Transient dipolar sound wave in a viscous compressible fluid

The dipolar sound wave generated by a sudden impulse in an unbounded viscous compressible fluid is studied on the basis of the linearized Navier–Stokes equations. Due to viscosity the spherical wavefront is diffuse with a width which grows with the square root of time. The wavefront is followed by a spherical shell of static potential flow. The shell itself surrounds an expanding spherical region of viscous flow. At long times the energy in each of the three regions is of comparable magnitude, and decays with a t−3/2t−3/2 power law.