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Régis Juvanon Du Vachat

Abstract

A non-normal-mode initialization scheme, that is, an initialization scheme that does not require an explicit computation of the normal modes of the linearized equations, is considered. Such a scheme is applied to a shallow-water limited-area model on a stereographic projection, for which the computation of the normal modes is too expensive due to nonseparability. The numerical tests for the initialization concern the problem of relaxation toward constant or time-variable boundary conditions, the consistency of the initialization scheme with the semi-implicit scheme of the model, and the effect of orography. The scheme is then applied to a similar limited-area model but with a stretched grid, whose domain is greatly extended in latitude with the regular grid domain being located at its center. Numerical tests are performed for the initialization of this model to assess the impact of using a more comprehensive linearization including most of the β terms. Certain diagnostic quantities, used to test the convergence of the initialization scheme, are computed during the simulations.

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Régis Juvanon Du Vachat

Abstract

The non-normal mode initialization, i.e., an initialization scheme which does not require an explicit computation of the eigenmodes of the linearized equations, is reviewed. The formulation of such a scheme is given in abstract form, in the case of the Machenhauer initialization scheme as well as in the case of higher-order schemes. The particular case of a stationary Rossby mode is examined in detail. In this case, the separation between slow modes and fast gravity modes is explicitly given, and it is conjectured that the formulation of non-normal mode initialization can be given only in such a case. An application to the shallow-water equations, which includes the main β-terms in the linearization is given as a result of the preceding formulation. Such a scheme extends the previous scheme proposed by Bourke and McGregor.

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Régis Juvanon du Vachat

Abstract

A formulation of normal modes for a limited-area model is proposed. The case of shallow water equations on a conformal projection is considered. This formulation is a generalization of Brière's proposal. It can handle the full variation of the Coriolis parameter and of the map scale factor; it is written in physical-space variables and does not need a rectangular domain to be applied as in Brière's scheme. It gives rise to stationary Rossby modes and gravity modes fully identified and easily separated on the basis of their frequency. By applying Machenhauer's initialization scheme, we rigorously deduce the vertical mode initialization proposed and demonstrated by Bourke and McGregor for a limited-area model.

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