BURGERS-EQUATION AND THE EVOLUTION OF NONLINEAR 2ND SOUND

A systematic, experimental and numerical search for subharmonic genera tion and/or amplification was conducted at intermediate times and mode rate Reynolds numbers in nonlinear second sound near the superfluid tr ansition. We found that the nonlinear acoustic waves are dynamically m onotonic in the sense that only energy cascades to smaller and smaller scales (until the dissipation scale) exist. There is no indication of a decay of monochromatic waves to waves of lower wave numbers. This p recludes the existence of a decay instability in Burgers' equation as has been discussed in the literature. We thus extend the theoretical p roof of Sinai concerning the absence of subharmonics in the solutions of Burger's equation to intermediate times.