten Ambaum
EGU General Assembly 2016, Vienna, 17 - 22 April
Atmospheric processes over complex terrain
* Submitted to Quarterly Journal of the Royal Meteorological Society
2
Clear-air turbulence CAT
Mountain wave breaking
Directional wind shear
HIGH ALTITUDE TURBULENCE
It is a “clear” turbulencebecause it occurs in theabsence of any visualclues such as clouds.
BREAKING MOUNTAIN WAVES
CAN GENERATE CAT
If the wave amplitude islarge enough the wavesbecome unstable andbreak.
WINDS THAT TURN WITH HEIGHT
Directional shear flowsare quite common inatmosphere.
MOTIVATIONS AND AIMS OF THIS STUDY
SUBJECT: Clear air turbulence generation (within thetroposphere) by mountain wave breaking and its triggering bythe effects of directional wind shear.
ULTIMATE AIM: formulate quantitative criteria for theoccurrence of this phenomenon based on differentconfigurations of orography and wind profiles.
METHOD: employment of a 3D non-hydrostatic (non-Boussinesq) numerical model.
𝑅𝑖𝑖𝑛 = 0.5 simulation using a mountain height Hof 1 km. The solid black lines are isotherms, thepurple contour lines are the magnitude of (𝑢’, 𝑣’)vector, the background field is the w velocity. Thevertical cross-section is taken at Y = - 10 km.
WAVE BREAKING
If wave breaking occurs:
𝑹𝒊𝒐𝒖𝒕 < 𝟎
𝑹𝒊𝒐𝒖𝒕 =𝑵𝟐
𝝏𝒖𝝏𝒛
𝟐
+𝝏𝒗𝝏𝒛
𝟐
u = U0+u’v = V0+v’N = N 0+ N’
In real conditions 𝑅𝑖 is a very noisy variable, with alarge vertical scale dependence, and even a flow witha 𝑹𝒊 > 𝟏 can be turbulent
AIM: Developing methods able to diagnose wave breakingwithout relying on the use of the (total) Richardson number.
If wave breaking occurs 𝑹𝒊𝒐𝒖𝒕 < 𝟎 in idealized flows!(and in simulations where the waves are well resolved)
SIMULATIONS SETUP – WRF MODEL
200 km
20 km
The larger the mountain height 𝐇the larger is the amplitude of the
excited waves
𝑵𝟎𝑯
𝑼𝟎
LINEAR FLOWS
NON LINEAR FLOWS
= 0.1 , 0.2, 0.5, 0.75, 1
N0 constant, U0 constant
H = 100m, 200m, 500m, 750m, 1 Km
∆x = ∆y = 2km
SIMULATIONS SETUP – WRF MODEL
𝑹𝒊𝒊𝒏 = 𝟏𝟔𝟖𝟒𝟐𝟏
WEAK SHEAR FLOWS
STRONG SHEAR FLOWS
𝑹𝒊𝒊𝒏 =𝑵𝟎𝟐
𝝏𝒖𝟎𝝏𝒛
𝟐
+𝝏𝒗𝟎𝝏𝒛
𝟐
𝟎. 𝟓
By changing the directional shear we are changing the distributionof environmental critical levels where: 𝐔 z ∙ 𝐤𝐇 = 0
SIMULATION RESULTS - REGIME DIAGRAM
Regime diagram classifying the flow bycategories based on the 𝑅𝑖𝑚𝑖𝑛 values.
convective instability
dynamic instability(potentially an index ofturbulence)
flow having kineticenergy available forturbulent mixing
non-turbulent flowwhere no wavebreaking events occur
𝑹𝒊𝒊𝒏 = 𝟏𝟔
8
SIMULATION RESULTS – FLOW TOPOLOGY
3D plots showing every point in the computationaldomain where 𝑹𝒊𝒐𝒖𝒕 < 𝟎. 𝟐𝟓. The plot refers to the18th hour of simulations and assume a 𝑁𝐻/𝑈 =1 (i.e. mountain height H = 1 km).
