Density perturbations in transonic sluing laser beams

A linearized theory is presented for density perturbations induced in a sluing laser beam as a function of time after beam turn-on and cross-flow Mach number M. The net local density perturbation is expressed as the sum of an isobaric and isentropic perturbation. A closed-form solution is obtained for M = 1, where the isentropic perturbations peak, and uniform heat addition in a circular beam. The results are compared with a corresponding one-dimensional beam. Poor agreement is found at large time, where the isentropic density perturbation varies as t and t((1/2)) for the one-dimensional and two-dimensional cases, respectively. An order-of-magnitude estimate for the final steady-state density perturbation, at M = 1, and the time scale in which it is achieved are obtained by consideration of nonlinear effects.