Selective decay by Casimir dissipation in fluids

Abstract

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.

References in corpus (4)

• A scale-invariant formulation of the anticipated potential vorticity method
• Geometric gradient-flow dynamics with singular solutions
• Multiscale Turbulence Models Based on Convected Fluid Microstructure
• The gradient of potential vorticity, quaternions and an orthonormal frame for fluid particles

Cited by in corpus (8)

• Noise and dissipation on coadjoint orbits
• Selective decay in fluids with advected quantities: MHD and Hall MHD
• Ehrenfest regularization of Hamiltonian systems
• Relaxation to magnetohydrodynamics equilibria via collision brackets
• Selective energy and enstrophy modification of two-dimensional decaying turbulence
• Structure preserving noise and dissipation in the Toda lattice
• A brief introduction to matrix hydrodynamics
• Selective decay for the rotating shallow-water equations with a structure-preserving discretization