Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 345 / 2 / c / ii

If $h_0{k}_T>\tan \theta$, each period contains two critical points satisfying $|h_x|=\tan \theta$, with supercritical intervals around the steepest parts. Internal-wave ray tracing sends neighbouring reflected rays towards caustics attached to those critical points; rays can reverse horizontal direction in the supercritical intervals and intersect rays reflected elsewhere on the sinusoid. At equality the inviscid reflected wavelength collapses locally. The physical pattern is therefore a set of intense finite-width beams and mixing regions once viscosity, scalar diffusion, and wave breaking regularize the ray caustics.