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Moist multi-scale models for the hurricane embryo

Published online by Cambridge University Press:  30 June 2010

ANDREW J. MAJDA ,
YULONG XING  and
MAJID MOHAMMADIAN
ANDREW J. MAJDA*
Affiliation:
Department of Mathematics and Climate, Atmosphere and Ocean Science, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
YULONG XING
Affiliation:
Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA
MAJID MOHAMMADIAN
Affiliation:
Department of Civil Engineering, University of Ottawa, Ontario, CanadaK1N 6N5
*
†Email address for correspondence: [email protected]
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Abstract

Determining the finite-amplitude preconditioned states in the hurricane embryo, which lead to tropical cyclogenesis, is a central issue in contemporary meteorology. In the embryo there is competition between different preconditioning mechanisms involving hydrodynamics and moist thermodynamics, which can lead to cyclogenesis. Here systematic asymptotic methods from applied mathematics are utilized to develop new simplified moist multi-scale models starting from the moist anelastic equations. Three interesting multi-scale models emerge in the analysis. The balanced mesoscale vortex (BMV) dynamics and the microscale balanced hot tower (BHT) dynamics involve simplified balanced equations without gravity waves for vertical vorticity amplification due to moist heat sources and incorporate nonlinear advective fluxes across scales. The BMV model is the central one for tropical cyclogenesis in the embryo. The moist mesoscale wave (MMW) dynamics involves simplified equations for mesoscale moisture fluctuations, as well as linear hydrostatic waves driven by heat sources from moisture and eddy flux divergences. A simplified cloud physics model for deep convection is introduced here and used to study moist axisymmetric plumes in the BHT model. A simple application in periodic geometry involving the effects of mesoscale vertical shear and moist microscale hot towers on vortex amplification is developed here to illustrate features of the coupled multi-scale models. These results illustrate the use of these models in isolating key mechanisms in the embryo in a simplified content.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 657 , 25 August 2010 , pp. 478 - 501
Copyright
Copyright © Cambridge University Press 2010

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