Statistical properties of decaying geostrophic turbulence

High-resolution, high-Reynolds-number numerical solutions of fully three-dimensional, decaying, geostrophic turbulence are examined. The results include the demonstration of a substantial degree of similarity between geostrophic and two-dimensional turbulence: transfer of energy to larger scales; transfer of potential enstrophy to smaller scales; vanishing energy dissipation as the Reynolds number increases; the emergence and growth to dominance of isolated, coherent vortices; and a competition between the vortices and Rossby waves, with an associated horizontal anisotropy when the latter are dominant. Properties that are distinct to geostrophic turbulence include the following: approximate three-dimensional wavenumber isotropy, with significant departures on large scales due to boundedness of the domain and on smaller scales due to anisotropic spectrum transfer rates; insensitivity of solution properties to anisotropy or vertical inhomogeneity in the dissipation; persistence of vertical inhomogeneity; development of inhomogeneity due to solid vertical boundaries; and the processes of alignment, attachment, and vertical straining associated with the finite vertical extent of the coherent vortices.