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A simple turbulence model for stably stratified wall‐bounded flows
Author(s) -
Karimpour F.,
Venayagamoorthy S. K.
Publication year - 2014
Publication title -
journal of geophysical research: oceans
Language(s) - English
Resource type - Journals
eISSN - 2169-9291
pISSN - 2169-9275
DOI - 10.1002/2013jc009332
Subject(s) - turbulence , stratified flows , scalar (mathematics) , stratified flow , direct numerical simulation , turbulent prandtl number , physics , prandtl number , turbulence modeling , mechanics , richardson number , reynolds number , mathematics , statistical physics , geometry , nusselt number , convection
In this study, we present a simple zero‐equation (algebraic) turbulence closure scheme as well as the standard k ‐ ϵ model for stably stratified wall‐bounded flows. We do this by proposing a parameterization for the turbulent Prandtl number ( Pr t ) for stably stratified flows under the influence of a smooth solid wall. The turbulent Prandtl number is the linking bridge between the turbulent momentum and scalar fluxes in the context of Reynolds‐averaged Navier‐Stokes (RANS) simulations. Therefore, it is important to use appropriate parameterizations for Pr t in order to define the right level of momentum and scalar mixing in stably stratified flows. To date, most of the widely used parameterizations for Pr t in stably stratified flows are based on data obtained from homogeneous shear flows experiments and/or direct numerical simulations (i.e., statistics are invariant under translations) and are usually formulated as functions of the gradient Richardson number ( Ri g ). The effect of the wall boundary is completely neglected. We introduce a modified parameterization for Pr t that takes into account the inhomogeneity caused by the wall coupled with the effects of density stratification. We evaluate the performance of the modified Pr t by using a zero‐equation turbulence model for the turbulent viscosity that was proposed by Munk and Anderson (1948) as well as the standard k ‐ ϵ model to simulate a one‐dimensional stably stratified channel flow. Comparison of the one‐dimensional simulation results with direct numerical simulation (DNS) of stably stratified channel flow results show remarkable agreement.