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David A. Schecter

′, υ ′) becomes the geostrophic velocity perturbation, l D becomes the constant Rossby deformation radius l R , and q̂ ′ becomes l 2 R times the quasigeostrophic PV perturbation. c. Basic kinematics of the DVRW–critical layer interaction A DVRW has a quasi-PV distribution of the form in which a is the complex wave amplitude, n is the azimuthal wavenumber, and c.c. denotes the complex conjugate of the preceding term. We will assume that the complex radial wavefunction Q̂ vanishes beyond

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Michael E. McIntyre

defined as a kinematically possible fluid flow with the vortex lines and stratification surfaces frozen into the fluid. Of course the usefulness of the PV concept as first published by Rossby, both for shallow water ( Rossby 1936 ) and for multilayer and continuous stratification ( Rossby 1940 ), lies in being able to avoid the Lagrangian description. This is useful because, for one thing, PV inversion is quintessentially an Eulerian or field-theoretic procedure. We may note that 1936 is also the year

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K. Ngan, P. Bartello, and D. N. Straub

-resolution simulations can be analyzed; the resulting eddy viscosity, which represents the effects of unresolved interactions, is then appended to the kinematic viscosity ( Domaradzki et al. 1987 , 1993 ). LES is a standard technique in the modeling of industrial flows. It also lies behind turbulence schemes used in atmospheric and oceanic models (e.g., the well-known Smagorinsky model). Nevertheless, the problem is more intricate in geophysical fluid dynamics. Here we desire information beyond the total

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