Dynamical instability 𝑹𝒊 < 𝟎. 𝟐𝟓
Convective instability 𝑹𝒊 < 𝟎
Turbulence generation (CAT)
REGIONS OF POTENTIAL
OCCURRENCE OF CAT
𝑹𝒊𝒊𝒏 = 𝟏𝟔 𝑹𝒊𝒊𝒏 = 𝟖 𝑹𝒊𝒊𝒏 = 𝟒
𝑹𝒊𝒊𝒏 = 𝟐 𝑹𝒊𝒊𝒏 = 𝟏 𝑹𝒊𝒊𝒏 = 𝟎. 𝟓
𝑹𝒊𝒐𝒖𝒕 < 𝟎. 𝟐𝟓 field
180 degrees
180 degrees
SIMULATION RESULTS - WIND FIELD
𝑹𝒊𝒊𝒏 = 𝟏
also 𝒖𝟎, 𝒗𝟎 ⊥ (𝒖′, 𝒗′)
𝒖𝟎, 𝒗𝟎(𝒖′, 𝒗′) Background field: magnitude of (𝒖′, 𝒗′)Contour line: 𝑹𝒊𝒐𝒖𝒕 < 𝟎. 𝟐𝟓
when 𝒖𝟎, 𝒗𝟎 ⊥ (𝒌, 𝒍)
for the wind profile employed in
these simulations: 𝒖, 𝒗 ∥ (𝒌, 𝒍)
SIMULATION RESULTS - THEORY
Adopting a zeroth-order WKB approximation
Assumption: the background flow is varying slowly along z if compared to the vertical wavelength of the waves
𝒎 =𝑵(𝒌𝟐 + 𝒍𝟐)𝟏/𝟐
(𝒖𝒐𝒌 + 𝒗𝟎𝒍)
but 𝑢0 and 𝑣0 vary with height because of the
directional shear
Helical wind profile employed in the simulations:
𝑢0 = 𝑈0𝑐𝑜𝑠(β𝑧)𝑣0 = 𝑈0𝑠𝑖𝑛(β𝑧)
→ ∞
when 𝒖𝟎, 𝒗𝟎 ⊥ (𝒌, 𝒍)also 𝒖𝟎, 𝒗𝟎 ⊥ (𝒖′, 𝒗′)
when 𝒌𝒖𝟎 + 𝒍𝒗𝟎 = 𝟎
At a critical level the second terms are the onlyones that diverge and, therefore, the dominantones. Under these conditions, the ( 𝒖, 𝒗)vector is parallel to the wave-number vector(𝒌, 𝒍).
𝜷 =𝑵𝟎
𝑼 𝑹𝒊𝒊𝒏
CAT FORECAST IMPLICATIONS
𝒖𝟎, 𝒗𝟎 ⊥ 𝒌, 𝒍 𝒗𝒔 𝒖𝟎, 𝒗𝟎 ⊥ (𝒖′, 𝒗′)
Fourier space spectrumof the mountain waveswould have to be computed
Physical space modeloutputs
Condition that may be used to diagnose wave breaking is: 𝒖𝟎, 𝒗𝟎 ⊥ 𝒖′, 𝒗′
instead of 𝒖𝟎, 𝒗𝟎 ⊥ (𝒌, 𝒍)
Further tests are necessary to confirm the applicability and the generalityof this result:
• different wind profiles,• less idealized flows,• realistic orography,• develop an algorithm using the 𝑢0, 𝑣0 ⊥ 𝑢′, 𝑣′ criterion.
SUMMARY AND FUTURE WORK
Results :• Regime diagram: in directional shear flows, wave breaking always occurs when 𝑵𝟎𝑯/𝑼𝟎 = 1.
However, for gradually stronger directional shears (lower 𝑅𝑖𝑖𝑛) wave breaking can occur overlower mountains.
• Flow topology: increasing the strength of the directional shear leads to wider regions of(potential) turbulence generation. For stronger shear flows wave breaking occurs at lowerlevels.
• In a wave breaking event, the background wind vector and the velocity perturbation vector areapproximately perpendicular.
Future work:
Aim: to diagnose wave breaking occurrence (and the potential for turbulence generation) over a3D isolated mountain.Method: running numerical simulations with different values of 𝑵𝟎𝑯/𝑼𝟎 and intensity of thebackground directional shear (quantified through 𝑹𝒊𝒊𝒏).
• Running numerical simulations with more realistic conditions: realistic orography, PBL, non-hydrostatic effects etc.
• Testing the applicability of the simulation results to more realistic flows.