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The accurate representation of geostrophic balance is an essentialrequirement for numerical modelling of geophysical flows. Significant effort isoften put into the selection of accurate or optimal balance representation bythe discretisation of the fundamental equations. The issue of accurate balancerepresentation is particularly challenging when applying dynamic meshadaptivity, where there is potential for additional imbalance injection wheninterpolating to new, optimised meshes.  In the context of shallow-water modelling, we present a new method forpreservation of geostrophic balance when applying dynamic mesh adaptivity. Thisapproach is based upon interpolation of the Helmholtz decomposition of theCoriolis acceleration. We apply this in combination with a discretisation forwhich states in geostrophic balance are exactly steady solutions of thelinearised equations on an f-plane; this method guarantees that a balanced andsteady flow on a donor mesh remains balanced and steady after interpolationonto an arbitrary target mesh, to within machine precision. We furtherdemonstrate the utility of this interpolant for states close to geostrophicbalance, and show that it prevents pollution of the resulting solutions byimbalanced perturbations introduced by the interpolation.

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