A Lagrangian theory of geostrophic adjustment for zonally-invariant flows on a rotating spherical earth

Nathan Paldor*, David Gerard Dritschel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
2 Downloads (Pure)

Abstract

We examine the late-time evolution of an inviscid zonally symmetric shallow-water flow on the surface of a rotating spherical earth. An arbitrary initial condition radiates inertia–gravity waves that disperse across the spherical surface. The simpler problem of a uniformly rotating (f-plane) shallow-water flow on the plane radiates these waves to infinity, leaving behind a nontrivial steady flow in geostrophic balance (in which the Coriolis acceleration balances the horizontal hydrostatic pressure gradient). This is called “geostrophic adjustment.” On a sphere, the waves cannot propagate to infinity, and the flow can never become steady due to energy conservation (at least in the absence of shocks). Nonetheless, when energy is conserved a form of adjustment still takes place, in a time-averaged sense, and this flow satisfies an extended form of geostrophic balance dependent only on the conserved mass and angular momentum distributions of fluid particles, just as in the planar case. This study employs a conservative numerical scheme based on a Lagrangian form of the rotating shallow-water equations to substantiate the applicability of these general considerations on an idealized aqua-planet for an initial “dam” along the equator in a motionless ocean.
Original languageEnglish
Article number066602
Number of pages13
JournalPhysics of Fluids
Volume33
Issue number6
Early online date3 Jun 2021
DOIs
Publication statusPublished - 3 Jun 2021

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