Yuval Ne’eman Distinguished Lectures in Geophysics, Atmosphere and Space Sciences Endowed by Raymond and Beverly Sackler
Prof. Rick Salmon, Scripps Institution of Oceanography, University of California San Diego, La Jolla, California, USA
Entropy Budget and Coherent Structures Associated With A Spectral Closure Model of Turbulence
It is possible to `derive' the eddy-damped quasi-normal Markovian model (EDQNM) by a method that replaces the exact equation for the Fourier phases with a solvable stochastic model. A quantity that appears in the probability distribution of the phases may be interpreted as the rate at which entropy is transferred from the Fourier phases to the Fourier amplitudes. In this interpretation, the decrease in phase entropy is associated with the formation of structures in the flow, and the increase in amplitude entropy is associated with the spreading of the energy spectrum in wavenumber space. We use Monte Carlo methods to sample the probability distribution of the phases predicted by the theory. This distribution contains a single adjustable parameter that corresponds to the triad correlation time in EDQNM. Flow structures form as the triad correlation time becomes very large, but the structures take the form of vorticity quadrupoles that do not resemble the monopoles and dipoles that are actually observed.