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

Nonlinear interactions between high frequency internal waves interacting with larger vertical and horizontal scale waves having inertial frequency are investigated using ray tracing techniques, analytic approximations to kinetic equations, solutions for the moments of a diffusive approximation to the resonant kinetic equation and Taylor's identity for relative dispersion.  Tracing high frequency waves in one and two inertial wave backgrounds demonstrates that the infinitesimal amplitude and finite amplitude limits are phenomenologically distinct: the finite amplitude state is characterized by the coalescing of the two small scale members of the triad and a transition to a bound wave phenomena.  This coalescence marks the transition from the coupled oscillator paradigm to a particle (wave packet) in a potential well paradigm.  Tracing high frequency waves in stochastic inertial wave backgrounds does not reveal any such transition.  Rather, the ray tracing results are phenomenologically consistent with the particle in a (stochastic) well paradigm, independent of amplitude.

Tracing high frequency waves in a stochastic background of inertial oscillations also provides estimates of the temporal evolution for the ensemble mean and variance of vertical wavenumber of a test wave distribution.  These estimates are compared to the evolution of the first and second moments of a diffusive approximation to the resonant kinetic equation.  The diffusive closure manages to describe the evolution of the first two moments at energy levels an order of magnitude smaller than background oceanic values and predicts {\em no} transport of action to smaller scales.  At realistic energy levels the growth of the second moment is inhibited relative to the first, implying a finite downscale action transport.  We demonstrate using Taylor's identity for relative dispersion that the transition occurs when the interaction timescale becomes smaller than the decorrelation time scale of the interaction process.  We argue that the action transport in this parameter regime is the averaged product of particle size (action density) and velocity (time rate of change of the first moment).  This concept is the genesis for the heuristically motivated Finescale Parameterization which summarizes current knowledge relating turbulent dissipation to finescale internal wave spectra.

About the presenter
Kurt Polzin

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Monday, May 6, 2013 - 3:30pm