Wind-Tunnel Experiment on Logarithmic-Layer Turbulence...

Boundary-Layer Meteorol (2010) 134:269–283DOI 10.1007/s10546-009-9451-x

ARTICLE

Wind-Tunnel Experiment on Logarithmic-LayerTurbulence under the Influence of Overlying DetachedEddies

Yasuo Hattori · Chin-Hoh Moeng · Hitoshi Suto ·Nobukazu Tanaka · Hiromaru Hirakuchi

Received: 16 January 2009 / Accepted: 5 November 2009 / Published online: 1 December 2009© Springer Science+Business Media B.V. 2009

Abstract A wind-tunnel experiment was carried out to test a hypothesis that the turbulencecharacteristics in the near-neutral surface layer are largely determined by detached eddiesfrom above. The surrogate detached eddies were generated by using an active turbulence gridinstalled at the front of the test section and the parameters of the grid were chosen such thatthe fully developed logarithmic layer downstream consists of a turbulent flow that has similarnormalized intensity to that typically observed in the near-neutral atmospheric surface layer.The effects of the detached eddies on turbulence characteristics were investigated by compar-ison with a second experiment without detached eddies. The influence of the detached eddieson the logarithmic layer was mostly on the coherent structures; the logarithmic layer withthe detached eddies revealed a multi-layer structure similar to that found in the atmospherewhere the lower part of the surface layer is dominated by sweep-like events and the upperpart by ejection-like events. Our experiments show that the mean velocity gradient and theReynolds shear stress were, however, not affected significantly by the detached eddies andhence the eddy viscosity.

Keywords Coherent structure · Detached eddy · Eddy viscosity · Surface layer ·Turbulence · Wind-tunnel experiment

Y. Hattori (B)Civil Engineering Research Laboratory, Central ResearchInstitute of Electric Power Industry, 1646 Abiko, Abiko-shi, Chiba-ken 270-1194, Japane-mail: [email protected]

Y. HattoriMMM Division, National Center for Atmospheric Research,P.O. Box 3000, Boulder, CO 80307-3000, USA

H. Suto · N. Tanaka · H. HirakuchiCentral Research Institute of Electric Power Industry,1646 Abiko, Abiko-shi, Chiba-ken 270-1194, Japan

C.-H. MoengNational Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307-3000, USA

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270 Y. Hattori et al.

1 Introduction

Accurate descriptions of turbulence statistics in the atmospheric surface layer are of practicalinterest not only for numerical weather prediction but also in engineering applications, suchas wind-resistance design for structures, assessment of pollutant dispersal, and estimationof wind energy potential. For instance, for wind-resistance design, most international codesand standards utilize a gust-loading-factor approach to calculating wind loads for structures(Zhou et al. 2002; Ishikawa 2004; IEC 2005). The gust-loading factor defined as the ratio ofpeak to mean value of wind loads is usually expressed in terms of turbulence statistics underthe near-neutral condition. There exists considerable scattering of calculations with currentcodes and standards due primarily to variations in the descriptions of turbulence statistics(Zhou et al. 2002). Thus, a better understanding of turbulence structure, which determinesthe turbulence statistics, in the surface layer under near-neutral conditions is needed to reduceuncertainties in the estimation of wind load.

It has been hypothesized that “surface-layer turbulence (in near-neutral conditions) isdetermined by detached eddies that largely originate in the shearing motion immediatelyabove the surface layer; as they descend into this layer, they are strongly distorted by thelocal shear and impinge onto the surface layer” as proposed by Högström et al. (2002). Thishypothesis has been supported by observations, rapid distortion theory, and large-eddy simu-lations (Drobinski et al. 2004, 2007; Carlotti and Drobinski 2004; Foster et al. 2006). On theother hand, some studies have suggested that the near-neutral logarithmic layer in the atmo-sphere is dominated by the “hairpin vortex packet” originated from below (Hommema andAdrian 2003; McNaughton 2004). The effect of overlying detached eddies on surface-layerturbulence remains a topic of interest.

