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Direct numerical simulation of stratified homogeneous turbulent shear flows

Gerz, T. and Schumann, U. and Elghobashi, S. E. (1989) Direct numerical simulation of stratified homogeneous turbulent shear flows. Journal of Fluid Mechanics, 200, pp. 563-594. DOI: 10.1017/S0022112089000765

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Official URL: http://www.jfm.damtp.cam.ac.uk/

Abstract

The exact time-dependent three-dimensional Navier-Stokes and temperature equations are integrated numerically to simulate stably stratified homogeneous turbulent shear flows at moderate Reynolds numbers whose horizontal mean velocity and mean temperature have uniform vertical gradients. The method uses shear-periodic boundary conditions and a combination of finite-difference and pseudospectral approximations. The gradient Richardson number Ri is varied between 0 and 1. The simulations start from isotropic Gaussian fields for velocity and temperature both having the same variances. The simulations represent approximately the conditions of the experiment by Komori et al. (1983) who studied stably stratified flows in a water channel (molecular Prandtl number Pr = 5). In these flows internal gravity waves build up, superposed by hot cells leading to a persistent counter-gradient heat-flux (CGHF) in the vertical direction, i.e. heat is transported from lower-temperature to higher-temperature regions. Further, simulations with Pr = 0.7 for air have been carried out in order to investigate the influence of the molecular Prandtl number. In these cases, no persistent CGHF occurred. This confirms our general conclusion that the counter-gradient heat flux develops for strongly stable flows (Ri [approximate] 0.5–1.0) at sufficiently large Prandtl numbers (Pr = 5). The flux is carried by hot ascending, as well as cold descending turbulent cells which form at places where the highest positive and negative temperature fluctuations initially existed. Buoyancy forces suppress vertical motions so that the cells degenerate to two-dimensional fossil turbulence. The counter-gradient heat flux acts to enforce a quasi-static equilibrium between potential and kinetic energy. Previously derived turbulence closure models for the pressure-strain and pressure-temperature gradients in the equations for the Reynolds stress and turbulent heat flux are tested for moderate-Reynolds-number flows with strongly stable stratification (Ri = 1). These models overestimate the turbulent interactions and underestimate the buoyancy contributions. The dissipative timescale ratio for stably stratified turbulence is a strong function of the Richardson number and is inversely proportional to the molecular Prandtl number of the fluid.

Item URL in elib:https://elib.dlr.de/53359/
Document Type:Article
Title: Direct numerical simulation of stratified homogeneous turbulent shear flows
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Gerz, T.UNSPECIFIEDUNSPECIFIED
Schumann, U.UNSPECIFIEDUNSPECIFIED
Elghobashi, S. E.Univ. of California, Irvine, CA, USAUNSPECIFIED
Date:1989
Journal or Publication Title: Journal of Fluid Mechanics
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:Yes
Volume:200
DOI :10.1017/S0022112089000765
Page Range:pp. 563-594
Status:Published
Keywords:shear-periodic boundary, pseudospectral, approximations
HGF - Research field:other
HGF - Program:other
HGF - Program Themes:other
DLR - Research area:no assignment
DLR - Program:no assignment
DLR - Research theme (Project):no assignment
Location: Oberpfaffenhofen
Institutes and Institutions:Institute of Atmospheric Physics
Deposited By: Freund, Jana
Deposited On:18 Feb 2008
Last Modified:31 Jul 2019 19:21

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