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

Abstract

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.

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

“…For a comprehensive review of the flow in its different stability regimes, see Ansorge & Mellado (2014), Deusebio et al (2014) and Shah & Bou-Zeid (2014b). The three stratified configurations considered in this work (summarized in table 1) can be attributed to the three stability regimes of weak (ri15), intermediate (ri31) and strong (ri62) stratification by means of their bulk evolution (cf.…”

“…Regarding numerical simulations, sufficiently resolved data in space and time became available just recently: for the neutrally stratified case of Ekman flow, Ansorge & Mellado (2014) provide high-resolution data in a domain large enough to study the large-scale dynamics associated with turbulence breakdown (cf. Shah & Bou-Zeid 2014b). Through more recent simulations (introduced in § 2 and discussed in § 3), data for stratified cases at higher Reynolds number became available and are discussed here.…”

Early Warning Signals for Regime Transition in the Stable Boundary Layer: A Model Study

“…Here, we base ourselves on the introductions to bifurcation theory by Seydel (2010) and Scheffer (2009) to introduce some key concepts. The equilibrium state of a dynamical system is generally a function of one or more external conditions.…”

Two phenomenological constants explain similarity laws in stably stratified turbulence

“…The DNS dataset is the one generated by Shah and Bou-Zeid [61] for the analysis of the budgets of key second-order statistics. Brief details and new results relevant for the present work are provided.…”