Propagating and evanescent internal waves in a deep ocean model

Author :M. S. Paoletti, Harry L. Swinney
Publication :Journal of Fluid Mechanics
Volume :706
Pages :571-583
Year :2012
Note :DOI: 10.1017/jfm.2012.284, arXiv:1202.5290v2

We present experimental and computational studies of the propagation of internal
waves in a stratified fluid with an exponential density profile that models the deep
ocean. The buoyancy frequency profile N.z/ (proportional to the square root of
the density gradient) varies smoothly by more than an order of magnitude over
the fluid depth, as is common in the deep ocean. The non-uniform stratification is
characterized by a turning depth zc, where N.zc/ is equal to the wave frequency ! and
N.z < zc/ < !. Internal waves reflect from the turning depth and become evanescent
below the turning depth. The energy flux below the turning depth is shown to decay
exponentially with a decay constant given by kc, which is the horizontal wavenumber
at the turning depth. The viscous decay of the vertical velocity amplitude of the
incoming and reflected waves above the turning depth agree within a few per cent
with a previously untested theory for a fluid of arbitrary stratification (Kistovich and
Chashechkin, J. Appl. Mech. Tech. Phys., vol. 39, 1998, pp. 729’737).