Do large structures control their own growth in a mixing layer? An assessment

Abstract

This study makes a specific comparison between two different two-dimensional free shear layers: the T-layer which develops in time from an initial tangential velocity discontinuity separating the two half-spaces; and the S-layer which develops downstream of the origin where two uniform streams of unequal velocity are brought into tangential contact. The method of comparison is to assume that the vorticity of the S-layer is given parabolically by a Galilean mapping of that of the T-layer; to satisfy the appropriate boundary conditions in the S-layer and to compute the velocity induced at any point in the S-layer by its vorticity field; and to compare this velocity to that which can be derived from the velocity of the T-layer at corresponding points by a Galilean transformation of the velocity itself. The purpose of this calculation is to assess approximately how far the flow in the S-layer is from parabolic and, in particular, to what extent the perturbations induced upstream by large concentrations of vorticity found downstream are instrumental in hastening or retarding the subharmonic instability that leads to the formation of these large structures. The calculations suggest that this elliptic influence, or the feedback, in a mixing layer is relatively small, at least for small velocity ratios.