In this study, we designed a wind-tunnel experiment to test the hypothesis that overly-ing detached eddies dominate the atmospheric surface layer in the near-neutral condition.We generate surrogate detached eddies using an active turbulence grid in the wind tunnel.The set-up of the experiment is described in Sect. 2. In Sect. 3, the experiments with andwithout the detached eddies are compared in order to investigate how detached eddies affectturbulence characteristics in the logarithmic layer. Summary and conclusions are given inSect. 4.

2 Experimental Set-up

2.1 Experimental Apparatus and Procedure

The experiment was conducted in an open-circuit wind tunnel at the Central Research Insti-tute of Electric Power Industry (CRIEPI). A schematic drawing of the wind tunnel, whichcomprises a motor-driven blower, a diffuser, a settling chamber, a construction cone, a testsection and an active turbulence grid, is shown in Fig. 1. The test section is 1,000×1,000 mm2

in area and 6,200 mm long, and the walls of the test section are made of smooth flat woodplates. The details of this apparatus except the active turbulence grid are described in Hattoriet al. (2000) and Hattori (2001). Here, we focus on the specifications of the active turbulencegrid.

The active turbulence grid devised by Makita et al. (1987) has been used to study isotropicturbulence at high Reynolds number (e.g. Makita et al. 1987; Mydlarski and Warhaft 1996;Poorte and Biesheuvel 2002; Kang et al. 2003; Savelsberg and Water 2008) and to controlthe turbulence statistics in a boundary layer (e.g. Sekishita et al. 2002; Larssen 2005; Yue

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Wind-Tunnel Experiment on Logarithmic-Layer Turbulence 271

Fig. 1 Schematic drawing of wind tunnel. Dimensions of mm

Fig. 2 Photograph of active turbulence grid in test section of wind tunnel

et al. 2008). Here, we used it to add a disturbance in the velocity field, which is random innature and consists of zero shear stress. The disturbance mimics detached eddies above theatmospheric surface layer. Figure 2 presents the photograph of our active turbulence grid,which was installed at the front of the test section. The design follows those of previousstudies, composed of (a) rotating grid bars with attached triangular agitator wings, (b) step-ping motors located at the end of each grid bars outside the wind tunnel, and (c) a controller.The mesh spacing L M between the grid bars was 110 mm, providing a scale of disturbancethat is much larger than the scale of shear turbulence generated in the boundary layer. Eachof the 18 grid bars with wings independently flapped with a stepping motor controlled by aprogram on PC.

The streamwise and the vertical (perpendicular to the surface of the test section) compo-nents of velocity fluctuations were measured with an X-type hot wire probe made of 3.1 µmdiameter tungsten. The sensitive length of the hot wires was 1.0 mm. The hot wire was builtinto a Wheatstone bridge (TSI IFA 300) and was operated at a constant overheat-ratio of1.75. The outputs of these wires were amplified, and then digitized with three sampling fre-quencies and times: (1 kHz, 260 s), (10 kHz, 26 s) and (100 kHz, 2.6 s). We have confirmedthat the sampling time and the number of data were sufficient to reach the reproducibilityof experiments, that is, the vertical profiles of turbulence statistics, including higher-ordermoments, do not change significantly with the increase in the sampling time and the data size.The instantaneous velocities were calculated with the look-up matrix developed by Lueptowet al. (1988), which consists of the relationship between output voltage and the velocities

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generated with the calibration for the X-type hot wire to be pitched in the free-stream withvarying velocity. The pitch angles were varied from −30◦ to +30◦ in 6◦ steps for 16 differentvelocities ranging from 0 to 10.0 m s−1.

The accuracy of hot-wire measurement was verified as follows. Turbulence measurementwas also carried out with a particle image velocimetry for boundary-layer flow with distur-bances from the active turbulence grid. We confirmed that the turbulence statistics measuredwith the hot-wire agreed well with those from the particle image velocimetry; the estimateduncertainties with a confidence level of 95% were below 3.7% for the streamwise mean veloc-ity, and 6.8 and 8.4% for the r.m.s. values of streamwise and vertical velocity fluctuations,respectively.

