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On Energy Cascades in General Flows
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  • Quentin Jamet,
  • Adekunle Ajayi,
  • Julien Lesommer,
  • Thierry Penduff,
  • Andrew McC. Hogg,
  • William K. Dewar
Quentin Jamet
Laboratoire de Glaciologie et Geophysique de l'Environnement, CNRS
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Adekunle Ajayi
Universite Grenoble Alpes /CNRS/IGE
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Julien Lesommer
Centre National de la Recherche Scientifique

Corresponding Author:[email protected]

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Thierry Penduff
Laboratoire de Glaciologie et Geophysique de l'Environnement, CNRS
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Andrew McC. Hogg
Australian National University
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William K. Dewar
Florida State University
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An important characteristic of geophysically turbulent flows is the transfer of energy between scales. It is expected that balanced flows pass energy from smaller to larger scales as part of the well-known upscale cascade while submesoscale and smaller scale flows can transfer energy eventually to smaller, dissipative scales. Much effort has been put into quantifying these transfers, but a complicating factor in realistic settings is that the underlying flows are often strongly spatially heterogeneous and anisotropic. Furthermore, the flows may be embedded in irregularly shaped domains that can be multiply connected. As a result, straightforward approaches like computing Fourier spatial spectra of nonlinear terms suffer from a number of conceptual issues. In this paper, we endeavor to compute cross-scale energy transfers in general settings, allowing for arbitrary flow structure, anisotropy and inhomogeneity. We employ a Green's function approach to the kinetic energy equation to relate kinetic energy at a point to its Lagrangian history. A spatial filtering of the resulting equation naturally decomposes kinetic energy into length scale dependent contributions and describes how the transfer of energy between those scales takes place. The method is applied to a numerical simulation of vortex merger, resulting in the demonstration of the expected upscale energy cascade. Somewhat novel results are that the energy transfers are dominated by pressure work, rather than kinetic energy exchange, and dissipation is a noticeable influence on the larger scale energy budgets.