Thursday, 1 May 2008
Palms ABCD (Wyndham Orlando Resort)
Abstract:
We present matched asymptotic expansions for concentrated
atmospheric vortices in the gradient wind regime using the
mathematical framework proposed recently in [Klein, 2004]
and utilized in the construction of multiscale models in
[Majda and Klein, 2003], [Klein and Majda, 2006]. Our presentation
extends related two-dimensional theories by Ting and Ling [Ling and Ting, 1988] and subsequent work by Reznik and co-workers
[Reznik, 1992] to three dimensions, allowing for weak vertical
shear and diabatic source terms. Preliminary results were
summarized in [Mikusky, 2007].
Bibliography Focusing on dry flows with explicitly prescribed diabatic forcings, we consider a nearly axisymmetric vortex and allow for strong vertical tilt comparable in magnitude to the vortex diameter. The vortex is embedded, in the sense of matched asymptotics, in a quasi-geostrophic background flow. We obtain a closed asymptotic theory that describes
- the motion of the vortex center, which turns out to be advected by the large-scale leading-order barotropic mean flow
- a vertical, shear-induced vortex tilt and an associated precession reminiscent of that found by Reasor and Montgomery [Reasor and Montgomery, 2004]
- the vortex core evolution, which is governed by momentum drag and radial advection of total angular momentum.
- Klein, 2004
- Klein, R. (2004). An Applied Mathematical View of Theoretical Meteorology (invited lecture ICIAM 2003), volume 116 of SIAM Proceedings in Applied Mathematics. SIAM.
- Klein and Majda, 2006
- Klein, R. and Majda, A. J. (2006). Systematic multiscale models for deep convection on mesoscales. Theoretical and Computational Fluid Dynamics, 20:525-552.
- Ling and Ting, 1988
- Ling, G. and Ting, L. (1988). Two-time scales inner solutions and motion of a geostrophic vortex. Scienta Sinica, XXXI(7).
- Majda and Klein, 2003
- Majda, A. J. and Klein, R. (2003). Systematic multi-scale models for the tropics. Journal of the Atmospheric Sciences, 60:393-408.
- Mikusky, 2007
- Mikusky, E. (2007). On the structure of concentrated atmospheric vortices in a gradient wind regime and its motion on synoptic scales. PhD thesis, Universität Hamburg, Fachbereich Geowissenschaften.
- Reasor and Montgomery, 2004
- Reasor, P. D. and Montgomery, M. T. (2004). A new look an the problem of tropical cyclones in vertical shear flow. Journal of the Atmospheric Sciences, 61(1).
- Reznik, 1992
- Reznik, G. M. (1992). Dynamics of singular vortices on a beta-plane. Journal of Fluid Mechanics, 240:405-432.
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