Vortical and Wave Modes in 3D Rotating Stratified Flows: Random Large Scale Forcing

Abstract

Utilizing an eigenfunction decomposition, we study the growth and spectra of energy in the vortical and wave modes of a 3D rotating stratified fluid as a function of $\epsilon =f/N$. Working in regimes characterized by moderate Burger numbers, i.e. $Bu=1/{\epsilon }^2<1$ or $Bu\ge 1$, 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 $\epsilon =1$, for $\epsilon <1$ 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 $\epsilon$ decreases: we see a shift from $k^{-1}$ to $k^{-5/3}$ scaling for $k_f<k<k_d$ (where $k_f$ and $k_d$ are the forcing and dissipation scales, respectively). On the other hand, when $\epsilon >1$ 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 $\epsilon =1$. With regard to the vortical modes, for $\epsilon \le 1$, the signatures of 3D quasigeostrophy are clearly evident. Specifically, we see a $k^{-3}$ scaling for $k_f<k<k_d$ and, in accord with an inverse transfer of energy, the vortical mode energy never saturates but rather increases for all $k<k_f$. In contrast, for $\epsilon >1$ and increasing, the vortical modes contain a progressively smaller fraction of the total energy indicating that the 3D quasigeostrophic subsystem plays an energetically smaller role in the overall dynamics.

18 pages, 6 figs. (abbreviated abstract)

References in corpus (4)

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• Discreteness and its effect on the water-wave turbulence
• Surface Quasigeostrophic Turbulence : The Study of an Active Scalar
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