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Exploiting self-organized criticality in stronglystratified turbulence

Chini, Gregory P. ; Michel, Guillaume ; Julien, Keith ; Rocha, Cesar ; Caulfield, C. P.

Journal of fluid mechanics, 2021-12, Vol.933 [Periódico revisado por pares]

Cambridge University Press (CUP)

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  • Título:
    Exploiting self-organized criticality in stronglystratified turbulence
  • Autor: Chini, Gregory P. ; Michel, Guillaume ; Julien, Keith ; Rocha, Cesar ; Caulfield, C. P.
  • Assuntos: Fluid mechanics ; Mechanics ; Physics
  • É parte de: Journal of fluid mechanics, 2021-12, Vol.933
  • Descrição: A multiscale reduced description of turbulent free shear flows in the presence of strongstabilizing density stratification is derived via asymptotic analysis of the Boussinesqequations in the simultaneous limits of small Froude and large Reynolds numbers. Theanalysis explicitly recognizes the occurrence of dynamics on disparate spatiotemporalscales, yielding simplified partial differential equations governing the coupled evolution ofslow large-scale hydrostatic flows and fast small-scale isotropic instabilities and internalwaves. The dynamics captured by the coupled reduced equations is illustrated in thecontext of two-dimensional strongly stratified Kolmogorov flow. A noteworthy featureof the reduced model is that the fluctuations are constrained to satisfy quasilinear (QL)dynamics about the comparably slowly varying large-scale fields. Crucially, this QLreduction is not invoked as an ad hoc closure approximation, but rather is derived in aphysically relevant and mathematically consistent distinguished limit. Further analysis ofthe resulting slow–fast QL system shows how the amplitude of the fast stratified-shearinstabilities is slaved to the slowly evolving mean fields to ensure the marginal stabilityof the latter. Physically, this marginal stability condition appears to be compatiblewith recent evidence of self-organized criticality in both observations and simulationsof stratified turbulence. Algorithmically, the slaving of the fluctuation fields enablesnumerical simulations to be time-evolved strictly on the slow time scale of the hydrostaticflow. The reduced equations thus provide a solid mathematical foundation for futurestudies of three-dimensional strongly stratified turbulence in extreme parameter regimesof geophysical relevance and suggest avenues for new sub-grid-scale parametrizations.
  • Editor: Cambridge University Press (CUP)
  • Idioma: Inglês
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  • Realização: ABCD-USP USP   Logos de Redes Sociais: Freepik

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