======Homogeneous Turbulent Shear Flows======
=====Direct Numerical Simulation by Matsumoto, Nagano and Tsuji=====

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====Description====

A sheared homogeneous turbulent field  is simulated, as shown schematically in
<imgref cas49-geom>.  The mean flow  is imposed in  
the \(x\)-direction  and is sheared in the \(y\)-direction at a constant shear 
rate \(S\). The initial non-dimensional shear rate \(Sk_o/\varepsilon_o\) is approximately 4.7.
Turbulence statistics are obtained up to a dimensionless time \(St=14\).
The flow does not have proper scales for non-dimensionalizing the governing equations, 
so that the computation is carried out in arbitrary units.

<imgcaption cas49-geom| Flow configuration>{{ figs:case049:cas49-geom.png | Flow configuration}}</imgcaption>

====Numerical Method====

The numerical method used for the present direct numerical simulation of homogeneous
sheared turbulence is based on the spectral method developed by Rogallo (1981). 

The time-dependent Navier Stokes and continuity equations are solved in a computational
box of size \(2\pi \times 2\pi \times 2\pi\). The equations are discretized using spectral 
methods, with \(64\times 64\times 64\) Fourier modes in the \(x\), \(y\) and \(z\) directions,
and a second order Runge-Kutta scheme for time integration. Remeshing is done at constant 
intervals, in order to advance the simulation in a coordinate system moving with mean flow 
(See Rogallo, 1981).

The velocity field is initialized to be an isotropic state in wave space, satisfying the 
continuity condition and the given energy spectrum,
\(E(k)= 8.417\times 10^{-3}k^2\) for \(k \le 11\) and 
\(E(k)= 8.417\times 10^{-3}\times (11^{11/3})k^{-5/3}\) for \(11 \le k \le 30\).

====Available Results====

Data available include:

  * Time development of Reynolds stresses
  * RMS values of fluctuating velocities, strain rates and pressure
  * Skewness and flatness factors
  * Length- and time-scales
  * Budget terms from the Reynolds stress equations
  * One dimensional energy spectra
  * Two point correlations

[[case049-plots|Sample plots]] of selected quantities are available.

The data can be downloaded as compressed archives from the links below, or as the single uncompressed file.

  * {{cdata:case049:hmsh-allfiles.zip|hmsh-allfiles.zip}}
  * {{cdata:case049:hmsh-allfiles.tar.gz|hmsh-allfiles.tar.gz}}

|    |   Datafile  |
| Dynamic field data |  {{cdata:case049:sh12_ut_hm1.dat|sh12_ut_hm1.dat}}  |


====References====

  - Matsumoto, A., Nagano, Y., Tsuji, T. (1991). Direct numerical simulation of homogeneous turbulent shear flow. //Proc. 5th Symposium on Computational Fluid Dynamics//, Tokyo.
  - Rogallo, R.S. (1981). Numerical Experiments in Homogeneous Turbulence, NASA TM 81315.

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Indexed data:
<data dbcase free_flow>
case       : 049
title      : Homogeneous Turbulent Shear Flows
author*    : Matsumoto, Nagano, Tsuji
year       : 1992
type       : DNS
flow_tag*  : homogeneous
</data>