Energy spectrum proportional to the squared phase speed of Rossby modes in the general circulation of the atmosphere

Žagar

2011

SOLA

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The characteristics of energy spectrum based on 3D normal mode energetics are investigated with the global analysis dataset provided by Japan Meteorological Agency (JMA) with the resolution of TL959L60. The energy spectrum of gravity modes exactly follows the −5/3 power law in the synoptic and mesoscales. In the synoptic scale, the spectral slope of total energy follows the −3 power law because Rossby waves are dominant compared to gravity waves. The energy level of gravity modes becomes larger than that of Rossby modes around the zonal wavenumber k = 80. This scale corresponds to 350 km in 45°circle. The total energy spectrum does not show a clear transition from −3 power slope to −5/3 power slope because the energy level of Rossby and gravity modes become comparable near the transition wavenumbers.

Section: Analysis Methods and Datamentioning

confidence: 99%

Erratum: Energy Spectra of Rossby and Gravity Waves [SOLA Vol.7(2011), pp.45-48]

Terasaki

Žagar

2011

SOLA

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“…i is the eigenfrequency of the Laplace's tidal equation, fi is the expansion coefficient of the external forcing of viscosity and diabatic heating rate, and rijk is the interaction coefficients for nonlinear wave-wave interactions calculated by the triple products of the 3D normal mode functions. As seen in Tanaka et al (2004), the ratio of the nonlinear term to the linear term is referred to as a spherical Rhines ratio Ri , which characterizes the turbulence regime Ri > 1, and the wave regime Ri < 1, and the scale where Ri = 1 is defined as the Rhines scale CR in this study:…”

Section: Equation and Datamentioning

confidence: 99%

“…According to the Rossby wave saturation theory (Tanaka et al 2004), Rossby waves break down when the local meridional gradient of potential vorticity becomes negative, < 0. The amplitudes of the waves are thus saturated bounded by the criterion given by this condition.…”

Section: Spectral Energy Slopementioning

confidence: 99%

“…1). The spectral characteristic for the barotropic component in the phase speed domain was argued by Tanaka et al (2004), by using the criterion of the < 0. Using 3D normal mode energetics, they investigated the characteristics of the energy spectrum for the barotropic component (Tanaka 1985).…”

mentioning

confidence: 99%

“…The energy slope of E = ac 2 was derived by Tanaka et al (2004) based on the criterion of the Rossby wave breaking, where E is total energy, c is a phase speed of Rossby wave, and a is a constant. The wave breaking occurs when the local meridional gradient of potential vorticity is negative, i.e., < 0, somewhere in the domain.…”

mentioning

confidence: 99%

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Barotropic Energy Spectrum by the Rossby Wave Saturation in the Zonal Wavenumber Domain

Terasaki

2007

SOLA

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In this study, characteristics of the energy slope for the barotropic component of the atmosphere are examined in the framework of the 3D normal mode decomposition. The energy slope of E = ac 2 was derived by Tanaka et al. (2004) based on the criterion of the Rossby wave breaking, where E is total energy, c is a phase speed of Rossby wave, and a is a constant. The wave breaking occurs when the local meridional gradient of potential vorticity is negative, i.e., < 0, somewhere in the domain. If the spectrum obeys the c 2 law, it should obey the 4 power of the zonal wavenumber n, because the phase speed c is related to the total wavenumber by c = /k 2 , and if we assume the isotropy for zonal wind u and the meridional wind v over the range of synoptic to short waves, the energy spectrum can be expressed as a function of n instead of k.The theoretical inference of the energy slope is examined using JRA-25 data. According to the result of the analysis, the spectral slope agrees quite well with the 4 power law for the barotropic component of the atmosphere. It is, however, confirmed that the spectrum obeys the 3 power law as in previous studies for the baroclinic atmosphere. It is also found that the barotropic energy spectrum obeys the saturation theory where energy cascades up, but it does not obey where energy cascades down. IntroductionThe energetics of atmospheric general circulation have been investigated by many researchers. The energy spectrum is characterized by 3 power law with respect to the horizontal wavenumber k over the synoptic to sub-synoptic scales (Wiin-Nielsen 1967;Boer and Shepherd 1983;Nastrom et al. 1984; Shepherd 1987). Using dimensional analysis, Kraichnan (1967) predicted a k 3 power law for 2D, isotropic and homogeneous turbulence in a downscale enstrophy cascading inertial subrange on the short-wave side of the scale of energy injection. Basdevant et al. (1981) showed the k 4 spectral slope in enstrophy cascading subrange by the barotropic nondivergent model with forcing. It was shown by Tung and Orland (2003) that not only enstrophy but also energy cascade down from synoptic to meso scales. The down scale energy cascade is responsible for a k 5/3 spectrum on the short-wave side where the energy cascade exceeds the enstrophy cascade. Tung and Orland (2003) demonstrated that the energy injected at the synoptic scale cascades up to planetary waves and zonal motions where another dissipation exists. Contrasted to the k 3 law over the synoptic to subsynoptic scales, there is no appropriate theory to describe the spectral characteristics at synoptic to planetary scales because of the existence of the energy source due to baroclinic instability. Welch and Tung (1998) argued that the theory of nonlinear baroclinic adjustment (Stone 1978) is responsible to determine the spectrum over the energy source range. They introduced a breaking criterion proposed by Garcia (1991) to determine the upper bound in meridional heat flux by the disturbances. According to the criterion, a Rossby wave break...

Time series analysis of normal mode energetics for Rossby wave breaking and saturation using a simple barotropic model

Matsunobu

Atmospheric Science Letters

2019

In this study, Rossby wave breaking and saturation are examined for an idealized situation using a simple barotropic spectral model. In the model, a Rossby wave is amplified by parameterized baroclinic instability. The increase of the wave energy stops at the level where the high and low potential vorticities (PVs) indicate overturning, which is equivalent to the fact that the meridional PV gradient becomes negative somewhere in the domain. In this study, it is shown theoretically that the criterion may be represented by the point when the wave energy exceeds a quarter of the originally proposed saturation level specified by E = (p s /g)c 2 in the spectral domain, by assuming a sinusoidal curve for the wave. Rossby wave saturation under the new definition proposed in this study could be followed by wave breaking, which occurs when the energy level of the background noise becomes comparable to that of harmonic waves of the amplified unstable wave. It is found that the criterion of PV overturning is equivalent to the energy level of wave saturation, and wave breaking is a distinct phenomenon from wave saturation. K E Y W O R D S barotropic model, dynamic/processes, normal mode energetics, Rossby wave, wave breaking, wave saturation