  The quasi-accumulation solutions of acoustic wave in a moving fluid are
obtained by using the Lagrange parameter variation method to solve the
differential equation that describes the interaction between the acoustic waves
and the flow. The results show that the nonlinear interaction causes the
period-doubling followed by the odd multiple half-period bifurcation and all
order subharmonics are generated subsequently, of which the amplitudes depend
not only on the acoustic Mach number but also on the Mach number of the flow.
The latter result indicates that the acoustic wave has been amplified by the
momentum of the flow. The result also shows that the amplitudes of the
generated subharmonics are proportional to the (the order number of the
approximation) powers of the acoustic Reynolds number (and hence the Reynolds
number of the flow). If the kinetic energy gained from momentum amplification
is greater than the energy loss due to the acoustic attenuation, which means,
the Reynolds number exceeds its critical value, a chain-reaction of the
period-doubling followed by the odd multiple half-period bifurcation can
continue to proceed so that the number of degrees of freedom in the flow
increases infinitely resulting a chaos.
