Comparison of variational balance models for the rotating shallow water equations

David Gerard Dritschel, Georg Gottwald, Marcel Oliver

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5 Citations (Scopus)
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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 (J. Fluid Mech., vol. 551, 2006, pp. 197–234) for small Rossby numbers Ro. This family of generalized large-scale semi-geostrophic (GLSG) models contains the L1-model introduced by Salmon (J. Fluid. Mech., vol. 132, 1983, pp. 431-444) 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 L1-member of the GLSG family is able to reproduce the balanced dynamics of the full shallow water equations on time scales of O(1/Ro) very well, all other members develop significant unphysical high wavenumber contributions in the ageostrophic vorticity which spoil the dynamics.
Original languageEnglish
Pages (from-to)689-716
Number of pages28
JournalJournal of Fluid Mechanics
Early online date7 Jun 2017
Publication statusPublished - 10 Jul 2017


  • Rotating flows
  • Shallow water flows
  • Variational methods


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