• Abarbanel, H. D. I., , D. D. Holm, , J. E. Marsden, , and T. S. Ratiu, 1986: Non-linear stability analysis of stratified fluid equilibria. Philos. Trans. Roy. Soc. London, 318A, 349409.

    • Search Google Scholar
    • Export Citation
  • Haynes, P. H., 1988: Forced, dissipative generalizations of finite-amplitude wave-activity conservation relations for zonal and nonzonal basic flows. J. Atmos. Sci., 45, 23522362.

    • Search Google Scholar
    • Export Citation
  • Holm, D. D., , J. E. Marsden, , T. Ratiu, , and A. Weinstein, 1985: Nonlinear stability of fluid and plasma equilibria. Phys. Rep., 123, 1116.

    • Search Google Scholar
    • Export Citation
  • Holopainen, E. O., 1978: A diagnostic study on the kinetic energy balance of the long-term mean flow and the associated transient fluctuation in the atmosphere. Geophysica, 15, 125145.

    • Search Google Scholar
    • Export Citation
  • Hoskins, B. J., , I. N. James, , and G. H. White, 1983: The shape, propagation and mean-flow interaction of large-scale weather systems. J. Atmos. Sci., 40, 15951612.

    • Search Google Scholar
    • Export Citation
  • Iwasaki, T., 2001: Atmospheric energy cycle viewed from wave–mean flow interaction and Lagrangian mean circulation. J. Atmos. Sci., 58, 30363052.

    • Search Google Scholar
    • Export Citation
  • Lorenz, E. N., 1955: Available potential energy of the maintenance of the general circulation. Tellus, 7, 157167.

  • Mak, M., , and M. Cai, 1989: Local barotropic instability. J. Atmos. Sci., 46, 32893311.

  • McIntyre, M. E., , and T. G. Shepherd, 1987: An exact local conservation theorem for finite amplitude disturbances to non-parallel shear flows, with remarks on Hamiltonian structure and on Arnol’d’s stability theorems. J. Fluid Mech., 181, 527565.

    • Search Google Scholar
    • Export Citation
  • Murakami, S., , R. Ohgaito, , and A. Abe-Ouchi, 2011: Atmospheric local energetics and energy interactions between mean and eddy fields. Part II: An example for Last Glacial Maximum climate. J. Atmos. Sci., in press.

    • Search Google Scholar
    • Export Citation
  • Orlanski, I., , and J. Katzfey, 1991: The life cycle of a cyclone wave in the Southern Hemisphere. Part I: Eddy energy budget. J. Atmos. Sci., 48, 19721998.

    • Search Google Scholar
    • Export Citation
  • Plumb, R. A., 1983: A new look at the energy cycle. J. Atmos. Sci., 40, 16691688.

  • Plumb, R. A., 1985: An alternative form of Andrews’ conservation law for quasi-geostrophic waves on a steady, nonuniform flow. J. Atmos. Sci., 42, 298300.

    • Search Google Scholar
    • Export Citation
  • Plumb, R. A., 1986: Three-dimensional propagation of transient quasi-geostrophic eddies and its relationship with the eddy forcing of the time-mean flow. J. Atmos. Sci., 43, 16571678.

    • Search Google Scholar
    • Export Citation
  • Ran, L., , and S. Gao, 2007: A three-dimensional wave-activity relation for pseudomomentum. J. Atmos. Sci., 64, 21262134.

  • Salmon, R., 1998: Lectures on Geophysical Fluid Dynamics. Oxford University Press, 378 pp.

  • Saltzman, B., 1957: Equations governing the energetics of the large scales of atmospheric turbulence in the domain of wavenumber. J. Meteor., 14, 513523.

    • Search Google Scholar
    • Export Citation
  • Simmons, A. J., , J. M. Wallace, , and G. W. Branstator, 1983: Barotropic wave propagation and instability, and atmospheric teleconnection patterns. J. Atmos. Sci., 40, 13631392.

    • Search Google Scholar
    • Export Citation
  • Tanaka, H., , E. Kung, , and W. E. Baker, 1986: Energetics analysis of the observed and simulated general circulation using three-dimensional normal mode expansions. Tellus, 38A, 412428.

    • Search Google Scholar
    • Export Citation
  • Trenberth, K. E., 1986: An assessment of the impact of transient eddies on the zonal flow during a blocking episode using localized Eliassen–Palm flux diagnostics. J. Atmos. Sci., 43, 20702087.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 83 83 19
PDF Downloads 69 69 10

Atmospheric Local Energetics and Energy Interactions between Mean and Eddy Fields. Part I: Theory

View More View Less
  • 1 Climate Research Department, Meteorological Research Institute, Tsukuba, Japan
© Get Permissions
Restricted access

Abstract

A new diagnostic scheme for the atmospheric local energetics is proposed. In contrast to conventional schemes, this scheme correctly represents the local features of the Lorenz energy cycle for time-mean and transient-eddy fields. The key point is that the energy equation is divided not into two but into three parts consisting of the mean, eddy, and interaction energy equations, when basic variables are divided into mean and eddy fields. The interaction energy itself vanishes when appropriate averaging is taken. However, the equation for interaction energy does not vanish and gives a relationship between the interaction energy flux and the two types of energy conversion terms. These three quantities give the complete information for the energy interactions between mean and eddy fields. The Lorenz energy diagram is reconstructed to include a representation of this relationship. A brief discussion about the relationship with wave activity analysis is also given.

Corresponding author address: Shigenori Murakami, Meteorological Research Institute, 1–1 Nagamine, Tsukuba, 305-0052 Japan. E-mail: shimurak@mri-jma.go.jp

Abstract

A new diagnostic scheme for the atmospheric local energetics is proposed. In contrast to conventional schemes, this scheme correctly represents the local features of the Lorenz energy cycle for time-mean and transient-eddy fields. The key point is that the energy equation is divided not into two but into three parts consisting of the mean, eddy, and interaction energy equations, when basic variables are divided into mean and eddy fields. The interaction energy itself vanishes when appropriate averaging is taken. However, the equation for interaction energy does not vanish and gives a relationship between the interaction energy flux and the two types of energy conversion terms. These three quantities give the complete information for the energy interactions between mean and eddy fields. The Lorenz energy diagram is reconstructed to include a representation of this relationship. A brief discussion about the relationship with wave activity analysis is also given.

Corresponding author address: Shigenori Murakami, Meteorological Research Institute, 1–1 Nagamine, Tsukuba, 305-0052 Japan. E-mail: shimurak@mri-jma.go.jp
Save