Numerical Analysis of Two-dimensional Unsteady Turbulent Shear Flow by Discrete Vortex Model

Abstract

For the calculation of two-dimensional turbulent shear flows by the discrete vortex model, a numerical scheme by which motions of a system composed of many vortices can be calculated accurately is proposed. It is verified that the rolling-up process of the vortex sheet presented by Rosenhead is calculated accurately by this scheme. The present method is applied to the study of an unsteady turbulent shear flow which is represented by two hundred vortices with random vortex strengths and with initial random locations given by random numbers. As a result it is found that a coherent structure with a spiral form is realized in the turbulent flow, and the thickness of the turbulent shear layer increases linearly with time. It is shown that the calculated mean velocity, longitudinal and transversal turbulent intensities, and the Reynolds stress develop with time in the self-similar manner governed by the length scale of the turbulent shear layer thickness.