EARLY-PERIOD DYNAMICS OF AN INCOMPRESSIBLE MIXING LAYER

The evolution of three-dimensional disturbances in an incompressible m ixing layer in an inviscid fluid is investigated as an initial-value p roblem. A Green's function approach is used to obtain a general space- time solution to the problem using a piecewise linear model for the ba sic flow, thereby making it possible to determine complete and closed- form analytical expressions for the variables with arbitrary input. St ructure, kinetic energy, vorticity, and the evolution of material part icles can be ascertained in detail. Moreover, these solutions represen t the full three-dimensional disturbances that can grow exponentially or algebraically in time. For large time, the behaviour of these distu rbances is dominated by the exponentially increasing discrete modes. F or the early time, the behaviour is controlled by the algebraic variat ion due to the continuous spectrum. Contrary to Squire's theorem for n ormal mode analysis, the early-time behaviour indicates growth at comp arable rates for all values of the wavenumbers and the initial growth of these disturbances is shown to rapidly increase. In particular, the disturbance kinetic energy can rise to a level approximately ten time s its initial value before the exponentially growing normal mode preva ils. As a result, the transient behaviour can trigger the roll-up of t he mixing layer and its development into the well-known pattern that h as been observed experimentally.