Numerical study of strongly nonlinear acoustic waves, shock waves, and streaming caused by a harmonically pulsating sphere

Abstract

The nonlinear propagation of spherical waves emitted from a sphere executing harmonic pulsations in an unbounded ideal gas is numerically studied without the restriction of small amplitude, namely, the weak nonlinearity. The energy dissipation due to viscosity and thermal conductivity is supposed to be negligible everywhere except for the discontinuous shock front. By the numerical analysis based on a high-resolution upwind finite difference scheme, the wave phenomena caused by the strongly nonlinear effect are revealed, which form several striking contrasts to the known results for the weakly nonlinear spherical waves. The profile of the emitted wave is rapidly distorted by the strongly nonlinear effect and shock waves are formed near the sphere. The most remarkable phenomenon is the occurrence of acoustic streaming (mean mass outflow), which gradually reduces the density of the gas near the sphere as time proceeds. In the case that the sphere pulsates with a small amplitude compared with its mean radius, beyond the shock formation distance, the wave profile is immediately transformed into an asymmetrical sawtooth-like profile. In the case that the amplitude of pulsation is comparable with the mean radius, two shocks can be formed in each wave cycle and in due course these two shocks merge into one shock. © 1994 American Institute of Physics.