期刊
PHYSICS OF FLUIDS
卷 33, 期 7, 页码 -出版社
AIP Publishing
DOI: 10.1063/5.0053092
关键词
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资金
- Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) [274762653]
- Ideen-und Risikofund 2020 at Universit_at Hamburg
The model derives a semi-geostrophic variational balance model for the three-dimensional Euler-Boussinesq equations on the nontraditional f-plane under the rigid lid approximation. It allows for a fully non-hydrostatic flow and maintains the balance relation elliptic under the assumption of stable stratification and sufficiently small fluctuations in all prognostic fields.
We derive a semi-geostrophic variational balance model for the three-dimensional Euler-Boussinesq equations on the nontraditional f-plane under the rigid lid approximation. The model is obtained by a small Rossby number expansion in the Hamilton principle, with no other approximations made. We allow for a fully non-hydrostatic flow and do not neglect the horizontal components of the Coriolis parameter; that is, we do not make the so-called traditional approximation. The resulting balance models have the same structure as the L-1 balance model for the primitive equations: a kinematic balance relation, the prognostic equation for the three-dimensional tracer field, and an additional prognostic equation for a scalar field over the two-dimensional horizontal domain, which is linked to the undetermined constant of integration in the thermal wind relation. The balance relation is elliptic under the assumption of stable stratification and sufficiently small fluctuations in all prognostic fields.
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