Internal waves in nonuniform stratifications

Internal waves are propagating disturbances in a stably stratified fluid. Linear internal wave propagation in a stratification with constant Brunt-Vaisala frequency $N$ is well-understood, both theoretically and experimentally. When $N$ varies with the vertical coordinate $z$, however, propagating internal waves bend with respect to the vertical, and can get scattered in a non-trivial manner, depending on the exact profile $N(z)$. Here, we discuss two scenarios, (i) a finite-thickness $N_{2}-$layer sitting atop a semi-infinite $N_{1}-$layer, and (ii) a finite-thickness $N_{2}-$layer sandwiched between two semi-infinite $N_{1}-$layers. The former is shown to support wave beam ducting even in the absence of evanescent layers, and is used to explain the observations of a vanishing wave beam near the upper ocean at the Keana ridge, Hawaii. The latter scenario, in the inviscid limit, is shown to be equivalent to the classical multiple beam light interferometer, and hence results in selective wave transmission based on spatial wavelengths. Results from laboratory experiments and linear viscous theory are presented for both the cases.