A Spectral Theory of Nonlinear Barotropic Motion above Irregular Topography

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Abstract
If a field of randomly distributed barotropic eddies interacts with underlying topographic features in a rotating reference frame, the flow is observed to develop, after a time the order of an eddy turnaround time τeddy = L/U a component of steady flow which is locked to the topography in the sense of anti-cyclonic circulation around bills. Thereafter, spectral energy transfer is inhibited and the forms both of the energy spectrum of the motion and of the spectrum of vorlicity-topography correlation are dependent on the topographic variance spectrum. If the topographic variation is weak, in that τtopo ≫ τeddy where τtopo = π/fδ is a topographic wave period with f twice the uniform rotation rate and δ a characteristic height of topography relative to the depth of fluid, the flow dynamics approaches that of two-dimensional turbulence. If topographic variation is strong. in that τtopo ≪ τeddy, energy readily scatters into smaller scales. decreasing τeddy until a balance is obtained between topograph... Abstract If a field of randomly distributed barotropic eddies interacts with underlying topographic features in a rotating reference frame, the flow is observed to develop, after a time the order of an eddy turnaround time τeddy = L/U a component of steady flow which is locked to the topography in the sense of anti-cyclonic circulation around bills. Thereafter, spectral energy transfer is inhibited and the forms both of the energy spectrum of the motion and of the spectrum of vorlicity-topography correlation are dependent on the topographic variance spectrum. If the topographic variation is weak, in that τtopo ≫ τeddy where τtopo = π/fδ is a topographic wave period with f twice the uniform rotation rate and δ a characteristic height of topography relative to the depth of fluid, the flow dynamics approaches that of two-dimensional turbulence. If topographic variation is strong. in that τtopo ≪ τeddy, energy readily scatters into smaller scales. decreasing τeddy until a balance is obtained between topograph...

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