25.1 INTRODUCTION

When a fluid, which will be called a contaminant fluid, is released into another miscible host fluid, one would like to describe the concentration ?( x, t), in units of mass per unit volume at the position located by vector x at time t, of contaminant fluid as it evolves in time and space. The release may be sudden, such as a large rupture in a storage vessel resulting in a contaminant cloud, or continuous, such as a slow leak or smokestack emission providing a contaminant plume, jet, or wake. The fluids may be liquids or vapors, and differences in density between the two fluids may influence the flow structure. Chemical reactions may take place, which both affect density differences and generate new contaminants. Mixing between the host and contaminant fluids that results in a change of concentration values can only take place through the action of molecular diffusivity, ?. Although this presentation is restricted to miscible fluids, small solid particles, for example in smoke or small aerosols, can often be treated in the same framework with the effects of molecular diffusivity replaced by the effects of Brownian motion.

Almost all fluid motion is in a turbulent state. That is, all variables such as velocity, pressure, and contaminant concentration are random variables...