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