Exact solutions for the fluid impulse for incompressible and compressible flows

In this paper, we consider the Kuz’min [Phys. Lett. A 96, 88 (1983)] and Oseledets [Russ. Math. Surv. 44, 210 (1989)] formulations for the fluid impulse density for the incompressible and compressible barotropic Euler equations. We give exact solutions for the fluid impulse density and discuss their physical significance. The compressible barotropic exact solution describes a density wave riding on a steady Burgers type vortex flow with the fluid impulse velocity component in the wave-propagation direction growing monotonically with time.In this paper, we consider the Kuz’min [Phys. Lett. A 96, 88 (1983)] and Oseledets [Russ. Math. Surv. 44, 210 (1989)] formulations for the fluid impulse density for the incompressible and compressible barotropic Euler equations. We give exact solutions for the fluid impulse density and discuss their physical significance. The compressible barotropic exact solution describes a density wave riding on a steady Burgers type vortex flow with the fluid impulse velocity component in the wave-propagation direction growing monotonically with time.