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https://hdl.handle.net/2115/7387

Quasisteady streaming with rarefaction effect induced by asymmetric sawtooth-like plane waves

英語

1996-09

American Institute of Physics

Physics of Fluids

8(9)

2537-2551

The nonlinear plane acoustic wave emitted from a harmonically oscillating plate into an ideal gas of semi-infinite extent develops into a sawtooth-like wave, as long as the energy dissipation is negligibly small everywhere except for discontinuous shock fronts. The present authors have recently studied the strongly nonlinear propagation process and, in particular, numerically shown that, contrary to the result of the conventional weakly nonlinear theory, streaming (mean mass flow) due to shocks occurs in the direction of wave propagation, and thereby the gas near the plate is rarefied as time proceeds [J. Acoust. Soc. Am. 94, 1632 (1993)]. In this paper, the analysis of strongly nonlinear problem is advanced by extending the numerical computation up to about 190 periods of oscillation of plate, which is about three times longer than the previous one. It is demonstrated that, in the course of time, a quasisteady state is established, where a low-density and high-entropy region formed near the plate continues to grow at almost constant rate and the quasisteady streaming endures outside the region. Furthermore, the weakly nonlinear problem is analytically examined by a perturbation method up to O(M3) [M( ≪1) is the acoustic Mach number]. The result shows that a sawtooth-like profile loses its symmetry in the second-order, and this causes weak streaming of O(M2). The decrease in density of the gas can be related to the accumulation of the third-order effects of production of entropy and generation of reflected wave at each shock front.

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Copyright © 1996 American Institute of Physics

1070-6631