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D.G. Dritschel, G.A. Gottwald, and M. Oliver,
Comparison of variational balance models for the rotating shallow water equations,
J. Fluid Mech. 822 (2017), 689-716.
Abstract:
We present an extensive numerical comparison of a family of balance
models appropriate to the semi-geostrophic limit of the rotating
shallow water equations, and derived by variational asymptotics in
Oliver (2006) for small Rossby numbers Ro. This family
of generalized large-scale semi-geostrophic (GLSG) models contains the
\(L_1\)-model introduced by Salmon (1983) as a special case. We use
these models to produce balanced initial states for the full shallow
water equations. We then numerically investigate how well these models
capture the dynamics of an initially balanced shallow water flow. It
is shown that, whereas the \(L_1\)-member of the GLSG family is able to
reproduce the balanced dynamics of the full shallow water equations on
time scales of \({\mathcal{O}}(1/{\mathrm{Ro}})\) very well, all other
members develop significant unphysical high wavenumber contributions
in the ageostrophic vorticity which spoil the dynamics.
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