Dissipation and Cascades to Small Scales in Numerical Models Using a Shape-Preserving Advection Scheme

John Thuburn Centre for Global Atmospheric Modelling, Department of Meteorology, University of Reading, Reading, United Kingdom

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Abstract

A nondivergent barotropic mode1 and a shallow-water model are presented that exploit a high-order shape-preserving scheme for the advection of vorticity or potential vorticity as well as tracers. The dissipation associated with the advection scheme is found to be due to the spreading of features as they are advected across a finite-resolution grid. The strength and scale selectivity of this dissipation are quantified using some simple tests. The resolved tracer variance and (potential) enstrophy are not conserved by the advection scheme; this can be interpreted as a cascade to unresolved scales. In simulations of turbulent mixing, satisfactory cascade of tracer variance, energy, and (potential) enstrophy are obtained without the need for any special parameterization of the cascade to unresolved scales.

Abstract

A nondivergent barotropic mode1 and a shallow-water model are presented that exploit a high-order shape-preserving scheme for the advection of vorticity or potential vorticity as well as tracers. The dissipation associated with the advection scheme is found to be due to the spreading of features as they are advected across a finite-resolution grid. The strength and scale selectivity of this dissipation are quantified using some simple tests. The resolved tracer variance and (potential) enstrophy are not conserved by the advection scheme; this can be interpreted as a cascade to unresolved scales. In simulations of turbulent mixing, satisfactory cascade of tracer variance, energy, and (potential) enstrophy are obtained without the need for any special parameterization of the cascade to unresolved scales.

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