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Abstract:
Our understanding of the impact of centrifugal forces on geophysical flows has a clear history. Motivated by a desire to understand meteorological processes in Earth’s atmosphere—and perhaps to clarify or correct conclusions drawn by his colleague—Rayleigh (1917) laid out a fundamental description of vortex flow. Using the inviscid equations of motion in cylindrical coordinates, assuming azimuthal symmetry, neglecting Earth’s rotation, and assuming barotropic flow, Rayleigh (1917) demonstrated that the “circulation” (or angular momentum per unit mass) rv must be conserved following fluid parcels in the absence of viscosity and diabatic processes. The same principle holds in a rotating coordinate system so long as rv is replaced by the full, or absolute angular momentum, and the Coriolis parameter is held fixed. In this presentation, we review a recent discovery in our understanding of the impact of centrifugal forces on geophysical flows on the sphere. Deriving a vector representation of the conservation of absolute angular momentum, examining the expression in the limit of small meridional arc length, and capitalizing on Ertel’s derivation of potential vorticity, we demonstrate the validity of a simple conservation principle that has important consequences for the behavior of fluid parcels. Several of these consequences are discussed.
