The Kinetic Energy of the Large-Scale Atmospheric Motion in Wavenumber-Frequency Space: I. Northern Hemisphere

Kao, S. K.; Wendell, L.L.

doi:10.1175/1520-0469(1970)027<0359:tkeotl>2.0.co;2

Cited by 53 publications

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“…As a method of investigating the energy distribution, the energy spectrum, i.e., energy distribution in the wavenumber space of the atmosphere, often has been investigated. It has been pointed out in numerous investigations, that the energy spectrum is proportional to the À3 power of the wavenumber, in the wavenumber region expressing large-scale motions of the atmosphere (e.g., Saltzman and Fleischer 1962;Wiin-Nielsen 1966;Kao and Wendell 1970;Julian et al 1970;Tanaka 1985;Nastrom and Gage 1985). This observational fact is often explained as an exposure of the feature of two-dimensional turbulence, based on the quasi two-dimensionality of the largescale motions of the atmosphere (Charney 1971).…”

Section: Introductionmentioning

confidence: 98%

The Scaling Law of Quasi-Geostrophic Turbulence with Weak Energy Dissipation

Iga

Watanabe

2003

Journal of the Meteorological Society of Japan

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When a problem without viscosity is considered as an ideal case, a small dissipation term is necessary in many numerical calculations. Quasi-geostrophic turbulence, which is described by the barotropic version of quasi-geostrophic potential vorticity equation, (also called Charney-Hasegawa-Mima equation as an equivalent) is one of these situations: a dissipation term must be added in order to prevent the energy from piling up in the large wavenumber region. Consequently, the total energy decreases gradually, which should be conserved in an ideal situation. In this article, the total energy dissipation rate in quasi-geostrophic turbulence is estimated, based on the assumption that the energy dissipated in this system is equal to the energy transported to the large wavenumber region. This estimation complements the dynamic scaling laws for the quasi-geostrophic turbulence developed by Watanabe et al. (1998): the parameter expressing the total energy dissipation, which was determined from the result of the numerical calculation in their study, is derived from the parameters of the setting of the numerical calculation. This estimation also suggests the means to determine the appropriate artificial hyperviscosity coefficient used in numerical simulations.

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Section: Introductionmentioning

confidence: 98%

The Scaling Law of Quasi-Geostrophic Turbulence with Weak Energy Dissipation

Iga

Watanabe

2003

Journal of the Meteorological Society of Japan

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“…The vertical spectrum of the horizontal wind at mesoscale also has a k -8 region that extends to scales of the order of 100 meters [Endlich et al, 1969]. Horizontal spectra of temperature and wind also fall off from synoptic scale as k -• [Kao and Wendell, 1970;Kao, 1970], although the horizontal dimensions of systems of comparable variance are approximately 10" times the vertical dimension. As discussed by Kao [1970], the k -• spectrum is believed to be characteristic of the domain of horizontal eddies, and, since the typical dimensions of the larger unstable layers lie within the k -• region, the origin of temperature irregularities at this scale should be sought in the effects of organized motion at this scale rather than in turbulent mixing.…”

Section: Discussionmentioning

confidence: 99%

Observations of hydrostatic instability in the free atmosphere

Mantis¹

1972

J. Geophys. Res.

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The distribution of lapse rates observed with a high resolution temperature sonde on two summer balloon flights is presented. Shallow layers of relative instability are observed in the stratosphere as well as the troposphere. Ten percent of the troposphere sounding had lapse rates in excess of 9.5 deg/km, and 10% of the stratosphere sounding had lapse rates in excess of 6.5 deg/km. This fraction of relatively unstable lapse rates must play a large role in determining the over-all diffusivity of the stratosphere. , 1971]. Improvements in the pressure-altitude measurement of the sounding system permit a more quantitative description of the frequency of occurrence of the unstable layers. This note reports on data. from two summer balloon ascents made with the new system. Both flights carried the GMD sonde in addition to the experimental sonde so that conventional temperature and pressure records were available for comparison. Pressure is measured in the experimental system by an a particle pressure gage developed at the University of Minnesota [Howard et al., 1968]. The gage measures the ionizing current produced by a weak a source, and with the present circuitry and source strength a measurement of pressure is obtained once every second at sea level pressure and approximately once every 3 sec at the tropopause. The accuracy of a single pressure measurement with the a particle gage is much the same as the accuracy of a single pressure measurement of the aneroid in the GMD system. Intercomparisons of both systems gave a standard deviation of the difference in pressure altitude of approximately 25 meters. The greater sampling rate of the a gage, however, makes it possible to remove much of the noise by smoothing. Temperature measurements made with an experimental sonde have shown that shallow layers of neutral stability or possibly hydrostatic instability are a common occurrence in the free atmosphere [Mantis and PepinThe accuracy of the a gage can be judged by the comparison of the balloon ascent rates

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“…In the space domain this 'inverse cascade' to lower k implies that the velocity (and density) turbulence will spread into the largest volume available in the system. Evidence for this dual cascade in two-dimensional turbulence has been found in the earth's atmosphere [Kao and Wendell, 1970] and magnetosphere [Kelley and Kintner, 1978]. Kelley and Ott [1978] suggest that the vortices emitted by upwelling bubbles not only form a wake but tend to fill the between-bubble regions (i.e., in an east-west direction) with velocity and density irregularities via this cascade to lower k values.…”

Section: ' • Bubble the Development Time Of L0 4 S Determined By ! Vementioning

confidence: 94%

A review of recent observations of equatorial scintillations and their relationship to current theories of F region irregularity generation

Basu¹,

Kelley²

1979

Radio Science

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Our understanding of transionospheric radio wave propagation problems associated with irregularities in the nighttime equatorial F region has grown enormously in the past few years. This has been achieved by making coordinated phase and amplitude scintillations from a host of geostationary and orbiting satellites and multitechnique irregularity measurements. The variety of supporting measurements include radar backscatter, in situ irregularity observations by rockets and satellites, and airglow and ionosonde observations aboard aircraft. Because of the great volume of work in this field the scope of the present review is limited to a description of these recent coordinated observations and a discussion of the relevant theories of irregularity generation. An attempt is then made to explain some aspects of equatorial scintillations on the basis of these new theoretical developments.

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The Kinetic Energy of the Large-Scale Atmospheric Motion in Wavenumber-Frequency Space: I. Northern Hemisphere

Cited by 53 publications

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The Scaling Law of Quasi-Geostrophic Turbulence with Weak Energy Dissipation

The Scaling Law of Quasi-Geostrophic Turbulence with Weak Energy Dissipation

Observations of hydrostatic instability in the free atmosphere

A review of recent observations of equatorial scintillations and their relationship to current theories of F region irregularity generation

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