Internal-wave attractor

A periodic spatial internal-wave ray toward which neighbouring ray paths converge after reflection in a confined stratified basin. A fixed point of an internal-wave ray return map is attracting when its derivative has magnitude below one. Viscous attenuation of an internal-wave beam and internal-wave breaking regularize the ideal concentration of energy. A spatial ray construction does not remove turning-level limitations of the WKB approximation.

Map one boundary intersection of an internal-wave ray to the next intersection with the same boundary after a specified reflection itinerary. A periodic ray is a fixed point. Linear contraction, $|R^{\prime }|<1$, gives an internal-wave attractor; the reversed itinerary, when invertible, has reciprocal multiplier and is locally repelling.