The decay of weak, homogeneous turbulence in the presence of a vertical body force and concentration gradient with a first-order reaction

Abstract

The effects of buoyancy, produced by a uniform vertical concentration gradient and body force, on a homogeneous turbulent field accompanied by a first-order chemical reaction, are analysed by considering a simplified model. A system of two-point correlation equations, which contains mean concentration gradient and body force terms, is constructed from the Navier-Stokes, convective diffusion and continuity equations. By well-known methods, these equations are converted into equations for the spectrum functions in the wave-number space and solutions for different spectral tensors are obtained by neglecting the contributions of the triple correlation terms. For carrying out the 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 buoyancy forces do alter the rate of decay. The buoyancy forces can either extract energy from the turbulent field or feed energy into it, depending upon the direction of the body force and the concentration gradient. Spectra are displayed graphically for several values of the reaction rate parameter for stabilizing, as well as destabilizing, buoyancy forces.