Comments on the Numerical Simulation of Homogeneous Stably-Stratified Turbulence

Abstract

The standard design for the direct numerical simulation of homogeneous stably-stratified turbulence assumes that the simulated turbulence is fully characterised by the gradient Richardson number. This assumption is justified only in sufficiently strong stratification when the Obukhov turbulent length scale, L, is essentially smaller than the depth of the computational domain, H. Otherwise simulations are not quite realistic because they cut off the large-scale part of the turbulence spectrum, namely, the scales comparable with or larger than H but smaller than L, that is just the eddies most sensitive to the stratification.Keywords Applicability limit · Depth of computational domain · Direct numerical simulation · Stably stratified turbulence · Turbulent length scale

The Influence of Boundary Layer Processes on the Diurnal Variation of the Climatological Near-Surface Wind Speed Probability Distribution over Land*

“…This quantity cannot exceed unity on theoretical grounds, and theoretical studies (Canuto et al 2008;Kantha and Carniel 2009;Zilitinkevich 2010;Ferrero et al 2011) suggest values in the range of 0.2-0.3, although large-eddy simulations (LESs) and results from observations suggest a broader range (Esau and Grachev 2007). This effect can be influenced to some extent by the specified value of the asymptotic flux Richardson number R ' in the turbulence scheme due to its control on the Prandtl number (P r ) in stable flows (see the online supplement, which describes the turbulence scheme).…”

A Hierarchy of Energy- and Flux-Budget (EFB) Turbulence Closure Models for Stably-Stratified Geophysical Flows

“…Our theory justifies it as a reasonable approximation for the strong-turbulence regime (0 < Ri < 0.25), and reveals its absolute inapplicability to the weak-turbulence regime (Ri > 1), where the Ri-dependence of T r P becomes an order of magnitude stronger: dRi r dP T /  4. Zilitinkevich (2010) has already pointed out strongly different Ri-dependences of T r P at large and small Ri in connection with conceptual inadequacy of the currently used design of DNS of the stably stratified turbulence for small Ri.…”

“…Historical overviews of the turbulence closure problem and recent developments in this area of knowledge have been discussed during the last decade by Canuto (2002Canuto ( , 2009), Canuto et al, (2001Canuto et al, ( , 2005Canuto et al, ( , 2008, Cheng et al (2002), Kurbatskii and Kurbatskaya (2006, 2010 and Zilitinkevich et al (2007Zilitinkevich et al ( , 2008Zilitinkevich et al ( , 2009). Most of the operationally used closures employ the concept of the downgradient turbulent transport, implying that the vertical turbulent fluxes of momentum i  ( 2 , 1  i ), potential temperature z F and other scalars are proportional to their mean gradients.…”