We performed two experiments: one has no additional disturbance, where all grid bars ofthe active turbulence grid remain at rest, and the other has a disturbance where each of theactive grid bars flaps in a random way. Only the latter experiment generated detached eddiesabove the logarithmic layer. The former is denoted as “case C” (conventional turbulenceboundary layer without detached eddies) and the latter is denoted as “case M” (mimickedturbulence boundary layer with detached eddies). For case M, the flapping angles of the gridbars were randomly varied in time, with the maximum angle at 60◦. The mean rotation speedwas set to 2 revolutions per sec. These parameters can significantly affect the turbulenceintensities in the logarithmic layer; for instance, as the maximum flapping angles of the gridbar increase, the intensities of velocity fluctuations also increase (Hattori et al. 2008). Unfor-tunately, there is no model to guide the selection of the flapping angles and the rotation speedbecause these factors may depend on the details of the generation mechanism of the distur-bances by an active turbulence grid. We have chosen these parameters by trial-and-error suchthat the generated turbulence intensities normalized by friction velocity in the logarithmiclayer are similar to those observed in the atmospheric surface layer, as shown in Sect. 3.

2.2 Flow Conditions

For both cases C and M, the velocity at the centreline of the test section (which is called thefree stream region) was 5 m s−1, and the downstream distance x from the active turbulencegrid to the measuring location was x/L M = 38. Below we will show that, at x/L M = 38,the generated turbulent flow in both cases consists of a logarithmic layer in a quasi-steadystate, and that the generated detached eddies represent a non-turbulent flow consisting of noshear stress.

The vertical profiles of the streamwise mean velocity U normalized by wall units, frictionvelocity uτ and kinematic viscosity ν of the fluid, at x/L M =25, 31 and 38, are shown inFig. 3 using a logarithmic scale in z, where z is the vertical distance from the surface. Themean velocities near the surface decrease due to shear-driven turbulence; the depth where themean velocities are affected by the turbulence is defined as the turbulent boundary layer. Thelower part of the turbulent boundary layer can be properly represented by the logarithmiclaw, U/uτ = 5.76log10(z/z0), where the roughness length z0 = 2.5 × 10−6 m for bothcases; this logarithmic layer corresponds to the surface layer in the atmosphere. The loga-rithmic layer height hs , defined as the location at which the mean velocity U deviates morethan 1.5 % from the logarithmic law, were 0.02 and 0.07 m for cases C and M, respectively.[A deeper logarithmic layer with the decline in wake due to the addition of a disturbance wasalso reported in previous experiments (e.g. Blair 1983; Castro 1984; Hancock and Bradshaw1989; Thole and Bogard 1996).] Note that, our lowest measuring level, z uτ /ν ∼ 100 inboth cases, is still much higher than the viscous layer. Figure 3 shows that the effects of the

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Fig. 3 Vertical profile of streamwise mean velocity U at various streamwise distance at x/L M = a 25, b 31and c 38. Triangles and circles are for cases C and M; dash-dot lines represent U/uτ = 5.76 log10(z/z0),where roughness length z0 = 2.5 × 10−6 m

detached eddies on the normalized mean wind profiles appear only above the logarithmiclayer.

Above the turbulent boundary layer, the mean velocity gradients disappear and the flowfield becomes almost uniform in height as shown in Fig. 3. Also, there exists no correlationbetween the streamwise and the vertical velocity fluctuations, and the probability density dis-tributions of these velocity fluctuations are approximately Gaussian (not shown). These indi-cate that zero shear stress is associated with the detached eddies generated by the active grid.

Figure 4 shows the turbulent boundary-layer thickness δ and the momentum thicknessθ against x/L M . Here, the boundary-layer thickness δ is defined at the height where themean velocity reaches 99% of the free-stream velocity Ue, and the momentum thicknessθ is estimated from the momentum loss due to the surface drag as shown in the followingequation,

θ =∞∫

0

U

Ue

(1 − U

Ue

)dz. (1)

For both cases, the turbulent boundary layer and the momentum thickness grow as x4/5, imply-ing that the boundary layer is fully developed in the streamwise direction (e.g. Schlichting1979). At x/L M = 38, δ = 0.1 m, θ = 0.07 m for case C and δ = 0.17 m, θ = 0.009 mfor case M, respectively. The Reynolds numbers based on θ(Reθ = Ueθ/ν) thus alsoincrease with x/L M , exceeding 2.3 × 103 at x/L M = 38, which is in the Reynolds numberindependent regime.

