The decay of weak, homogeneous turbulence in the presence of a vertical body force and concentration gradient with a firstorder reaction
Abstract
The effects of buoyancy, produced by a uniform vertical concentration gradient and body force, on a homogeneous turbulent field accompanied by a firstorder chemical reaction are analyzed by considering a simplified model. A system of twopoint correlation equations, which contains mean concentrationgradient and bodyforce terms, is constructed from the NavierStokes, convective diffusion, and continuity equations. These equations are converted into equations for the spectrum functions in the wavenumber space, and solutions for different spectral tensors are obtained by neglecting the contributions of the triple correlation terms. For numerical calculations, it is assumed that the turbulence is initially isotropic and the concentration fluctuations initially zero. It turns out that the turbulence decays with time, although the buoyant forces alter the rate of decay. The buoyant forces can either extract energy from the turbulent field or feed energy into it, depending on the direction of the body force and the concentration gradient.
 Publication:

Applied Scientific Research
 Pub Date:
 December 1975
 Bibcode:
 1975ApScR..31..321R
 Keywords:

 Buoyancy;
 Chemical Reactions;
 Decay Rates;
 Turbulent Flow;
 Vertical Distribution;
 Concentration (Composition);
 Convective Flow;
 Flow Distribution;
 Molecular Diffusion;
 Thermal Diffusion;
 Turbulence Effects;
 Turbulent Diffusion;
 Fluid Mechanics and Heat Transfer