Statistics – Computation
Scientific paper
Nov 2000
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000phdt........38h&link_type=abstract
Thesis (PhD). UNIVERSITY OF CALIFORNIA, BERKELEY, Source DAI-B 61/07, p. 3661, Jan 2001, 73 pages.
Statistics
Computation
1
Scientific paper
Other than the Great Red Spot, almost all long-lived vortices in the weather layer on Jupiter exist multiply at their latitudes in staggered rows of cyclones and anti-cyclones called Kármán vortex streets. Examples include the White Ovals and the small anti- cyclones at 40°S. We model these vortex streets with computational solutions of the 1½ layer quasigeostrophic (QG) equations with finite Rossby deformation radius. Using a contour dynamics (CD) method, we find all possible steady state vortex streets, and classify them according to the three possible configurations of their streamlines and stagnation points. Over wide ranges of parameter space, the steady states are stable to linear and finite-amplitude perturbations. Because the QG equations conserve energy and momentum, and because potential vorticity is advectively conserved, any initial condition maintains over time its original values of energy, momentum, potential circulation and enstrophy, etc. With such a Hamiltonian method, one would need to be improbably lucky with one's initial conditions to accurately match the conserved quantities of the vortex streets on Jupiter. A more realistic model should include two effects of turbulence: merger of small vortices and the filamentation from large vortices. We model these effects in the solution of the QG equations on a two-dimensional grid with weak forcing and dissipation. The previously large and undifferentiated parameter space develops a small, robust attractor and large basins of attraction. The location of the attractor, i.e., the values of its ``conserved quantities'', depends only on the level of forcing and not on the initial conditions. We then use an analogous forced and dissipated CD model with contour surgery to duplicate these results. The CD model is much easier to interpret, and we use it to develop a simple physical explanation of where and why the attractor forms. Essentially, one type of steady state, which occupies zero area in parameter space, is an attractor for the other two types when they are forced and dissipated. The presence of this attractor has important implications for models of the Jovian weather layer, because it significantly restricts the number of independent parameter values.
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