Weakly nonlinear models for turbulent free shear flows
Abstract
A weakly nonlinear theory is developed to provide closure models for turbulent free shear flows with a minimum of empiricism. The theory uses an instability wave description of the dominant largescale structures in these flows. The local characteristics of these structures are described using linear inviscid theory. The amplitudes of the largescale turbulent fluctuations are determined from an energy integral analysis. As an exploratory evaluation of the present weakly nonlinear theory, three models are developed to study the structural dynamics of the turbulent motions of different scales in free mixing layers. Model 1 considers the turbulent fluctuations of both large and small scales and contains two model constants. Model 2 neglects the effects of small scales on the development of mean flow and contains only one model constant. The first two models describe an ensemble of many realizations of the largescale structures. Model 3 simulates the unsteady aerodynamics of the mixing layers associated with a single realization of the passage of a train of largescale structures. Model 3 contains no model constraints. In all the models, predictions are made for the axial development and the distributions of the mean flow of the turbulent free mixing layer. These include the shear layer growth rates, the mean velocity profiles and the Reynolds stresses. In the last model, predictions of the time dependent behavior of the layer at the large scale are made. The predictions show good agreement with experiments. It is hoped that this weakly nonlinear theory that originates from observed physical phenomena will provide efficient tools for the modeling of other turbulent free shear flows.
 Publication:

Ph.D. Thesis
 Pub Date:
 January 1990
 Bibcode:
 1990PhDT........42L
 Keywords:

 Inviscid Flow;
 Mixing Layers (Fluids);
 Nonlinearity;
 Shear Flow;
 Shear Layers;
 Turbulent Flow;
 Turbulent Mixing;
 Unsteady Aerodynamics;
 Mathematical Models;
 Mixing;
 Physical Factors;
 Time Dependence;
 Velocity Distribution;
 Fluid Mechanics and Heat Transfer