Energy and enstrophy cascades in the geostrophic vortex with slowly varying inertia–gravity wave spirals

Abstract

Although geostrophically balanced mesoscale vortices and unbalanced small-scale turbulence have been well studied, the link between them is not entirely clear, especially in the vertical dimension. The inertia–gravity wave (IGW) spiral plays an important role in the energy and enstrophy cascades between the geostrophic vortex and the small-scale turbulence. Since the vertical velocity cannot be measured in practice, the slowly varying IGW spiral formula in a vortex is used to distinguish the direction of vertical velocity. The vertical deformation of the vortex with IGW spirals results in a vertical semi-circulating cycle of the energy cascades: the energy cascades forward from the geostrophic vortex scale to small scales in the IGW spiral at one depth, flows along the IGW spiral, and then inversely cascades to the geostrophic vortex scale at another depth. Some small-scale energy at one depth eventually reaches large scales at another depth, which can prevent some energy from falling into small-scale dissipation, allowing the geostrophic vortex to continue for months in the ocean. A vertical full-circulating cycle is formed by connecting every IGW spiral in different geostrophic vortices and jets, similar to the energy exchange in the capillaries of the human body. The vertical closed zero-flux line of enstrophy cascades caused by the IGW spiral in a geostrophic vortex isolates the enstrophy at different scales to reduce the dissipation. Due to the IGW spiral, the energy and enstrophy spectra in the geostrophic vortex are −1 and 1 at small scales, respectively.