Mathematical Description of Turbulent Flows

by Angelos N. Findikakis, (A.M.ASCE), Sr. Engr.; Hydr./Hydrology Grp., Bechtel Civ. and Minerals Inc., P.O. Box 3965, San Francisco, Calif. 94119,
Robert L. Street, (M.ASCE), Prof.; Dept. of Civ. Engrg., Stanford Univ., Stanford, Calif. 94305,

Serial Information: Journal of the Hydraulics Division, 1982, Vol. 108, Issue 8, Pg. 887-903

Document Type: Journal Paper


The mathematical description of uniform density and thermally stratified flows in terms of space averages is reviewed. The governing equations are presented and the use of alternative space filters is discussed. Different models for Sub-Grid-Scale (SGS) turbulent transport are examined. A simple algebraic model for the SGS Reynolds stresses and turbulent heat flumes in thermally stratified flows is presented. The model is cast in eddy viscosity - eddy diffusivity form. Its derivation is based on making appropriate closure approximations in the differential equations for the Reynolds stresses and the turbulent heat fluxes and introducing simplifying assumptions to reduce these equations to a system of algebraic equations. The solution of this system yields eddy coefficients which are functions of a local SGS turbulence length scale and the local structure of the velocity and the temperature fields. The variation of these coefficients with a local Richardson number is examined. Potential numerical problems which can be caused by improper formulation of the model are discussed.

Subject Headings: Turbulent flow | Thermal analysis | Eddy (fluid dynamics) | Mathematical models | Mathematics | Stratified flow | Reynolds stress | Density currents

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