Group velocity and the linear response of stratified fluids to internal heat or mass sources

Abstract

This paper uses group velocity arguements to recreate the gravity wave field a time T after a heat pulse. The T-1 decay of the displacement is shown to be a geometrical consequence of dispersion in two dimensions. The growing response to a maintained source can be understood as the result of energy being pumped into the gravity wave modes, whose group velocity is near zero, faster than it can spread in physical space due to dispersion. A steady response is shown to be possible only if the heat source distribution has no projection onto the modes of zero group velocity. If the fluid is bounded both above and below, the vertical wavenumbers of gravity wave modes are quantized. Unless the layer depth is resonantly tuned, there are no normal modes of zero group velocity and a steady response develops. The same arguments allow the work of Smith and Lin to be generalized to more complicated situations. -from Author