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G. Badin, M. Oliver, and S. Vasylkevych,
Geometric Lagrangian averaged Euler-Boussinesq and primitive equations,
J. Phys. A: Math. Theor. 51 (2018), 455501, doi:10.1088/1751-8121/aae1cb.
Abstract:
In this article we derive the equations for a rotating stratified
fluid governed by inviscid Euler-Boussinesq and primitive equations
that account for the effects of the perturbations upon the mean. Our
method is based on the concept of geometric generalized Lagrangian
mean recently introduced by Gilbert and Vanneste, combined with
generalized Taylor and horizontal isotropy of fluctuations as
turbulent closure hypotheses. The models we obtain arise as
Euler-Poincaré equations and inherit from their parent systems
conservation laws for energy and potential vorticity. They are
structurally and geometrically similar to Euler-Boussinesq-\(\alpha\)
and primitive equations-\(\alpha\) models, however feature a different
regularizing second order operator.
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