-
G. Özden and M. Oliver,
Variational balance models for the three-dimensional
Euler-Boussinesq equations with full Coriolis force,
Phys. Fluids 33 (2021), 076606.
Abstract:
We derive a semi-geostrophic variational balance model for the
three-dimensional Euler--Boussinesq equations on the non-traditional
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. In particular, we assume neither
hydrostaticity, nor do we neglect the horizontal components of the
Coriolis parameter, i.e., we do not make the so-called "traditional
approximation". The resulting balance models has the same structure
as the "L1 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.
Download the paper in
PDF
format.