TOWARDS ENHANCING AND DELAYING DISTURBANCES IN FREE SHEAR FLOWS

The family of shear flows comprising the jet, wake, and the mixing lay er are subjected to perturbations in an inviscid incompressible fluid. By modelling the basic mean hows as parallel with piecewise linear va riations for the velocities, complete and general solutions to the lin earized equations of motion can be obtained in closed form as function s of all space variables and time when posed as an initial-value probl em. The results show that there is a continuous spectrum as well as th e discrete spectrum that is more familiar in stability theory and ther efore there can be both algebraic and exponential growth of disturbanc es in time. These bases make it feasible to consider control of such f lows. To this end, the possibility of enhancing the disturbances in th e mixing layer and delaying the onset in the jet and wake is investiga ted. It is found that growth of perturbations can be delayed to a cons iderable degree for the jet and the wake but, by comparison, cannot be enhanced in the mixing layer. By using moving coordinates, a method f or demonstrating the predominant early and long time behaviour of dist urbances in these flows is given for continuous velocity profiles. It is shown that the early time transients are always algebraic whereas t he asymptotic limit is that of an exponential normal mode. Numerical t reatment of the new governing equations confirm the conclusions reache d by use of the piecewise linear basic models. Although not pursued he re, feedback mechanisms designed for control of the flow could be devi sed using the results of this work.