The above results show that, (1) our wind-tunnel turbulent boundary layer consists ofa well-defined logarithmic layer, and (2) the detached eddies above the logarithmic layergenerated by our active turbulence grid contain no shear stress at x/L M = 38.

We also checked the normalized power spectra f E11( f )/σ 2u and f E33( f )/σ 2

w in the freestream for case M, where f is the frequency and σu and σw are standard deviations of thestreamwise and vertical velocity fluctuations, u and w, respectively, in Fig. 5. The compari-son of their peak frequencies shows that the length scale of u is much larger than that of w,and the integral length scales Λu and Λw , which were estimated from the power spectra withthe assumptions of Taylor’s hypothesis and exponential auto-correlation function (Sullivan

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20 30 40 500.05

0.1

0.2

δ [m

]

x/LM

20 30 40 500.002

0.01

0.02

θ [m

]

x/LM

4/5

4/5

(a)

(b)

Fig. 4 Evolution of a boundary-layer thickness δ, and b the momentum thickness θ . Triangles and circlesare for cases C and M

et al. 2003), are 2.9 and 0.8 m, respectively. These integral scales of the detached eddies inthe free stream are significantly larger than the dominant turbulent eddies in the shear-gen-erated boundary layer, which is on the order of the thickness δ(∼= 0.17 m). The anisotropyof the free-stream flow in our experiments is quite large compared to previous experiments(e.g. Mydlarski and Warhaft 1996). This may be due to the details of the generation mecha-nism of the free-stream disturbance by an active turbulence grid, which we believe is beyondthe scope of the present study.

3 Results and Discussion

3.1 Velocity Variances, Fluxes and Eddy Viscosity

The vertical profiles of the intensities of streamwise and vertical velocity fluctuations andthe Reynolds shear stress −uw, normalized by the friction velocity uτ and the logarithmiclayer height hs , for both cases are shown in Fig. 6. The logarithmic layer depth is used hereto normalize the height because, (1) this study focuses on just the surface layer, and (2) this

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Fig. 5 Power spectra of streamwise and vertical velocity fluctuations u and w in the free stream (at thecentreline of the wind tunnel) at x/L M = 38 for case M. Open and closed circles are for u and w

experiment does not simulate the outer layer well and cannot be used to estimate the wholeboundary-layer depth, which is often used to scale atmospheric data. For the same reasons,we plot the wind-tunnel data for z/hs < 1, i.e., just the logarithmic layer. Figure 6 shows thatthe detached eddies significantly increase the magnitude of σu/uτ in the logarithmic layer,from about 2 in case C to abut 2.7 in case M. [Note, however, that previous experiments bye.g. Hancock and Bradshaw (1989), which also included an overlying disturbance but witha scale smaller than that of case M, showed a noticeable effect on σu only above the loga-rithmic layer. So the effect of the disturbance on σu in the logarithmic layer may depend onthe scale of the disturbance.] The major influence of detached eddies on σw is in its verticaldistribution; σw decreases with height in case C but increases with height in case M. Thewall greatly attenuates the vertical velocity fluctuations due to the detached eddies.

The magnitudes of the normalized turbulence intensities in the logarithmic layer in caseM are σu/uτ = 2.6 – 2.8 and σw/uτ =1 – 1.3, which agree with the observations reportedin Table 1; the agreement is expected because we have tuned the parameters of the activegrid to reach this agreement. The more interesting aspect of our result is the increase of σw

with height in case M. Monin–Obukhov (M–O) theory predicts a uniform σw in the surfacelayer; however, many observations of the near-neutral surface layer (e.g., Högström 1990;Högström et al. 2002; Drobinski et al. 2004) show an increase of σw with z near the surface(the lower region of the surface layer). Högström et al. (2002) argued that the increase rate ofσw is due to large-scale disturbances above the surface layer (i.e., overlying detached eddies),and is related to the length scale of detached eddies above the surface layer, Le, as:

(σw/uτ )2 ≈ 1 + (z/Le)

2/3. (2)

This length scale Le must depend on the source of detached eddies, but Högström et al.(2002) showed that its common value is roughly 1/3 of the surface-layer height. Our case Mreveals the following relationship:

