======Homogeneous Isotropic Flow with/without Mean Temperature Gradient======
=====Simulation by Iida and Kasagi=====

----

====Description====

Direct numerical simulation (DNS) of homogeneous decaying, almost isotropic, turbulence with a 
mean temperature gradient imposed in one direction was carried out by using a spectral method. 
Each term in the budget equations of the Reynolds stresses and turbulent heat flux were 
calculated, together with turbulence spectra and lengthscales.


====Simulation Details====

The numerical databases to be analysed are of decaying homogeneous anisotropic turbulence 
with a mean temperature gradient (<imgref cas47-geom>).

<imgcaption cas47-geom| Flow configuration>{{ figs:case047:cas47-geom.png | Flow configuration}}</imgcaption>

These computations were carried out by Iida and Kasagi (1991) using a spectral method 
with 96<sup>3</sup> grid points on a cubic box of side \(L = 2\pi\), with periodic conditions
imposed across its boundaries.

The Navier-Stokes equations and energy equation were solved for an incompressible fluid with
dimensionless kinematic viscosity \(\nu=1/300\). Cases are reported for Prandtl numbers 
\(Pr = 0.2\), \(0.71\) and \(1.5\).

The initial energy spectrum was given as follows:
\[ E(k) = (q_ok/k_p^2) \exp(-k/k_p) \]
where \(k\) is the three-dimensional wave number, \(q_o = 0.49\) and \(k_p = 5.0\).
The initial distribution of the Reynolds stresses is a fairly small anisotropy, with
\(\overline{u^2} = \overline{v^2} < \overline{w^2}\).

A constant mean temperature gradient, which would create a turbulent heat flux, was imposed 
in the \(y\) direction, with non-dimensional gradient \(dT/dy=-1\). In most cases the
initial thermal field had no fluctuations, although for one case with \(Pr=0.71\) non-zero
initial thermal fluctuations were imposed, with the same spectral distribution as the
dynamic field.

====Available Results====

Data available include:

  * Time development of the Reynolds stresses, temperature variance and turbulent heat flux
  * Budgets of the above second moments
  * Dynamic and thermal inertial lengthscales
  * One dimensional energy spectra and two-point correlations

[[case047-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:case047:isth-allfiles.zip|isth-allfiles.zip}}
  * {{cdata:case047:isth-allfiles.tar.gz|isth-allfiles.tar.gz}}

|  |   Datafile  |
| Dynamic and thermal field data |  {{cdata:case047:is_2_ut_hm1.dat|is_2_ut_hm1.dat}}  |

====References====

  - Iida, O., Kasagi, N. (1991). Prandtl number effect on scalar transport in homogeneous isotropic turbulence, //Proc. 5th Symposium of Numerical Fluid Dynamics//, Tokyo, Japan.
  - Iida, O., Kasagi, N. (1993). Redistribution of the Reynolds Stresses and destruction of the turbulent heat flux in homogeneous decaying turbulence. //Proc. 9th Turbulent Shear Flow Symposium//, Kyoto, Japan.

----

Indexed data:
<data dbcase free_flow>
case       : 047
title      : Homogeneous Isotropic Flow with/without Mean Temperature Gradient
author*    : Iida, Kasagi
year       : 1992
type       : DNS
flow_tag*  : homogeneous, scalar
</data>