Asymptotic solution to linearized Euler system for homentropic fluids

We present an asymptotic method for solving the linearized Euler equations for homentropic (entropy-constant) fluids within the geometrical acoustics limit, without resorting to any decomposition of the perturbed field a priori. The asymptotic solution obtained therefrom provides a preliminary answer to the long-standing question of whether disturbances that propagate at approximately the speed of sound relative to the unperturbed flow are purely irrotational. The answer is no. Likewise, convected disturbances with nearly solenoidal velocity fields have been shown to be capable of transporting pressure perturbations. Accordingly, the results suggest that performing the flow decomposition under an a priori uniqueness condition before the complete solution is known may yield misleading consequences.