(σw/uτ )2 ≈ 0.8 + [z/ (0.5hs)]

2/3 (3)

for z/hs<0.15. Comparing Eqs. 2 and 3, the length scale of our disturbance is about 1/2 ofthe logarithmic layer height hs , which is close to, but somewhat larger than, the observed

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Fig. 6 Vertical profile ofintensities of streamwise velocityfluctuations a u and b w and cReynolds shear stresses−uw. Triangles and circles arefor cases C and M

value of 1/3. These comparisons suggest that our experiment with an active turbulence gridcan mimic reasonably well the detached eddies in the atmosphere and their effect on theturbulence statistics in the logarithmic layer.

Figure 6c compares the vertical profiles of the normalized Reynolds shear stresses betweenthe two cases; the Reynolds stress is hardly affected by the detached eddies. Because theReynolds shear stress for both cases is almost the same, whereas σu for case M is largerthan that of case C, it implies that the detached eddies reduce the correlation coefficient

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Table 1 Comparison of turbulence intensities of streamwise and vertical velocity fluctuations between presentexperiment (case M) and observations in the near-neutral surface layer

Present (case M) Counihan(1975)

Högström(1990)

Grant (1992) Drobinski et al.(2004)

Kunkel andMarusic (2006)

σu/uτ 2.6 – 2.8 2.5 2.78 2.3 2.2–2.4 2.4–3.3

σw/uτ 1.0 – 1.3 1.25 1.1 1.0–1.4 1.2–1.4

Fig. 7 Vertical profile of eddyviscosity KM . Triangles andcircles are for cases C and M

R−uw[= −uw/(σuσw)] in the logarithmic layer; R−uw in cases C and M is 0.4 and 0.3,respectively. The reduction in R−uw is also observed in the surface layer under the influenceof detached eddies (Högström 1990; Högström et al. 2002). They pointed out that the smallerpositive correlation of R−uw is likely due to inactive turbulence motions (Townsend 1961;Bradshaw 1967) generated by detached eddies above the surface layer. Inactive turbulentmotions contribute to the turbulence intensities but not to the turbulence shear stress. It hasbeen shown (e.g., Grant 1992) that the correlation coefficient over the sea, which is morehorizontally uniform and with less occurrence of overlying detached eddies, is larger than thatoverland. Our wind-tunnel experiments provide evidence of the contributions of an overlyinginactive turbulence motion to the turbulence structure of the surface layer.

As shown in Figs. 3 and 6, the detached eddies do not affect the vertical profiles of the nor-malized mean velocity and the Reynolds shear stress in the logarithmic layer. This means thatthe normalized values of the eddy viscosity KM , which is defined as KM = −uw/∂U/∂z, arealso not affected by the detached eddies, as shown in Fig. 7. This implies that PBL schemesin numerical weather prediction models may apply the same eddy viscosity to conditionswith and without the influence of detached eddies.

3.2 Structural Characteristics

We first examine the behaviour of higher order moments, which are statistical measures ofcoherent motions (Nagano and Tagawa 1988). The vertical profiles of skewness factors of uand w are presented in Fig. 8. The detached eddies affect S(u) in the whole logarithmic layer;S(u) in case M is positive near the surface and then decreases to zero gradually with z, sug-gesting a decrease in low-speed fluid motion shown in case C, while S(u) in case C is almost

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Fig. 8 Vertical profiles of theskewness factor of a streamwiseand b vertical velocityfluctuations. Triangles and circlesare for cases C and M

zero near the surface and then becomes negative higher up. On the other hand, the effect ofthe detached eddies on S(w) is negligible near the surface, and then becomes noticeable withz; below z/hs ∼= 0.5, S(w) for both cases is about 0.1, while above z/hs ∼= 0.5, S(w) for caseM remains constant with z while that for case C increases with z. Note that, the skewnessfactors of u and w in case M are consistent with the observation of Högström (1990), whereasS(u) for case C takes on an opposite sign compared with observations.

