On the limiting effect of the Earth's rotation on the depth of a stably stratified boundary layer

Mironov, Dmitrii; Fedorovich, Evgeni

doi:10.1002/qj.631

Cited by 14 publications

(10 citation statements)

References 42 publications

(72 reference statements)

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“…Note that the normalization of height (y axis here) is carried out using the depth (turbulent length scale) of the neutral simulations. Other scales can be used for normalization (Mironov & Fedorovich (2010), for example, pointed to several depth scales for stable boundary layers that are consistent with TKE and momentum budgets), but, to emphasize the effect of static stability on turbulence at a given dimensional distance from the wall, we use the fixed neutral-case turbulent Ekman layer length scale for normalization. Figure 12 presents the vertical variation of 2q 2 = u i u i (twice the TKE) at various stabilities and at different Reynolds numbers.…”

Section: Profiles Of the Gradient Richardson Number Tke And Stressmentioning

confidence: 99%

Direct numerical simulations of turbulent Ekman layers with increasing static stability: modifications to the bulk structure and second-order statistics

Shah

Bou‐Zeid

2014

J. Fluid Mech.

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Direct numerical simulations of stably stratified Ekman layers are conducted to study the effect of increasing static stability on turbulence dynamics and modelling in wall-bounded flows at three moderate Reynolds numbers. The flow field is analysed by examining the mean profiles of wind speed, potential temperature and momentum flux, as well as streamwise velocity and temperature spectra. The maximum stabilizing buoyancy flux that a flow can sustain while remaining fully turbulent is found to depend on the Reynolds number. The flows with the highest Reynolds number display a relatively well-developed inertial range and logarithmic layer, and are found to bear similarities to much higher-Reynolds-number flows like the ones encountered in the atmospheric boundary layer. In particular, the near-wall mean profiles follow the Monin-Obukhov similarity theory. However, several flow features, such as the critical Richardson number and the stress-strain alignment, are found to maintain significant dependence on the Reynolds number. The budgets of turbulence kinetic energy (TKE), vertical velocity variance, momentum and buoyancy fluxes, and temperature variance are analysed. The results indicate that the effect of stability on turbulence is first directly manifested in the vertical velocity variance budget, and results in damping of vertical motions. This then leads to a reduction in the downward transport of horizontal momentum components towards the surface, and consequently to a decrease in the shear production term in the TKE budget: changes in the vertical profile of TKE shear production with increasing Richardson number are significant and have a larger impact on TKE than direct buoyancy destruction. The reduction in vertical velocity variance also results in significant drops in the production terms in the momentum flux, buoyancy flux and temperature variance budgets. Various assumptions and parameters related to low-order turbulence closures are investigated. The results suggest that the vertical velocity variance is a more appropriate parameter than the full TKE on which to base eddy-diffusivity and viscosity models.

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Section: Profiles Of the Gradient Richardson Number Tke And Stressmentioning

confidence: 99%

Direct numerical simulations of turbulent Ekman layers with increasing static stability: modifications to the bulk structure and second-order statistics

Shah

Bou‐Zeid

2014

J. Fluid Mech.

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“…Following, for instance, Mironov and Fedorovich (2010) we take the friction velocity, u * , the surface Obukhov length, L 0 , and the Coriolis force, f, as scales for the surface layer, and u * , f and the Brunt-Väisälä frequency, N, as scales for the turbulent flow above the surface layer, with N 'imposed' at height h representing the potential temperature gradient at this height and for some distance above.…”

Section: Introductionmentioning

confidence: 99%

“…or, equally, Mironov and Fedorovich (2010) give an equation for this functional form. The two sets of scales lead to classifying a stable boundary layer in terms of surfaceflux conditions and 'imposed' or 'external' conditions, and to sub-classifications of surface-flux dominated and external-stability dominated.…”

Section: Introductionmentioning

confidence: 99%

Wind-Tunnel Simulation of the Wake of a Large Wind Turbine in a Stable Boundary Layer. Part 1: The Boundary-Layer Simulation

Hancock

Pascheke

2013

Boundary-Layer Meteorol

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Abstract:Measurements have been made in both a neutral and a stable boundary layer as part of an investigation of the wakes of wind turbines in an offshore environment, in the EnFlo stratified flow wind tunnel. The working section is long enough for the flow to have become very nearly invariant with streamwise distance. In order to be systematic, the flow profile generators of Irwintype spires and surface roughness were the same for both neutral and stable conditions. Achieving the required profiles by adjusting the flow generators, even for neutral flow, is a highly iterative art, and the present results indicate that it will be no less iterative for a stable flow (as well as there being more conditions to meet), so this was not attempted in the present investigation. The stablecase flow conformed in most respects to Monin-Obukhov similarity in the surface layer. A linear temperature profile was applied at the working section inlet, resulting in a near-linear profile in the developed flow above the boundary layer and 'strong' imposed stability, while the condition at the surface was 'weak'. Aerodynamic roughness length (mean velocity) was not affected by stability even though the roughness Reynolds number < 1, while the thermal roughness length was much smaller, as is to be expected. The neutral case was Reynolds-number independent, and by inference, the stable case was also Reynolds-number independent.

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“…A particular case of such flows is stratified Ekman flow where static stability acts on top of the stabilizing effect of rotation (Mironov & Fedorovich 2010). Turbulent Ekman flow is the limit of the planetary boundary layer over a homogeneous smooth surface with a constant geostrophic forcing.…”

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confidence: 99%

Analyses of external and global intermittency in the logarithmic layer of Ekman flow

Ansorge

Mellado

2016

J. Fluid Mech.

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Existence of non-turbulent flow patches in the vicinity of the wall of a turbulent flow is known as global intermittency. Global intermittency challenges the conventional statistics approach when describing turbulence in the inner layer and calls for the use of conditional statistics. We extend the vorticity-based conditioning of a flow to turbulent and non-turbulent sub-volumes by a high-pass filter operation. This modified method consistently detects non-turbulent flow patches in the outer and inner layers for stratifications ranging from the neutral limit to extreme stability, where the flow is close to a complete laminarization. When applying this conditioning method to direct numerical simulation data of stably stratified Ekman flow, we find the following. First, external intermittency has a strong effect on the logarithmic law for the mean velocity in Ekman flow under neutral stratification. If instead of the full field, only turbulent sub-volumes are considered, the data fit an idealized logarithmic velocity profile much better; in particular, a problematic dip in the von Kármán measure κ in the surface layer is decreased by approximately 50 % and our data only support the reduced range 0.41 κ 0.43. Second, order-one changes in turbulent quantities under strong stratification can be explained by a modulation of the turbulent volume fraction rather than by a structural change of individual turbulence events; within the turbulent fraction of the flow, the character of individual turbulence events measured in terms of turbulence dissipation rate or variance of velocity fluctuations is similar to that under neutral stratification.

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On the limiting effect of the Earth's rotation on the depth of a stably stratified boundary layer

Cited by 14 publications

References 42 publications

Direct numerical simulations of turbulent Ekman layers with increasing static stability: modifications to the bulk structure and second-order statistics

Direct numerical simulations of turbulent Ekman layers with increasing static stability: modifications to the bulk structure and second-order statistics

Wind-Tunnel Simulation of the Wake of a Large Wind Turbine in a Stable Boundary Layer. Part 1: The Boundary-Layer Simulation

Analyses of external and global intermittency in the logarithmic layer of Ekman flow

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