[GTP] Friendly Reminder - GTP Seminar TODAY!

[Liz Aikin]

GTP Seminar

Title:  AN OCEANIC ULTRA-VIOLET CATASTROPHE, WAVE-PARTICLE DUALITY AND A 
STRONGLY NONLINEAR CONCEPT OF GEOPHYSICAL TURBULENCE

Presenter: Kurt Polzin
Affiliation:  Woods Hole Oceanographic Institution

Today, Monday, May 6, 2013
Mesa Lab Main Seminar Room
Lecture at 3:30pm

Abstract:
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.