Propagating and evanescent internal waves in a deep ocean model

TL;DR

This study investigates how internal waves propagate and decay in a deep ocean model with variable stratification, combining experiments and simulations to validate a theory on wave reflection and evanescence.

Contribution

It provides experimental and computational validation of a theory describing internal wave reflection and decay in nonuniform stratification conditions.

Findings

Internal waves reflect at the turning depth where N(z) = ω

Energy flux decays exponentially below the turning depth

Viscous decay matches the theoretical predictions within a few percent

Abstract

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 nonuniform 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 turning depth. 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 viscous decay of the vertical velocity amplitude 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. 39, 729-737 (1998)].