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The problem of parameterizing the interactions of larger scales and smallerscales in fluid flows is addressed by considering a property of two-dimensionalincompressible turbulence. The property we consider is selective decay, inwhich a Casimir of the ideal formulation (enstrophy in 2D flows, helicity in 3Dflows) decays in time, while the energy stays essentially constant. This paperintroduces a mechanism that produces selective decay by enforcing Casimirdissipation in fluid dynamics. This mechanism turns out to be related incertain cases to the numerical method of anticipated vorticity discussed in\cite{SaBa1981,SaBa1985}. Several examples are given and a general theory ofselective decay is developed that uses the Lie-Poisson structure of the idealtheory. A scale-selection operator allows the resulting modifications of thefluid motion equations to be interpreted in several examples as parameterizingthe nonlinear, dynamical interactions between disparate scales. The type ofmodified fluid equation systems derived here may be useful in modellingturbulent geophysical flows where it is computationally prohibitive to rely onthe slower, indirect effects of a realistic viscosity, such as in large-scale,coherent, oceanic flows interacting with much smaller eddies.

Selective decay by Casimir dissipation in fluids