Figure 9 present the probability density function (p.d.f.) distributions of u and w atz/hs = 0.3 and 1. At z/hs = 0.3, the detached eddies enhance the streamwise velocity fluc-tuations with large positive values (u/σu > 3), and suppress those with large negative values(u/σu < −3) so that the u field in case M tends to be positively skewed. On the other hand,the p.d.f. of w for both cases are very similar, suggesting negligible effects of the detachededdies at this height. Higher up, at z/hs = 1.0, the detached eddies affect the p.d.f. distribu-tions of both u and w. Comparing the p.d.f. between the two cases, we see that the effect ofthe detached eddies is to increase S(u) but to decrease S(w). These results imply that thedetached eddies affect coherence structures such as ejection-like motions, which are typicalcoherent motions in the shear-driven surface layer Lin et al. (1996).

To more quantitatively understand the effects of the detached eddies on the coherentmotions, we carry out a quadrant analysis with a threshold (Lu and Willmarth 1973). Thefluid motions are divided into four quadrants with i = 1, 2, 3 and 4 in the (u, w) plane accordingto contributions to the Reynolds shear stress:

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-6 -4 -2 0 2 4 610-5

10-4

10-3

10-2

10-1

100p.

d.f.

u/σu

6 -4 -2 0 2 4w/σ

w

-6 -4 -2 0 2 410-6

10-5

10-4

10-3

10-2

10-1

100

p.d.

f.

u/σu

-4 -2 0 2 4w/σ

w

(a)

(b)

Fig. 9 Probability density function of streamwise and vertical velocity fluctuations at z/hs = a 0.3 and b 1.0.Triangles and circles are for cases C and M

Ci,O = 1

uwlim

T →∞1

T

T∫

0

u (t) w (t)Ii (t, O) dt for

∣∣∣∣ uw

σuσw

∣∣∣∣ > O, (4)

where Ii (t, O) is a detection function with a threshold O . The ratio of contributions to theReynolds shear stress from ejection- and sweep-like events against O at z/hs = 0.3 and 1.0is shown in Fig. 10. For case C, C4,O/C2,O is less than 1 and decreases with the value ofO at both levels. This indicates that contributions from ejection-like events (w > 0, u < 0represented by the second quadrant C2,O) are dominant in the whole logarithmic layer andthey become more noticeable with increasing in O . For case M, C4,O/C2,O becomes largercompared with case C, indicating that the detached eddies lead to the activation of sweep-likeevents (w<0, u>0 represented by the fourth quadrant C4,O). In particular, in the lower partof the logarithmic layer, at z/hs = 0.3, the contributions from sweep-like events are largerthan those from the ejection-like events, and they become more noticeable with the increasein O .

The above difference of the coherent motions in the logarithmic layer with and without thedetached eddies is compared to observations. For the coherent motions in the near-neutral sur-face layer, two different ideas have been proposed; one is based on turbulence generation bysurface shear (Hommema and Adrian 2003; McNaughton 2004; Kunkel and Marusic 2006)and the other is based on turbulence generation by impinging eddies from above towards

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Fig. 10 Ratio of contribution tothe Reynolds shear stress fromejection- and sweep-like eventsagainst hole size O at z/hs= a 0.3 and b 1.0. Triangles andcircles are for cases C and M

0 2 4 60.0

0.5

1.0

1.5

C4,

O/C

2,O

O

0 2 4 60.0

0.5

1.0

1.5C

4,O/C

2,O

O

(a)

(b)

the surface (Högström et al. 2002; Drobinski et al. 2004, 2007). The present study suggeststhat the effects of detached eddies in the atmosphere might explain this inconsistency, asdiscussed below.

We showed that the logarithmic layer with detached eddies (case M) has a multi-layer struc-ture. At z/hs = 0.3, the detached eddies generate sweep-like events by enhancing high-speedstreamwise flow (Fig. 9a) and sweep-like events become more dominant than ejection-likeevents (Fig. 10a). At z/hs = 1, the detached eddies affect both the streamwise and verticalvelocity fluctuations (Fig. 9b) that suppress ejection-like events, but ejection events still dom-inate compared to sweep-like events (Fig. 10b). The multi-layer structure is also observed inthe atmospheric surface layer (Drobinski et al. 2004, 2007). Observational data with sonicanemometers near the surface and high-resolution Doppler lidar during CASES-99 (Coop-erative Atmosphere Surface Exchange Study field campaign in October 1999) showed thatthere exist two sub-layers in the surface layer; the lower layer is controlled by the blockingof impinging eddies due to inactive turbulence motions (Hunt and Morrison 2000; Hunt andCarlotti 2001) and the upper layer is affected by wind shear. They used a quadrant analysis(but with no mention of the effects of a threshold) to demonstrate the dominant contributionof ejections in the upper layer but dominant sweeps in the lower layer. The present experimentof case M strongly supports their observation.

