Propagating and evanescent internal waves in a deep ocean model

Details Propagating and evanescent internal waves in a deep ocean model Propagating and evanescent internal waves in a deep ocean model

2012-02-23

arxiv.org/abs/1202.5290v1

Physics

Fluid Dynamics

10 pages, 5 figures, 2 tables, submitted to the Journal of Fluid Mechanics

Scientific paper

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) smoothly varies by nearly an order of magnitude over the fluid depth, rather than being constant or piecewise-constant as in prior studies. In addition to being nonuniform, the stratification is characterized by a turning depth $z_c$, where $N(z_c)$ is equal to the wave frequency $\omega$ and $N(z < z_c) < \omega$. Internal waves reflect from the turning depth and become evanescent below. The energy flux below the turning depth is shown to decay exponentially with a decay constant given by $ k_c$, which is the horizontal wavenumber at the turning depth. The vertical velocity fields of the incoming and reflected waves above the turning depth agree within a few percent with a previously untested theory for a fluid of arbitrary stratification [Kistovich and Chashechkin, J. App. Mech. Tech. Phys. \textbf{39}, 729-737 (1998)].

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