The Discretised Population Model of Turbulence

Abstract Turbulence influences fluid-dynamic phenomena in two ways, namely: 1. By increasing the fluxes of momentum, energy and material resulting from time-average gradients of velocity, temperature and mass fraction; and 2. By increasing or diminishing the sources per unit volume of the same entities, as a consequence of rapid fluctuations of their values. Both are of equal importance in practice; but the pioneers of present-day turbulence modelling (Boussinesq, Prandtl and Kolmogorov) paid attention only to the former; so their less-innovative followers have done likewise. The present paper seeks to redress the balance, by describing an entirely different type of turbulence model; this concentrates on sources rather than fluxes; and therefore can simulate practically-important phenomena about which all popular turbulence models must necessarily remain silent. It is here called the Discretised Population Model , its earlier-used name, viz. Multi-Fluid Model, having perhaps confused rather than enlightened. It can handle sources of all kinds, e.g. body-force, radiative, biochemical; but it is exemplified here by reference to sources associated with chemical reaction.