Thanks to conventional time-scale or space-scale decomposition (e.g., Fourier transform, coarse graining, multiscale window transform), the cross-scale kinetic energy flux of oceanic flows is attracting more and more attentions and has already been a hot topic in physical oceanography. This conventional framework struggles to quantify the cross-scale energy flux resulting from the interaction between vortical and wavy motions, largely due to the lack of a proper approach for decomposing the full flow and its governing equation into vortical and wavy components. Recently, we proposed a dynamical vortical-wavy decomposition and it is straightforwardly anticipated to dedicate a follow-up study to incorporate the scale separation into the dynamical decomposition. This study exactly aims at combining the newly dynamical and conventional scale decompositions; as such, we are allowed to derive the crossscale kinetic energy flux equations for vortical and wavy motions respectively. The preliminary application of the derived energy equations to a tide-resolving and submesoscale-admitting oceanic simulation has been conducted.
 

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