Drobinski et al. (2004) also revealed the change in the shape of the power spectrum ofw due to the multi-layer structure in the surface layer: their power spectrum of w showed aplateau in the middle frequency range in the upper layer but not in the lower part. Our powerspectra of w at z/hs = 0.3 and 1.0 for case M agree with this observation, and are shown

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Fig. 11 Power spectra of verticalvelocity fluctuations at z/hs= a 0.3 and b 1.0. Triangles andcircles are for cases C and M

in Fig. 11. This compares the power spectra of the vertical velocity fluctuations f E33( f ) atz/hs = 0.3 and 1 normalized by uτ , z, and mean velocity U at z between the two cases.Note that our wind-tunnel flows exhibit a rather limited range of the inertial sub-range due tolow Reynolds number. Our turbulent layer as in generated over a smooth surface and henceis not a “fully rough” turbulent layer like the atmospheric boundary layer (e.g. Garratt 1992).The applications of smooth-wall wind-tunnel results to the atmospheric boundary layer havebeen questioned; however, some studies have indicated that the turbulence structure in thelogarithmic layer is rather similar between aerodynamic rough- and smooth-wall flows (e.g.Volino et al. 2007). The spectral analysis shows that the attached eddies reduce the peakenergy in the energy-containing eddy range and enhance the energy at both tails of high andlow frequencies. This change is more pronounced towards the top of the logarithmic layer,where the f E33( f ) in case M reveals a plateau in the middle frequency range, correspondingto observations in the atmospheric surface layer (Drobinski et al. 2004), and may be relatedto a multi-layer structure found in the surface layer.

4 Summary and Conclusions

To test the hypothesis that “surface-layer turbulence (in near-neutral conditions) is deter-mined by detached eddies…above the surface layer” proposed by Högström et al. (2002), wecarried out a wind-tunnel experiment, with an active turbulence grid, to generate surrogate

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detached eddies and to study their effect on the logarithmic layer turbulence. The param-eters of the grid were chosen such that the fully developed logarithmic layer downstreamconsists of a turbulent flow that has similar intensity (after being normalized by surface fric-tion velocity) to that typically observed in the near-neutral atmospheric surface layer. Theeffects of detached eddies on the logarithmic layer were investigated by comparison with asecond experiment without detached eddies. We found that detached eddies greatly enhancethe intensity of the streamwise velocity fluctuations, but have little effect on the mean veloc-ity, the intensity of vertical velocity fluctuations, and the Reynolds shear stress. Therefore,detached eddies reduce the correlation coefficient between streamwise and vertical velocityfluctuations, but do not modify the eddy viscosity. The most significant changes to the log-arithmic layer due to detached eddies appear in the distributions of velocity spectra, p.d.f.,skewness, and hence coherent motions such as ejection-like and sweep-like events. With theaddition of detached eddies, the lower part of the logarithmic layer becomes dominated bysweep-like events due to the impinging eddies from above, while ejection-like events due tosurface shear still dominate the upper part of the surface layer. This agrees with observationsof a multi-layer structure in the atmospheric surface layer, e.g. Drobinski et al. (2004, 2007).

Acknowledgements The authors would like to thank Dr. Sun, JuanZhen and Dr. Soichiro Sugimoto forhelp in the collaboration between NCAR and CRIEPI and Mr. Takayoshi Mizuno for help in the wind-tunnelexperiments. The authors also would like to thank Dr. Tomomi Ishikawa, Dr. Takenobu Michioka and Dr.Naoto Kihara for fruitful discussions on the understanding of experimental results. C.-H. Moeng’s work issupported by the National Center for Atmospheric Research, USA, which is sponsored by the National ScienceFoundation.

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