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SUMMARY:Explicit and exact solutions concerning the Atlantic Circumpolar C
 urrent with variable density in spherical coordinates - Calin-Iulian Marti
 n (Universität Wien)
DTSTART:20220927T130000Z
DTEND:20220927T133000Z
UID:TALK178385@talks.cam.ac.uk
DESCRIPTION:We use spherical coordinates to devise a new exact solution to
  the governing equations of geophysical fluid dynamics for an inviscid and
  incompressible fluid with a general density distribution and subjected to
  forcing terms. The latter are of paramount importance for the modeling of
  realistic flows\, that is\, flows that are observed in some averaged sens
 e in the ocean. Owing to the employment of spherical coordinates we do not
  need to resort to approximations (e.g.\, of f- and &beta\;-plane type) th
 at simplify the geometry in the governing equations. Our explicit solution
  represents a steady purely azimuthal stratified flow with a free surface 
 that - thanks to the inclusion of forcing terms and the consideration of t
 he Earth&#39\;s geometry via spherical coordinates - makes it suitable for
  describing the Antarctic Circumpolar Current and enables an in-depth anal
 ysis of the structure of this flow. In line with the latter aspect\, we em
 ploy functional analytical techniques to prove that the free surface disto
 rtion is defined in a unique and implicit way by means of the pressure app
 lied at the free surface. We conclude our discussion by setting out relati
 ons between the monotonicity of the surface pressure and the monotonicity 
 of the surface distortion that concur with the physical expectations.
LOCATION:Seminar Room 1\, Newton Institute
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