The CASL algorithm for quasi-geostrophic flow in a cylinder

Authors:
C. Macaskill;W. E. P. Padden;D. G. Dritschel
Affiliations:
School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006, Australia;School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006, Australia;Mathematical Institute, University of St. Andrews North Haugh, St. Andrews KY16 9SS, Scotland, UK
Venue:
Journal of Computational Physics
Year:
2003

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Abstract

The contour-advective semi-Lagrangian (CASL) algorithm is a hybrid Lagrangian-Eulerian numerical algorithm combining contour dynamics, for the advection of a materially conserved dynamical tracer, with spectral techniques, for the computation of the associated flow field. It benefits from the accuracy of contour dynamics, and the efficiency of spectral methods, and in applications to 'quasi-geostrophic' rotating, stratified flows, has no time-step restriction for numerical stability. It abandons the expensive aspect of contour dynamics the computation of contour integrals to obtain the flow field - and the inaccurate (and costly) aspect of spectral methods - the advection of materially conserved tracers (requiring a time-step restriction for numerical stability and numerical diffusion). The two approaches are tied together by a fast method of converting tracer contours to gridded field values (Lagrangian → Eulerian) and the bilinear interpolation of the flow field from the grid to points on the contours (Eulerian → Lagrangian). Here, we extend this method, originally developed for horizontally periodic flows, to flows within a cylindrical domain. Among other applications, this permits a comparison with experiments, which are often conducted in a cylindrical domain. We demonstrate the accuracy of the algorithm in a few test cases, then examine the differences between cylindrical and periodic domains for both simple vortex interactions and complex quasi-geostrophic turbulence.