Governing Equations and Spectra for Atmospheric Motion and Transports in Frequency, Wave-Number Space

Kao, S. K.

doi:10.1175/1520-0469(1968)025<0032:geasfa>2.0.co;2

Cited by 40 publications

(23 citation statements)

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“…It is important here to remark that the spacetime spectral energy equations formulated above differ from those formulated by Kao (1968) and applied by Kao and Lee (1977) not only in the methods of computing the space-time spectra but also in their physical interpretations.…”

Section: Space-time Spectral Energy Equationsmentioning

confidence: 97%

“…As the data length becomes longer the band width can be reduced.2 Kao (1968) estimated space-time power spectra by direct use of eq. (3).…”

Section: Space-time Spectral Formulasmentioning

confidence: 99%

“…Kao's (1968) spectral energy equation should not be confused with the time-Fourier decomposition of wavenumber spectral energy equations as formulated by Kao (1980) to analyze the evolution of wavenumber energy spectra.…”

Section: Space-time Spectral Energy Equationsmentioning

confidence: 99%

“…Space-time spectral analysis methods developed by the author have also been applied to observed data by Gruber (1974), Zangvil (1975), Hartmann (1976), Sato (1977), Fraedrich and Bottger (1978), Shafer (1979), Pratt (1977Pratt ( , 1979, Venne and Stanford (1979), Pan (1979), Bottger and Fraedrich (1980), Krishnamurti (1979), Krishnamurti and Ardanuy (1980), Depradine (1980Depradine ( , 1981, Zangvil andYanai (1980, 1981), Straus and Shukla (1981) and Miyakoda et al (1981). In this section some of the highlights of the above papers are given as examples of the applications of a space-time spectral analysis to large-scale atmospheric waves.…”

Section: Applications To Atmospheric Wavesmentioning

confidence: 99%

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Space-Time Spectral Analysis and its Applications to Atmospheric Waves

Hayashi

1982

Journal of the Meteorological Society of Japan

217

146

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Section: Space-time Spectral Energy Equationsmentioning

confidence: 97%

“…As the data length becomes longer the band width can be reduced.2 Kao (1968) estimated space-time power spectra by direct use of eq. (3).…”

Section: Space-time Spectral Formulasmentioning

confidence: 99%

Section: Space-time Spectral Energy Equationsmentioning

confidence: 99%

Section: Applications To Atmospheric Wavesmentioning

confidence: 99%

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Space-Time Spectral Analysis and its Applications to Atmospheric Waves

Hayashi

1982

Journal of the Meteorological Society of Japan

217

146

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“…Saltzman (1957) expanded the energy equations into the wavenumber domain and showed that the kinetic energy of the cyclone-scale waves is transformed into both the planetary waves and the short waves in terms of nonlinear wavewave interactions. The study by Saltzman was followed by Kao (1968) and Hayashi (1980) who extended this approach to the wavenumber-frequency domain making use of the two-dimensional Fourier expansion or the space-time spectral method. The energy decomposition was further pursued in the meridional mode domain using spherical harmonics (Eliasen and Machenhauer, 1965) and in the vertical mode domain using empirical orthogonal functions (Holmstrom, 1963).…”

Section: Introductionmentioning

confidence: 99%

Global Energetics Analysis by Expansion into Three-Dimensional Normal Mode Functions during the FGGE Winter

Tanaka

1985

Journal of the Meteorological Society of Japan

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A diagnostic energetics scheme is developed in order to investigate the energy flows among three-dimensional normal modes (Hough modes in horizontal) in the atmosphere. This scheme is applied to the GFDL version of the FGGE level IIIb data during the winter from December 1978 to February 1979.The resultant energy flow is summarized as follows: available potential energy generated at zonal baroclinic modes (especially at the vertical mode m=4) is directly converted into kinetic energy of the planetary scale barotropic mode. Kinetic energy of the cyclone scale baroclinic mode is transformed into zonal and eddy kinetic energies of the barotropic mode. Parameterizing the horizontal scale of waves by their eigenfrequencies, we find for vertically trapped modes, the kinetic energy spectrum follows approximately the 3 power of the frequency. However, for the propagative Rossby modes, the spectrum obeys the -5/3 power law and merges continuously with the spectrum of the gravity modes. It is concluded from the results that the energy spectrum depends on the vertical propagation properties; the energy spectrum of the propagative Rossby waves is similar to that of gravity waves in the frequency domain. The trapped and the critical modes gain their energy through the interactions mentioned above, whereas we find the propagative modes lose a part of energy through nonlinear mode-mode interactions.

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