Abstract
Direct numerical simulation of the turbulent Ekman layer over a smooth wall is used to investigate bulk properties of a planetary boundary layer under stable stratification. Our simplified configuration depends on two non-dimensional parameters: a Richardson number characterizing the stratification and a Reynolds number characterizing the turbulence scale separation. This simplified configuration is sufficient to reproduce global intermittency, a turbulence collapse, and the decoupling of the surface from the outer region of the boundary layer. Global intermittency appears even in the absence of local perturbations at the surface; the only requirement is that large-scale structures several times wider than the boundary-layer height have enough space to develop. Analysis of the mean velocity, turbulence kinetic energy, and external intermittency is used to investigate the large-scale structures and corresponding differences between stably stratified Ekman flow and channel flow. Both configurations show a similar transition to the turbulence collapse, overshoot of turbulence kinetic energy, and spectral properties. Differences in the outer region resulting from the rotation of the system lead, however, to the generation of enstrophy in the non-turbulent patches of the Ekman flow. The coefficient of the stability correction function from Monin–Obukhov similarity theory is estimated as $$\beta \approx 5.7$$ in agreement with atmospheric observations, theoretical considerations, and results from stably stratified channel flows. Our results demonstrate the applicability of this set-up to atmospheric problems despite the intermediate Reynolds number achieved in our simulations.
Highlights
The characteristics of a planetary boundary layer (PBL) crucially depend on its density stratification
If turbulence is treated as an on–off process, a runaway cooling at the surface is often seen in PBL models and large-eddy simulations (LES) applied under very stable conditions (Jiménez and Cuxart 2005; Wiel et al 2012; Huang et al 2013)
The flow depends only weakly on the Reynolds number as we demonstrate by a comprehensive flow description including hodographs, the integral value of the turbulence dissipation rate as well as vertical profiles of velocity, TKE, and external intermittency
Summary
The characteristics of a planetary boundary layer (PBL) crucially depend on its density stratification. Monin–Obukhov similarity theory (MOST, Obukhov 1971) lacks the ability to properly reproduce turbulent fluxes under weak-wind conditions (Ha et al 2007), i.e. in the very stable regime From atmospheric observations, it is unclear if stratification can become strong enough to suppress turbulent mixing entirely (Mauritsen and Svensson 2007), and it proves problematic to locally classify a very stable PBL as turbulent or non-turbulent. If turbulence is treated as an on–off process, a runaway cooling at the surface is often seen in PBL models and large-eddy simulations (LES) applied under very stable conditions (Jiménez and Cuxart 2005; Wiel et al 2012; Huang et al 2013) It is a well-accepted hypothesis that the cessation of turbulence is not an on–off process but rather a complex transition beginning with the local absence of turbulence in an otherwise turbulent boundary layer. (3) Does Ekman flow differ from other configurations used to study the PBL such as channelflow surrogates? How do large scales in the flow interact with stratification?
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