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Abstract: Initially this paper reviews the mathematical issues surrounding thehydrostatic HPE and non-hydrostatic NPE primitive equations that have beenused extensively in numerical weather prediction and climate modelling. Cao andTiti 2005, 2007 have provided a new impetus to this by proving existence anduniqueness of solutions of viscous HPE on a cylinder with Neumann-like boundaryconditions on the top and bottom. In contrast, the regularity of solutions ofNPE remains an open question. With this HPE regularity result in mind, thesecond issue examined in this paper is whether extreme events are allowed toarise spontaneously in their solutions. Such events could include, for example,the sudden appearance and disappearance of locally intense fronts that do notinvolve deep convection. Analytical methods are used to show that for viscousHPE, the creation of small-scale structures is allowed locally in space andtime at sizes that scale inversely with the Reynolds number.



Autor: J. D. Gibbon, Darryl D. Holm

Fuente: https://arxiv.org/



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