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Fluids 2017, 2(3), 36; doi:10.3390/fluids2030036

An Oceanic Ultra-Violet Catastrophe, Wave-Particle Duality and a Strongly Nonlinear Concept for Geophysical Turbulence

1
Woods Hole Oceanographic Institution, Woods Hole, MA 02540, USA
2
Rensselaer Polytechnic Institute, Troy, NY 12180, USA
*
Author to whom correspondence should be addressed.
Academic Editor: Pavel S. Berloff
Received: 12 March 2017 / Revised: 14 June 2017 / Accepted: 16 June 2017 / Published: 29 June 2017
(This article belongs to the Collection Geophysical Fluid Dynamics)
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Abstract

There is no theoretical underpinning that successfully explains how turbulent mixing is fed by wave breaking associated with nonlinear wave-wave interactions in the background oceanic internal wavefield. We address this conundrum using one-dimensional ray tracing simulations to investigate interactions between high frequency internal waves and inertial oscillations in the extreme scale separated limit known as “Induced Diffusion”. Here, estimates of phase locking are used to define a resonant process (a resonant well) and a non-resonant process that results in stochastic jumps. The small amplitude limit consists of jumps that are small compared to the scale of the resonant well. The ray tracing simulations are used to estimate the first and second moments of a wave packet’s vertical wavenumber as it evolves from an initial condition. These moments are compared with predictions obtained from the diffusive approximation to a self-consistent kinetic equation derived in the ‘Direct Interaction Approximation’. Results indicate that the first and second moments of the two systems evolve in a nearly identical manner when the inertial field has amplitudes an order of magnitude smaller than oceanic values. At realistic (oceanic) amplitudes, though, the second moment estimated from the ray tracing simulations is inhibited. The transition is explained by the stochastic jumps obtaining the characteristic size of the resonant well. We interpret this transition as an adiabatic ‘saturation’ process which changes the nominal background wavefield from supporting no mixing to the point where that background wavefield defines the normalization for oceanic mixing models. View Full-Text
Keywords: wave-wave interactions; internal waves; mixing; Anderson localization wave-wave interactions; internal waves; mixing; Anderson localization
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Polzin, K.L.; Lvov, Y.V. An Oceanic Ultra-Violet Catastrophe, Wave-Particle Duality and a Strongly Nonlinear Concept for Geophysical Turbulence. Fluids 2017, 2, 36.

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