The mathematical fluid dynamics of atmospheric and oceanic flows

Robin S. Johnson (U Newcastle upon Tyne)

May 17. 2023, 15:15 — 16:00

In this talk, we aim to show that the dynamics of both the atmosphere and the oceans can be described by starting with the general equations of fluid dynamics and invoking only the  thin-shell approximation. The equations are written in rotating, spherical coordinates, with a suitable adjustment to accommodate the Earth’s geoid. The thin-shell approximation ensures that all the attributes of the flow are retained in the asymptotic solution, including the essential elements that accurately represent the spherical geometry. The overall approach is predicated on the philosophy that permeates mathematical fluid dynamics: never approximate unless necessary. In consequence, the way in which the reduced (asymptotic) equations arise is clear, as are the errors involved; indeed, higher-order correction terms are accessible.


    The emphasis here will be on the atmosphere, because this is the more technically challenging application. This involves the perturbation of a (stationary) background state of the atmosphere; we show, in outline, how the perturbation includes all the dynamics and the thermodynamics of the motion. We will note that the familiar results, both steady and unsteady, associated with theoretical models of the atmosphere, are recovered from this one formulation (but within a more general framework), as well as a number of additional, novel  applications.


    We end by briefly outlining how the corresponding formulation can be applied to oceanic flows.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
The Dynamics of Planetary-scale Fluid Flows (Thematic Programme)
Adrian Constantin (U of Vienna)
David Dritschel (U of St Andrews)
Nathan Paldor (HU of Jerusalem)