Propagation of N-Waves Caused by Temperature Variation of a Wall

The weakly nonlinear propagation of waves, which are generated in a half-space filled with a perfect gas through the heat addition, is studied from the standpoint of nonlinear acoustics. The wall temperature varies sinusoidally only during a half cycle. The result of analysis shows that the weak flow is induced at the outer edge of the thin boundary layer adjacent to the wall and thereby an acoustic wave is radiated to the outer wave region. The wave behavior in a far field can exactly be settled by solving Burgers equation. At a high acoustic Reynolds number, with the aid of the so-called equal-areas rule, it is shown that the entire wave profile develops into an N-wave with a long tail. In the farther far field, the tail diminishes and so the wave is reduced to an ordinary N-wave.