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Weekly Seminar: Fall 2008

Date: November 7

Time: 11:00 AM
Location: Maryland Hall 110
Speaker: Dr. Jai Sukhatme

Title:"Vortical and Wave Modes in Rotating Stratified Turbulence"

Abstract

Utilizing an eigenfunction decomposition, we study the growth and spectra of energy in the vertical (geostrophic) and wave (ageostrophic) modes of a three-dimensional (3D) rotating stratified fluid as a function of the Burger number, depending on the Coriolis parameter and the Brunt-Vaisala frequency. Working in regimes characterized by moderate Burger numbers, our results indicate profound change in the character of vortical and wave mode interactions with respect to Bu = 1. As with the reference state of Bu = 1, for Bu < 1 the wave mode energy saturates quite quickly and the ensuing forward cascade continues to act as an efficient means of dissipating ageostrophic energy. Further, these saturated spectra steepen as Bu decreases: we see a shift from k−1 to k−5/3 scaling for kf < k < kd (where kf and kd are the forcing and dissipation scales, respectively). On the other hand, when Bu > 1 the wave mode energy never saturates and comes to dominate the total energy in the system. In fact, in a sense the wave modes behave in an asymmetric manner about Bu = 1. With regard to the vortical modes, for Bu?1, the signatures of 3D quasigeostrophy are clearly evident. Specifically, we see a k−3 scaling for kf < k < kd and, in accord with an inverse transfer of energy, the vortical mode energy never saturates but rather increases for all k < kf. In contrast, for Bu > 1 and increasing, the vortical modes contain a progressively smaller fraction of the total energy indicating that the 3D quasigeostrophic subsystem, though always present, plays an energetically smaller role in the overall dynamics.