Variations in Wave Energy and Amplitudes along the Energy Dispersion Paths of Nonstationary Barotropic Rossby Waves

Li, Yaokun; Jiping, Chao; Kang, Yong

doi:10.1007/s00376-020-0084-9

Cited by 5 publications

(10 citation statements)

References 15 publications

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“…This equation suggested that the variability of wave energy along a ray was jointly determined by the divergence of the group velocity and the product of the wave scale and the gradients of the basic flow, manifesting the energy divergence or convergence and the eddy momentum transport, respectively. Following our previous study [9], the divergence of the group velocity was expressed as a ratio between the difference in the group velocity flux and the volume it passed through during a short time interval. This method made it easy to solve wave energy and hence amplitude.…”

Section: Discussionmentioning

confidence: 99%

“…However, we cannot directly differentiate Equations ( 4) and (5) to calculate the divergence of the group velocity because the group velocity values neighboring a ray are unknown [26]. Inspired by Lighthill [26] and Karoly and Hoskins [27] who dealt with the situation that satisfies ∇ • → c g = 0, we propose an available method [9] to calculate the divergence of the group velocity:…”

Section: Wave Energy Equation In the Non-uniform Basic Flowmentioning

confidence: 99%

“…The second one is that it can provide a reference to the results for the observed basic flow. Hoskins and Karoly [9] pointed out that analytical results are necessary because many of the results obtained from the observed basic flow are of little difference from those obtained from an analytical one. For a zonally non-uniform basic flow, there is yet no relevant research on varying wave energy and amplitude.…”

Section: Analytical Horizontally Non-uniform Basic Flowmentioning

confidence: 99%

“…They suggested that westward waves tend to have larger total wavelengths and increased meridional group velocities that benefit a cross-equatorial propagation. Li et al [9] emphasized the variations in amplitude and wave energy along the ray paths by proposing a new method to calculate the divergence of the group velocity.…”

Section: Introductionmentioning

confidence: 99%

“…As a result, there is no relevant research on wave energy and amplitude variations along the wave rays. Recently, Li et al [9] calculated wave energy and amplitude along the wave rays under horizontally uniform basic flows to discuss developing Rossby waves by applying the criterion of Lu and Zeng [20], which states that developing waves should accompany the growth of both wave energy and amplitude. Inspired by their work, this paper tries to discuss the variations in wave energy and amplitude along the wave rays by deriving the wave energy equation in the horizontally non-uniform basic flow.…”

Section: Introductionmentioning

confidence: 99%

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Variations in Wave Energy and Amplitudes along the Ray Paths of Barotropic Rossby Waves in Horizontally Non-Uniform Basic Flows

Jiping

Kang

2021

Atmosphere

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A non-divergent barotropic model on a sphere transformed to Mercator coordinates is used to examine the variations in wave energy and amplitude along the energy dispersion paths of barotropic Rossby waves in non-uniform basic flows. Wave energy can be easily solved by specifying the divergence of the group velocity along the corresponding rays. In an analytical non-uniform basic flow that represents the basic features of the observed one at middle latitudes, waves with different periods decay accompanying the decreases in wave energy and amplitude and the increase in the total wavenumber. This implies that the waves are trapped and the energy is eventually absorbed by the basic flow. For the observed non-uniform basic flow that can represent the basic features of the non-divergent wind field at 200 hPa, the situation is more complicated. The significant increase in wave energy can be caused by either the convergence of wave energy or the barotropic energy absorption from the basic flow or both of them. A significant increase in amplitude can also be observed if the total wavenumber varies moderately. This means waves can significantly develop. Waves may decay if both wave energy and amplitude decrease. Waves may propagate without significant developing or decaying to realize a long distance propagation. The propagating waves are mainly caused by oscillating wave energy as well as amplitude.

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Section: Discussionmentioning

confidence: 99%

Section: Wave Energy Equation In the Non-uniform Basic Flowmentioning

confidence: 99%

Section: Analytical Horizontally Non-uniform Basic Flowmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Variations in Wave Energy and Amplitudes along the Ray Paths of Barotropic Rossby Waves in Horizontally Non-Uniform Basic Flows

Jiping

Kang

2021

Atmosphere

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Variations in Amplitudes and Wave Energy along the Energy Dispersion Paths for Rossby Waves in the Quasigeostrophic Barotropic Model

Jiping

Kang

2022

Adv. Atmos. Sci.

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The energy dispersion of magnetic Rossby waves in zonally nonuniform basic states

2023

Phys. Scr.

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The energy dispersion of magnetic Rossby waves was investigated by applying two-dimensional incompressible magnetohydrodynamic equations in both zonally varying basic flow and basic magnetic field. A derived cubic dispersion relation suggests that there are at most three types of magnetic Rossby wave. Two of them represent waves that gradually tend to Alfvén waves during the energy dispersion process. The energy dispersion trajectories (wave rays) finally move with the zonal group velocity that tends to be equal to the zonal phase speed after being reflected by at least one turning location at which the meridional group velocity equal to zero. Along the marching rays, both the wave action density and wave energy tend to be constant values while the wave amplitude will decrease with increasing total wavenumber. The third one represents a wave that gradually have the constant meridional wavenumber, wave action density, wave energy, and wave amplitude. However, the difference in the zonal group velocity and the zonal phase speed suggests that the wave is still dispersive. This type of wave will disappear if specifying uniform basic magnetic field. The cubic dispersion relation is then reduced to a quadratic one. Correspondingly, the remaining two dispersion relations feature a fast- and a slow-propagating magnetic Rossby wave, respectively. They finally tend to be Alfvén waves with no energy dispersion when the energy dispersion process completes.

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Variations in Wave Energy and Amplitudes along the Energy Dispersion Paths of Nonstationary Barotropic Rossby Waves

Cited by 5 publications

References 15 publications

Variations in Wave Energy and Amplitudes along the Ray Paths of Barotropic Rossby Waves in Horizontally Non-Uniform Basic Flows

Variations in Wave Energy and Amplitudes along the Ray Paths of Barotropic Rossby Waves in Horizontally Non-Uniform Basic Flows

Variations in Amplitudes and Wave Energy along the Energy Dispersion Paths for Rossby Waves in the Quasigeostrophic Barotropic Model

The energy dispersion of magnetic Rossby waves in zonally nonuniform basic states

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