• Bannon, P. R., 1995: Potential vorticity conservation, hydrostatic adjustment, and the anelastic approximation. J. Atmos. Sci., 52 , 23022312.

    • Search Google Scholar
    • Export Citation
  • Bannon, P. R., 1996: On the anelastic approximation for a compressible atmosphere. J. Atmos. Sci., 53 , 36183628.

  • Durran, D. R., 1989: Improving the anelastic approximation. J. Atmos. Sci., 46 , 14531461.

  • Klein, R., 2000: Asymptotic analyses for atmospheric flows and the construction of asymptotically adaptive numerical methods. Z. Angew. Math. Mech., 80 , 765777.

    • Search Google Scholar
    • Export Citation
  • Laprise, R., 1992: The Euler equations of motion with hydrostatic pressure as an independent variable. Mon. Wea. Rev., 120 , 197207.

  • Lipps, F. B., , and R. S. Hemler, 1982: A scale analysis of deep moist convection and some related numerical calculations. J. Atmos. Sci., 39 , 21922210.

    • Search Google Scholar
    • Export Citation
  • Lott, F., 2003: Large-scale flow response to short gravity waves breaking in a rotating shear flow. J. Atmos. Sci., 60 , 16911704.

  • Majda, A. J., , and R. Klein, 2003: Systematic multiscale models for the Tropics. J. Atmos. Sci., 60 , 393408.

  • Nance, L. B., , and D. Durran, 1994: A comparison of the accuracy of three anelastic systems and the pseudo-incompressible system. J. Atmos. Sci., 51 , 35493565.

    • Search Google Scholar
    • Export Citation
  • Nolan, D. S., , and M. T. Montgomery, 2002: Nonhydrostatic, three-dimensional perturbations to balanced, hurricane-like vortices. Part I: Formulation, linearized evolution, and stability. J. Atmos. Sci., 59 , 29893020.

    • Search Google Scholar
    • Export Citation
  • Nolan, D. S., , and L. D. Grasso, 2003: Nonhydrostatic, three-dimensional perturbations to balanced, hurricane-like vortices. Part II: Symmetric response and nonlinear simulations. J. Atmos. Sci., 60 , 27172745.

    • Search Google Scholar
    • Export Citation
  • Nolan, D. S., , M. T. Montgomery, , and L. D. Grasso, 2001: The wavenumber one instability and trochoidal motion of hurricane-like vortices. J. Atmos. Sci., 58 , 32433270.

    • Search Google Scholar
    • Export Citation
  • Nolan, D. S., , Y. Moon, , and D. P. Stern, 2007: Tropical cyclone intensification from asymmetric convection: Energetics and efficiency. J. Atmos. Sci., in press.

    • Search Google Scholar
    • Export Citation
  • Ogura, Y., , and N. A. Philips, 1962: Scale analysis of deep and shallow convection in the atmosphere. J. Atmos. Sci., 19 , 173179.

  • Scinocca, J. F., , and T. G. Shepherd, 1992: Nonlinear wave-activity conservation laws and Hamiltonian structure for the two-dimensional anelastic equations. J. Atmos. Sci., 49 , 527.

    • Search Google Scholar
    • Export Citation
  • Skamarock, W. C., , J. B. Klemp, , J. Dudhia, , D. O. Gill, , D. M. Barker, , W. Wang, , and J. G. Powers, 2005: A description of the Advanced Research WRF version 2. NCAR Tech. Note NCAR/TN-468+STR, 88 pp.

  • Wicker, L. J., , and W. C. Skamarock, 2002: Time-splitting methods for elastic models using forward time schemes. Mon. Wea. Rev., 130 , 20882097.

    • Search Google Scholar
    • Export Citation
  • Wilhelmson, R., , and Y. Ogura, 1972: The pressure perturbation and the numerical modeling of a cloud. J. Atmos. Sci., 29 , 12951307.

  • Yamazaki, Y. H., , and W. R. Peltier, 2001: The existence of subsynoptic-scale baroclinic instability and the nonlinear evolution of shallow disturbances. J. Atmos. Sci., 58 , 657683.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 24 24 0
PDF Downloads 11 11 0

Linear Anelastic Equations for Atmospheric Vortices

View More View Less
  • 1 Naval Research Laboratory, Monterey, California
  • | 2 Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida
© Get Permissions
Restricted access

Abstract

A linear anelastic-vortex model is derived using assumptions appropriate to waves on vortices with scales similar to tropical cyclones. The equation set is derived through application of a multiple-scaling technique, such that the radial variations of the thermodynamic fields are incorporated into the reference state. The primary assumption required for the model is that the horizontal variations in the thermodynamic variables describing the reference state are appreciably longer than the waves on the vortex. This new version of the anelastic system makes no approximation to the requirements for hydrostatic and gradient wind balance, or the buoyancy frequency, in the core of the vortex. A small but measurable improvement in the performance of the new equation set is demonstrated through simulations of gravity waves and vortex–Rossby waves in a baroclinic vortex.

Corresponding author address: Dr. Daniel Hodyss, Naval Research Laboratory, 7 Grace Hopper Ave., Monterey, CA 93943-5502. Email: danhodyss@yahoo.com

Abstract

A linear anelastic-vortex model is derived using assumptions appropriate to waves on vortices with scales similar to tropical cyclones. The equation set is derived through application of a multiple-scaling technique, such that the radial variations of the thermodynamic fields are incorporated into the reference state. The primary assumption required for the model is that the horizontal variations in the thermodynamic variables describing the reference state are appreciably longer than the waves on the vortex. This new version of the anelastic system makes no approximation to the requirements for hydrostatic and gradient wind balance, or the buoyancy frequency, in the core of the vortex. A small but measurable improvement in the performance of the new equation set is demonstrated through simulations of gravity waves and vortex–Rossby waves in a baroclinic vortex.

Corresponding author address: Dr. Daniel Hodyss, Naval Research Laboratory, 7 Grace Hopper Ave., Monterey, CA 93943-5502. Email: danhodyss@yahoo.com

Save