Analysis of Vertical Turbulent Heat Flux Limit in Stable Conditions with a Local Equilibrium, Turbulence Closure Model

Abstract

Assuming that the vertical turbulent heat flux vanishes at extremely stable conditions, one should expect its maximal absolute value to occur somewhere at moderate stability, between a neutral and extremely stable equilibrium. Consequently, in some situations duality of solutions may be encountered (e.g. two different values of temperature difference associated with the same values of heat flux and wind speed). A quantitative analysis of this feature with a local equilibrium Reynolds-stress model is presented. The fixed-wind / fixed-shear maximum has been identified both in the bulk and in single-point flux-gradient relationships (that is, in the vertical temperature gradient and wind-shear parameter domain). The value of the Richardson number corresponding to this maximum is derived from the model equations. To study the possible feedback in strongly stable conditions, weak and intense cooling scenarios have been simulated with a one-dimensional numerical, high-resolution atmospheric boundary-layer model. Despite the rapid cooling, flow decoupling at the surface has not been observed; instead, a stability-limited heat flux is maintained, with a gradual increase of the Richardson number towards the top of the turbulent layer, with some signs of oscillatory behaviour at intermediate heights. Vertical changes of wind shear and the Brunt-Väisälä frequency display a remarkably non-monotonic character, with some signs of a gradually developing instability.

The maximum sustainable heat flux in stably stratified channel flows

“…Qualitatively similar behaviour has been reported in (more realistic) multilayer Reynolds‐Averaged Navier‐Stokes (RANS) models by e.g. Derbyshire (), Delage et al (), Shi et al (), Costa et al (), Acevedo et al () and łobocki (). Apart from those parametrized approaches, studies with turbulence‐resolving models like large‐eddy simulation (LES) have been mostly limited to the continuous turbulent, weakly stable case.…”

Collapse of turbulence in stably stratified channel flow: a transient phenomenon

“…In contrast to the weakly stable boundary layer, the very stable boundary layer (VSBL) is poorly understood (for a recent review, we refer to Mahrt ()). Although from an experimental point of view considerable effort has been made to improve our understanding (Cuxart et al , ; Poulos et al , ; Grachev et al , ; Hoch and Calanca, ; Wyngaard, ; Mahrt, ; Sun et al , ), the number of numerical studies on VSBL dynamics has been limited so far: most of the work has been restricted to the continuously turbulent regime (with exceptions mainly from conceptual studies such as those of McNider et al (), Van de Wiel et al (), Costa et al (), Acevedo et al () and Łobocki ()). In strongly stratified conditions, parametrization of radiative and turbulent transport processes is far from trivial (Edwards, ).…”

Numerical simulation of stratified flow around a tall building of a complex shape

“…The turbulent transport is modelled using the Level 3 second-order turbulence closure scheme, as introduced by Mellor and Yamada [41,42], with realizability limitations and model constants developed by Nakanishi and Niino [47]. For more details, see [37]. While integrating this model with constant boundary conditions, we found it sufficient to run the model for just 5 mins with a one-second time step.…”