PROPAGATION OF STRONGLY NONLINEAR PLANE-WAVES

The nonlinear propagation of plane waves at high acoustic Reynolds number is studied without the restriction of low amplitude, namely, the weak nonlinearity. The wave is emitted from an infinite plate executing harmonic oscillations into a perfect gas. The method of analysis is based on the simple wave theory up to the shock formation time, and beyond the time on the numerical calculation by means of the upwind finite difference scheme (and partly the weakly nonlinear theory is used jointly with it). The initial sinusoidlike wave profile is progressively distorted as the wave propagates and this leads to the formation of shocks, as well as in the propagation of the weakly nonlinear wave. Then it evolves into a sawtoothlike wave as a whole. The strongly nonlinear wave, however, possesses the following outstanding distinctive features, as contrasted with its counterpart in the weakly nonlinear regime: (i) shock waves that form in a near field propagate with supersonic speed in a quasi-steady state; (ii) the waveform does not have any symmetry between the rarefactive phase and the compressive phase in a wave cycle; (iii) acoustic streaming occurs in one direction after shock formation; and (iv) the leading shock and the following shock are merged into one shock.