Turbulent wave attractors in large-aspect ratio domains.

Abstract

<div>Ocean abyss is an example of a system with continuous stratification subject to large-scale tidal forcing. Owing to specific dispersion relation of internal waves, the domains bounded by sloping boundaries may support wave patterns with wave rays converging to closed trajectories (geometric attractors) as result of iterative focusing reflections. Previously the behavior of kinetic energy in wave attractors has been investigated in domains with comparable scales of depth and horizontal length. As the geometric aspect ratio of the domain increases, the dynamic pattern of energy focusing may significantly evolve both in laminar and turbulent regimes. The present paper shows that the energy density in domains with large aspect ratio can significantly increase. In numerical simulations the input forcing has been introduced at global scale by prescribing small-amplitude deformations of the upper bound of the liquid domain. The evolution of internal wave motion in such system has been computed numerically for different values of the forcing amplitude. The behavior of the large-aspect-ratio system has been compared to the well-studied case of the system with depth-to-length ratio of order unity.  A number of most typical situations has been analyzed in terms of behavior of integral mechanical quantities such as total dissipation, mean kinetic energy and energy fluctuations in laminar and turbulent cases. The relative mean kinetic energy (normalized by the kinetic energy of the liquid domain undergoing rigid-body oscillations with the amplitude of the wavemaker), may increase by order of magnitude as compared to low-aspect-ratio system.<br>It was shown previously, that in the case of aspect ratio close to unity, the transition to wave turbulence regime is associated with a cascade of triadic wave-wave interactions. Now it is shown that for large aspect ratios the energy cascade in the system is due to generation of superharmonic waves corresponding to integer (including zero) multiples of the forcing frequency. As forcing amplitude increases beyond certain value, an abrupt change is observed in behavior of relative mean kinetic energy and spectra, accompanied with appearance of additional harmonic components corresponding to half-integer (including 1/2) and integer multiples of the forcing frequency.  </div><div> </div>