Skip to main content Accessibility help

Moist multi-scale models for the hurricane embryo


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.

Corresponding author
Email address for correspondence:
Hide All
Biello, J. A. & Majda, A. J. 2005 A new multiscale model for the Madden–Julian oscillation. J. Atmos. Sci. 62, 16941721.
Biello, J. A. & Majda, A. J. 2006 Modulating synoptic scale convective activity and boundary layer dissipation in the IPESD models of the Madden–Julian oscillation. Dyn. Atmos. Oceans 42, 152215.
Biello, J. A. & Majda, A. J. 2009 Intraseasonal multi-scale moist dynamics of the tropical troposphere. Commun. Math. Sci. 8, 519540.
Biello, J. A., Majda, A. J. & Moncrieff, M. W. 2007 Meridional momentum flux and superrotation in the multi-scale IPESD MJO model. J. Atmos. Sci. 64, 16361651.
Dunkerton, T. J., Montgomery, M. T. & Wang, Z. 2008 Tropical cyclogenesis in a tropical wave critical layer: easterly waves. Atmos. Chem. Phys. Discuss. 8, 1114911292.
Emanuel, K. A. 1989 The finite-amplitude nature of tropical cyclogenesis. J. Atmos. Sci. 46, 34313456.
Emanuel, K. A. 1994 Atmospheric Convection. Oxford University Press.
Frank, W. M. & Roundy, P. E. 2006 The role of tropical waves in tropical cyclogenesis. Mon. Wea. Rev. 134, 23972417.
Grabowski, W. W. 2001 Coupling cloud processes with the large-scale dynamics using the cloud-resolving convection parameterization (CRCP). J. Atmos. Sci. 58, 978997.
Grabowski, W. W. 2004 An improved framework for superparameterization. J. Atmos. Sci. 61, 19401952.
Grabowski, W. W. & Smolarkiewicz, P. K. 1996 Two-time-level semi-Lagrangian modeling of precipitating clouds. Mon. Weather Rev. 124, 487497.
Hendricks, E. A., Montgomery, M. T. & Davis, C. A. 2004 The role of “vortical” hot towers in the formation of tropical cyclone Diana (1984). J. Atmos. Sci. 61, 12091232.
Klein, R. 2000 Asymptotic analyses for atmospheric flows and the construction of asymptotically adaptive numerical methods. Z. Angew. Math. Mech. 80, 765777.
Klein, R. & Majda, A. J. 2006 Systematic multiscale models for deep convection on mesoscales. Theor. Comput. Fluid Dyn. 20, 525551.
Lipps, F. B. & Hemler, R. S. 1982 A scale analysis of deep moist convection and some related numerical calculations. J. Atmos. Sci. 39, 21922210.
Majda, A. J. 2003 Introduction to PDEs and Waves for the Atmosphere and Ocean. Courant Lecture Notes in Mathematics, vol. 9. American Mathematical Society.
Majda, A. J. 2007 a Multiscale models with moisture and systematic strategies for superparameterization. J. Atmos. Sci. 64, 27262734.
Majda, A. J. 2007 b New multiscale models and self-similarity in tropical convection. J. Atmos. Sci. 64, 13931404.
Majda, A. J. & Biello, J. A. 2004 A multiscale model for tropical intraseasonal oscillation. Proc. Natl Acad. Sci. USA 101, 47364741.
Majda, A. J. & Klein, R. 2003 Systematic multiscale models for the tropics. J. Atmos. Sci. 60, 393408.
Majda, A. J., Mohammadian, M. & Xing, Y. 2008 Vertically sheared horizontal flow with mass sources: a canonical balanced model. Geophys. Astrophys. Fluid Dyn. 102, 543591.
Majda, A. J. & Stechmann, S. 2009 A simple dynamic model with features of convective momentum transport. J. Atmos. Sci. 66, 373392.
Majda, A. J. & Xing, Y. 2009 New multi-scale models on mesoscales and squall lines. Commun. Math. Sci. 8, 113134.
Mohammadian, A. M. & LeRoux, D. Y. 2008 Fourier analysis of a class of upwind schemes in shallow water systems for gravity and Rossby waves. Intl J. Numer. Methods Fluids 57, 389416.
Molinari, J., Lombardo, K. & Vollaro, D. 2007 Tropical cyclogenesis within an equatorial Rossby wave packet. J. Atmos. Sci. 64, 13011317.
Molinari, J., Vollaro, D. & Corbosiero, K. L. 2004 Tropical cyclone formation in a sheared environment: a case study. J. Atmos. Sci. 61, 24932509.
Montgomery, M. T., Nicholls, M. E., Cram, T. A. & Saunders, A. B. 2006 A vortical hot tower route to tropical cyclogenesis. J. Atmos. Sci. 63, 355386.
Nolan, D. S. 2007 What is the trigger for tropical cyclogenesis? Aust. Meteorol. Mag. 56, 241266.
Ritchie, E. A. & Holland, G. J. 1997 Scale interactions during the formation of Typhoon Irving. Mon. Weather Rev. 125, 13771396.
Sobel, A. H., Nilsson, J. & Polvani, L. M. 2001 The weak temperature gradient approximation and balanced tropical moisture waves. J. Atmos. Sci. 58, 36503665.
Xing, Y., Majda, A. J. & Grabowski, W. W. 2009 New efficient sparse space-time algorithms for superparameterization on mesoscales. Mon. Weather Rev. 137, 43074324.
Zhang, D.-L. & Bao, N. 1996 Oceanic cyclogenesis as induced by a mesoscale convective system moving offshore. Part II. Genesis and thermodynamic transformation. Mon. Weather Rev. 124, 22062225.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed