Weakly decaying turbulence in an equivalent-barotropic fluid

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Abstract
Numerical solutions are analyzed for the evolution of turbulent flow in an equivalent-barotropic fluid (i.e., a shallow water layer in the limit of strong rotation) from random, narrow-band initial conditions with small viscosity. Particular attention is given to the regime of small deformation radius: the solutions are weakly dissipative of both energy and potential enstrophy; after a brief initial interval of broadening in wave number, the shapes of the energy and potential enstrophy spectra are nearly invariant in time but their centroids move toward larger scales, and coherent vortex structures spontaneously develop with a preferred shape of axisymmetric potential vorticity monopoles. An asymptotic model is derived for small deformation radius, and its behavior exhibits the essential features of the equivalent-barotropic model. Solutions are analyzed for increasing deformation radii, ranging from small to infinite (i.e., nondivergent, two-dimensional flow). In this sequence, both the dynamical evolution rates (e.g., dissipation) and the degree of non-Gaussianity (intermittency) increase substantially. In particular, the spatial sparseness of the coherent vortices increases with deformation radius.