NONLINEAR CROSSTRANSFORMATION OF AMPLITUDE-FREQUENCY MODULATION OF QUASI-MONOCHROMATIC ACOUSTIC-SIGNALS

This work is devoted to the investigation of evolution of intense quas i-monochromatic signals in the case of infinite acoustic Reynolds numb ers. The consideration is based on the zero viscocity limit solution o f the Burgers equation, which reduces the Hopf-Cole solution to a ''ma ximum'' principle. This limit solution permits an easy way to get the profile of the waves, position of shocks and their velocities at arbit rary times. The process of transformation of an initial quasi-monochro matic wave into a sawtooth wave is considered. It is shown that the no nlinearity leads to suppression of the initial amplitude modulation an d to the transformation of the initial frequency modulation into a sho ck amplitude modulation. The amplitude of the low frequency component generated by a quasi-monochromatic wave is found. It is shown that the interaction of this component with high frequency waves leads to phas e modulation, which increases with distance. The amplitudes of the new components of the spectrum are found. It is shown that when the value of phase modulation is small, the amplitudes of the satellites do not depend on the distance or the number of harmonics of the primary wave .