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

Abstract

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.

A Model for Turbulence Spectra in the Equilibrium Range of the Stable Atmospheric Boundary Layer

“…As the Reynolds number of the observed ABL is much higher than that of the DNS, some differences in turbulence spectra can be expected; for example, the inertial subrange is much narrower in the latter (Chung & Matheou, ; Shah & Bou‐Zeid, ). The Kolmogorov scale (see introduction in section ) in the Lake EC data is about four decades away from the Dougherty‐Ozmidov scale; that is, we observe a large region of the isotropic inertial subrange, suggesting that turbulence is still well defined rather than being intermittent as shown in results (Ansorge & Mellado, ; Flores & Riley, ).…”

“…"spatial" denotes the spatial spectra of temperature at height 1.75 m."H1 mean," "H2 mean," "H3 mean," and "H4 mean" denote the spatial mean of temporal spectra at four fiber optics measurement heights, respectively. region of the isotropic inertial subrange, suggesting that turbulence is still well defined rather than being intermittent as shown in DNS results (Ansorge & Mellado, 2016;Flores & Riley, 2011).…”

Scale Dependence of Atmosphere–Surface Coupling Through Similarity Theory

“…In neutrally stratified Ekman flow, an equilibrium is acquired between the suppression of turbulence due to rotation and the boundary-layer growth over a non-rotating flat plate manifest in a statistically steady state. While there is debate on the universality of the von Kármán constant (Spalart et al 2008), the extent of the logarithmic layer, and effects of entrainment (Ansorge and Mellado 2016), the existence of a layer over which the wind-speed profile adheres to an approximately logarithmic profile is a wellestablished consensus. Indeed, when considering the temporal and spatial average of the wind speed-profiles-the best estimate of the ensemble average available-our simulations exhibit a well-established logarithmic region that deepens as the Reynolds number increases (Fig.…”

“…We resort here to the direct numerical simulation (DNS) of a turbulent Ekman flow above a smooth surface as a physical model of the PBL. Still, the numerical simulation cannot achieve the Reynolds numbers commonly encountered in geophysical boundary layers (Moin and Mahesh 1998); recently, however, data at a sufficiently high Reynolds number and domain size to allow for a well-resolved logarithmic part of the wind speed profile have become available (Ansorge and Mellado 2016), and herein, an additional simulation with a further decrease of viscosity by about 70% is added. One reason why MOST is used so widely is its applicability in different stratification regimes; here, we limit the scope to stable and neutral stratification.…”

Ramp‐Like PM Accumulation Process and Z‐Less Similarity in the Stable Boundary Layer

“…Regardless of whether Reynolds-Averaged Navier-Stokes equation simulations or large eddy simulations is used, it is difficult to parameterize multiscale turbulence and subgrid or subscale turbulence processes in the SBL (Mellado et al, 2018;Shah & Bou-Zeid, 2014). The large length scale separation at high Reynolds numbers in stably stratified atmospheric turbulence cannot be resolved by direct numerical simulations (Ansorge & Mellado, 2016;Smyth & Moum, 2000).…”