Geostrophic balance preserving interpolation in mesh adaptive linearised shallow-water ocean modelling

J. R. Maddison*, C. J. Cotter, P. E. Farrell

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The accurate representation of geostrophic balance is an essential requirement for numerical modelling of geophysical flows. Significant effort is often put into the selection of accurate or optimal balance representation by the discretisation of the fundamental equations. The issue of accurate balance representation is particularly challenging when applying dynamic mesh adaptivity, where there is potential for additional imbalance injection when interpolating to new, optimised meshes.

In the context of shallow-water modelling, we present a new method for preservation of geostrophic balance when applying dynamic mesh adaptivity. This approach is based upon interpolation of the Helmholtz decomposition of the Coriolis acceleration. We apply this in combination with a discretisation for which states in geostrophic balance are exactly steady solutions of the linearised equations on an f-plane; this method guarantees that a balanced and steady flow on a donor mesh remains balanced and steady after interpolation onto an arbitrary target mesh, to within machine precision. We further demonstrate the utility of this interpolant for states close to geostrophic balance, and show that it prevents pollution of the resulting solutions by imbalanced perturbations introduced by the interpolation. (C) 2011 Elsevier Ltd. All rights reserved.

Original languageEnglish
Pages (from-to)35-48
Number of pages14
JournalOcean modelling
Volume37
Issue number1-2
DOIs
Publication statusPublished - 2011

Keywords

  • Finite element method
  • Geostrophic balance
  • FLOW
  • EQUATIONS
  • UNSTRUCTURED MESHES
  • Interpolation
  • CONSERVATIVE INTERPOLATION
  • Helmholtz decomposition
  • FINITE-ELEMENT PAIR
  • PROJECTION
  • STABILITY
  • Shallow-water equations
  • Discontinuous Galerkin

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