A PROBLEM IN THE THEORY OF MIXING LAYERS

The classical problem of the free steady mixing layer which is formed as the result of the interaction between two parallel homogeneous flow s which move with different velocities and come into contact in a cert ain section is considered. Subject to the additional condition that th e first derivative of the solution in a class of self-similar function s is positive, a boundary-value problem is studied, for values of the self-similarity index m > 0, which describes the mixing of two viscous streams of the same fluid for m = 1 [1] and for m = 2 [2]. The method of investigation used [3-5] enables the third-order non-linear equati on to be reduced to a first-order equation and enables the correspondi ng solutions phi(zeta) to be constructed in a parametric form as a fun ction of the values of m. A knowledge of the behaviour of the velocity profile of the main stream can be used to investigate the how stabili ty. The results obtained form the basis of the subsequent construction of the solution of Lock's problem [6] and the investigation of the un iqueness of the solutions obtained. (C) 1997 Elsevier Science Ltd.