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Thursday 23 May 2013: Towards an energy-conserving deep-atmosphere quasi-hydrostatic dynamical core
Dr. Marine Tort - Laboratoire de Meteorologie Dynamique, Ecole Polytechnique, Palaiseau, France
Amory 128 15:00-16:00
Atmosphere dynamics of our planet is quite well described by traditional primitive equations based on the so-called shallow atmosphere approximation. However, to model planetary atmospheres, we can not make the shallow approximation anymore because of the low planet radius (such as Titan) or the depth of their atmospheres (such as Jupiter or Saturn). The full Coriolis force needs then to be taken into account, in addition to all metric terms [2].
We derived the curl (vector-invariant) form of the equations in general, time-dependant curvilinear coordinates leading naturally to a variational formulation. This suggests to use absolute angular momentum instead of relative velocity as a prognostic variable. The choice of a discreet form of the Hamiltonian H leads to a straightforward generalization of energy-conserving Sadourny's discretization [1], reusing most of the primitive-equation dynamical core.
References:
[1] R. Sadourny The Dynamics of Finite-Difference Models of the Shallow-Water Equations Journal of Atmospheric Sciences, 1975a, Vol 32, p 680/689.
[2] A.A White and R.A Bromley Dynamical Consistent Quasi-Hydrostatic Equations for Global Models with a Complete Coriolis Force Quarterly Journal of the Royal Meteorological Society, 1995, Vol 121, p 339/418
