Mathematics – Logic
Scientific paper
Dec 2010
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010agufm.p31a1522a&link_type=abstract
American Geophysical Union, Fall Meeting 2010, abstract #P31A-1522
Mathematics
Logic
[5704] Planetary Sciences: Fluid Planets / Atmospheres
Scientific paper
We derive analytical expressions for zonal flow velocity for fluid in both thin and thick shells in the theoretical limit of perfectly mixed and strictly conserved potential vorticity (PV), which results in an ideal PV "staircase." Fluid shell thickness and width of the PV steps are free parameters in our model. We set the constant value of PV on each step from the amount available in the planetary vorticity reservoir. Assuming symmetry about the equator and continuous velocity profiles, for both models we derive analytical expressions for the net angular momentum per unit mass, L, of the fluid. Setting the value of L then uniquely determines the integration constants and corresponding unique velocity profiles. Distinguishing characteristics between the thin and deep shell flows include differences in jet strength for given step widths and at different latitudes. Most notably, there are differences in concavity per PV step and in the relation between PV and velocity. These features can be explained in terms of the topological β parameters for thin and deep shell fluids. Barotropic stability is also investigated.
Allen Lorraine A.
Aurnou Jonathan M.
Wicht Johannes
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