On the use of the thin-shell approximation for modelling atmospheric flows

Robin S. Johnson (U Newcastle upon Tyne)

Jan 20. 2020, 09:30 — 10:30

The general equations for a viscous, compressible gas, written in rotating, spherical coordinates, with variable viscosity and general heat-source terms, are examined in the thin-shell approximation. Without any additional simplifying assumptions, an asymptotic solution appropriate to our atmosphere is constructed; this automatically generates the perturbation of a background state. The background state describes a stationary atmosphere, whereas the perturbation of this contains all the familiar dynamics and thermodynamics; the asymptotic structure has all the hallmarks of a uniformly valid solution. The perturbation equations take the form, in the troposphere, which corresponds to that typical for the description of Ekman and geostrophic flows (in spherical coordinates with variable viscosity), but with a forcing term that depends – in a far from obvious way – on the perturbation temperature field. Furthermore, this connection to the temperature field enables the first law of thermodynamics to be used to identify the heat sources driving the motion. The classical Ekman and geostrophic flows are recovered (but with the bonus that their validity can be precisely described) and, as new examples, the Hadley-Ferrel-polar cell structure is obtained, as well as the Walker circulation. In addition, we mention that higher-order terms can readily be constructed and that essentially the same system of equations holds in all regions of the atmosphere.

Further Information
Venue:
ESI Boltzmann Lecture Hall
Recordings:
Recording
Associated Event:
Mathematical Aspects of Geophysical Flows (Workshop)
Organizer(s):
Adrian Constantin (U of Vienna)
George Haller (ETH Zurich)