Exact analytic self-similar solution of a wave attractor field

Abstract

Stratified and rotating fluids support obliquely propagating internal waves. A symmetry-breaking shape of the fluid domain focuses them on a wave attractor. For a trapezoidal basin, it is here shown how to determine the internal wave field analytically. This requires solving the wave equation on a closed domain–an ill-posed Cauchy problem–whose solution exhibits a remarkable self-similar spatial structure. These results are relevant for mixing and mean flow generation in oceans, atmospheres and stars whose symmetry is generally broken and where internal waves are tidally forced.