• Benjamin, T. B., 1967: Internal waves of permanent form in fluids of great depth. J. Fluid Mech., 29, 559592.

  • Bennett, A. F., 1976: Open boundary conditions for dispersive waves. J. Atmos. Sci., 33, 176182.

  • Ekman, V. W., 1904: On dead-water: Being a description of the so-called phenomenon often hindering the headway and navigation of ships in Norwegian fjords and elsewhere, and an experimental investigation of its causes etc. Norwegian North Polar Expedition, 1893–1896: Scientific Results, F. Nansen, Ed., Fridtjof Nansen Fund for the Advancement of Science, 1–152.

  • Franklin, B., 1905: The Writings of Benjamin Franklin. Vol. 3. The Macmillan Company, 483 pp.

  • Garner, S. T., 1986: A radiative upper boundary condition adapted for f-plane models. Mon. Wea. Rev., 114, 15701577.

  • Haertel, P. T., G. N. Kiladis, A. Denno, and T. M. Rickenbac, 2008: Vertical-mode decompositions of 2-day waves and the Madden–Julian oscillation. J. Atmos. Sci., 65, 813833.

    • Search Google Scholar
    • Export Citation
  • Hayashi, Y., 1976: Non-singular resonance of equatorial waves under the radiation condition. J. Atmos. Sci., 33, 183201.

  • Kasahara, A., and P. L. da Silva Dias, 1986: Response of planetary waves to stationary tropical heating in a global atmosphere with meridional and vertical shear. J. Atmos. Sci., 43, 18931911.

    • Search Google Scholar
    • Export Citation
  • Khouider, B., and A. J. Majda, 2006: Multicloud convective parametrizations with crude vertical structure. Theor. Comput. Fluid Dyn., 20, 351375.

    • Search Google Scholar
    • Export Citation
  • Kiladis, G. N., M. C. Wheeler, P. T. Haertel, K. H. Straub, and P. E. Roundy, 2009: Convectively coupled equatorial waves. Rev. Geophys., 47, RG2003, doi:10.1029/2008RG000266.

    • Search Google Scholar
    • Export Citation
  • Klemp, J. B., and D. R. Durran, 1983: An upper boundary condition permitting internal gravity waves radiation in numerical mesoscale models. Mon. Wea. Rev., 111, 430444.

    • Search Google Scholar
    • Export Citation
  • Lindzen, R., 2003: The interaction of waves and convection in the tropics. J. Atmos. Sci., 60, 30093020.

  • Majda, A. J., and M. Shefter, 2001: Models for stratiform instability and convectively coupled waves. J. Atmos. Sci., 58, 15671584.

  • Mapes, B. E., 1998: The large-scale part of tropical mesoscale convective system circulations: A linear vertical spectral band model. J. Meteor. Soc. Japan, 76, 2955.

    • Search Google Scholar
    • Export Citation
  • Mapes, B. E., 2000: Convective inhibition, subgridscale triggering, and stratiform instability in a toy tropical wave model. J. Atmos. Sci., 57, 15151535.

    • Search Google Scholar
    • Export Citation
  • Nicholls, M. E., R. A. Pielke, and W. R. Cotton, 1991: Thermally forced gravity waves in an atmosphere at rest. J. Atmos. Sci., 48, 18691884.

    • Search Google Scholar
    • Export Citation
  • Ono, H., 1975: Algebraic solitary waves in stratified fluids. J. Phys. Soc. Japan, 39, 10821091.

  • Pandya, R. E., and D. R. Durran, 1996: The influence of convectively generated thermal forcing on the mesoscale circulation around squall lines. J. Atmos. Sci., 53, 29242951.

    • Search Google Scholar
    • Export Citation
  • Purser, R. J., and S. K. Kar, 2001: Radiative upper boundary conditions for a nonhydrostatic atmosphere. NOAA/NWS/NCEP Office Note 433, 26 pp.

  • Raupp, C. F. M., P. L. S. Dias, E. G. Tabak, and P. Milewski, 2008: Resonant wave interactions in the equatorial waveguide. J. Atmos. Sci., 65, 33983418.

    • Search Google Scholar
    • Export Citation
  • Raymond, D. J., and Z. Fuchs, 2007: Convectively coupled gravity and moisture modes in a simple atmospheric model. Tellus, 59A, 627640.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 3 3 3
PDF Downloads 4 4 4

Leaky Rigid Lid: New Dissipative Modes in the Troposphere

View More View Less
  • 1 Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts
  • | 2 Courant Institute of Mathematical Sciences, New York University, New York, New York
Restricted access

Abstract

An effective boundary condition is derived for the top of the troposphere, based on a wave radiation condition at the tropopause. This boundary condition, which can be formulated as a pseudodifferential equation, leads to new vertical dissipative modes. These modes can be computed explicitly in the classical setup of a hydrostatic, nonrotating atmosphere with a piecewise constant Brunt–Väisälä frequency.

In the limit of an infinitely strongly stratified stratosphere, these modes lose their dissipative nature and become the regular baroclinic tropospheric modes under the rigid-lid approximation. For realistic values of the stratification, the decay time scales of the first few modes for mesoscale disturbances range from an hour to a week, suggesting that the time scale for some atmospheric phenomena may be set up by the rate of energy loss through upward-propagating waves.

Corresponding author address: Lyubov Chumakova, MIT 2-376, 77 Massachusetts Ave., Cambridge, MA 02139. E-mail: lyuba@math.mit.edu

Abstract

An effective boundary condition is derived for the top of the troposphere, based on a wave radiation condition at the tropopause. This boundary condition, which can be formulated as a pseudodifferential equation, leads to new vertical dissipative modes. These modes can be computed explicitly in the classical setup of a hydrostatic, nonrotating atmosphere with a piecewise constant Brunt–Väisälä frequency.

In the limit of an infinitely strongly stratified stratosphere, these modes lose their dissipative nature and become the regular baroclinic tropospheric modes under the rigid-lid approximation. For realistic values of the stratification, the decay time scales of the first few modes for mesoscale disturbances range from an hour to a week, suggesting that the time scale for some atmospheric phenomena may be set up by the rate of energy loss through upward-propagating waves.

Corresponding author address: Lyubov Chumakova, MIT 2-376, 77 Massachusetts Ave., Cambridge, MA 02139. E-mail: lyuba@math.mit.edu
Save