Physics – Fluid Dynamics
Scientific paper
Nov 2003
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003aps..dfd.dn003s&link_type=abstract
American Physical Society, Division of Fluid Dynamics 56th Annual Meeting, November 23-25, 2003, East Rutherford, New Jersey, ME
Physics
Fluid Dynamics
Scientific paper
Classical theories of balanced dynamics appeal to either small Rossby number (midlatitude synoptic scale or planetary scale) or small Froude number (midlatitude mesoscale or tropics). Existing attempts to unify the two regimes are ad hoc and generally violate conservation laws. However a fundamental condition for balanced dynamics is a separation in timescales between the (slow) vortical and (fast) inertia-gravity-wave components. Using the timescale ratio as a small parameter, a unified theory of balance emerges. It has the automatic benefit that the leading order system is Hamiltonian and has good conservation properties. In midlatitudes, the small Froude number and small Rossby number regimes (both quasi-geostrophy and planetary geostrophy) are encompassed. In the tropics, a new definition of an equatorial Rossby number allows a small Rossby number balance (analogous to planetary geostrophy) as well as the more familiar small Froude number balance. The ultimate goal is a unified set of balance equations for the sphere.
Saujani Simal
Shepherd Theodore
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