Acoustic energy and momentum in a moving medium
By exploiting the mathematical analogy between the propagation of sound in a nonhomogeneous potential flow and the propagation of a scalar field in curved space-time, various wave "energy" and wave "momentum" conservation laws are established in a systematic manner. In particular, the acoustic energy conservation law due to Blokhintsev appears as the result of the conservation of a mixed covariant and contravariant energy-momentum tensor, while the exchange of relative energy between the wave and mean flow, first noted by Longuet-Higgins and Stewart in the context of ocean waves, appears as the covariant conservation of the doubly contravariant form of the same energy-momentum tensor.
Stone
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Department of Physics, University of Illinois, 1110 West Green Street, Urbana, Illinois 61801, USA.