The nonlinear effects on the characteristics of gravity wave packets: dispersion and polarization relations

Zhang, S.-D.; Yi, Feifei; Wang, J.-F.

doi:10.1007/s005850000242

Cited by 4 publications

(11 citation statements)

References 16 publications

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“…A detailed analysis on the temporal variations of wavelengths and frequencies for a freely propagating gravity wave in a fully nonlinear regime was presented by Zhang et al [2000]. It is difficult to quantitatively explain what kind of physical mechanism is responsible for this decrease of wavelength and frequency, possible causes may be the joint effects of nonlinearity [ Zhang et al , 2000] and complex background consisted of waves 0 and 1. Moreover, such a result has never been presented by any previous works relative to the resonant interaction of gravity waves.…”

Section: Analyses Of the Computation Resultsmentioning

confidence: 99%

“…First, the wavelength (as presented in Figure 2) in our simulation shows evident decrease. Zhang et al [2000] has pointed out that the nonlinearity tends to decrease the wavelengths, which is due to the fact that the nonlinear terms in equation (1) (such as u , w ) tend to generate higher wave harmonics. Moreover, the variation of wave parameters cause an obvious departure of the energy propagation path of the excited wave from its ray path derived from the linear ray theory.…”

Section: Discussionmentioning

confidence: 99%

“…Evidently, a scheme with high accuracy and stability is necessary. The FICE scheme was shown to be of excellent accuracy and stability [ Hu and Wu , 1984] and was successfully utilized in the study of nonlinear propagations of gravity waves [ Zhang and Yi , 1999; Zhang et al , 2000, Zhang and Yi , 2002], so we adopt it in the present simulation. The computational method of solving (1) and mesh choosing have been described in detail by Hu and Wu [1984] and Zhang and Yi [1999]. Periodical boundaries are adopted to specify the lateral boundaries.…”

Section: Numerical Modelmentioning

confidence: 99%

“…These properties allow our simulation to be more close to the resonant interaction of gravity waves in a realistic atmosphere. Because the finite‐implicit‐continuous‐Eulerian (FICE) scheme [ Hu and Wu , 1984] is proved to be a well‐formulated numerical scheme for simulating the long time propagation and evolution of gravity waves [ Zhang and Yi , 1999; Zhang et al , 2000; Zhang and Yi , 2002], so it is adopted in this paper. A brief description of the numerical model and computational method are introduced in section 2.…”

Section: Introductionmentioning

confidence: 99%

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A numerical study on the propagation and evolution of resonant interacting gravity waves

Zhang¹

2004

J. Geophys. Res.

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[1] Starting from the nonrotating, fully nonlinear basic atmospheric kinetic equations, the nonlinear propagation and evolution of resonant interacting gravity wave packets with small initial amplitudes in a two-dimensional compressible atmosphere have been simulated. The complete nonlinear resonant interaction process of the gravity wave packets is exhibited. The numerical results show that a downward propagating gravity wave is excited by two up-going gravity waves initially due to the resonant interaction, and the wavelength of the excited gravity wave decreases with time. During the whole nonlinear propagation and evolution, although the total wave energy for the interacting triad is almost conservative, obvious wave energy exchange among the three interacting gravity waves is observed. Wave energy tends to transfer from the wave with larger amplitude to that with smaller amplitude, and this energy transfer trend seems to be independent of the initial wave energies of the interacting waves. A detailed numerical analysis shows that when a gravity wave is excited by resonant interaction, its energy continuously grows up from 0 J to a considerable level (5.44 Â 10 5 J). This process is irreversible rather than periodic and will be finished within a characteristic time (15 hours for the presented case). More simulation examples are also carried out to study the effects of the small initial amplitudes and wavelengths on the energy exchange, which shows that although the characteristic time is not sensitive to the small initial amplitudes, it depends on the wavelengths, and both the initial amplitudes and wavelengths can affect the net wave energy exchange of the resonant interaction.INDEX TERMS: 3334

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Section: Analyses Of the Computation Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Numerical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A numerical study on the propagation and evolution of resonant interacting gravity waves

Zhang¹

2004

J. Geophys. Res.

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“…Although is based essentially on the linear gravity wave theory, according to Zhang et al [2000], it can still be feasible in the nonlinear circumstance they considered. Fritts [1984] provided a measure of the importance of nonlinearity by considering the ratio of the horizontal perturbation velocity ( u′ ) to the horizontal phase speed ( c ) of the wave.…”

Section: Introductionmentioning

confidence: 99%

Numerical modeling of a gravity wave packet ducted by the thermal structure of the atmosphere

Hickey

2007

J. Geophys. Res.

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[1] A time-dependent and fully nonlinear numerical model is employed to solve the Navier-Stokes equations in two spatial dimensions and to describe the propagation of a Gaussian gravity wave packet generated in the troposphere. A Fourier spectral analysis is used to analyze the frequency power spectra of the wave packet, which propagates through and dwells within several thermal ducting regions. The frequency power spectra of the wave packet are derived at several discrete altitudes, which allow us to determine the evolution of the packet. This spectral analysis also clearly reveals the existence of a stratospheric duct, a mesospheric and lower thermospheric duct, and a duct lying between the tropopause and the lower thermosphere. In addition, we determine the spatially localized wave kinetic energy density and the horizontally averaged, time-resolved, normalized vertical velocity. Examination of these diagnostic variables allows us to better understand the process of wave ducting and the vertical transport of wave energy among multiple thermal ducts. The spectral analysis allows us to unambiguously identify the ducted wave modes. These results compare favorably with those derived from a full-wave model.Citation: Yu, Y., and M. P. Hickey (2007), Numerical modeling of a gravity wave packet ducted by the thermal structure of the atmosphere,

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A numerical study of propagation characteristics of gravity wave packets propagating in a dissipative atmosphere

Zhang

2002

J.‐Geophys.‐Res.

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[1] By using a two-dimensional, full-implicit-continuous-Eulerian (FICE) scheme, we simulated the nonlinear propagation and evolution of gravity wave packets in a compressible, nonisothermal and dissipative atmosphere. The numerical results show that when an upgoing gravity wave packet is generated in the lower mesosphere, it can propagate along its ray path until it reaches lower thermosphere. However, upon reaching the lower thermosphere, the wave packet and associated energy propagate almost horizontally, which departs obviously from the prediction of linear gravity wave theory under WKB approximation in the nondissipative case. Further discussion indicates that the influences of nonlinearity and background temperature are not strong enough to restrict completely the upward energy propagation of the wave packet and that the influence of constant molecular viscosity on the characteristics (energy propagation path and wave parameters) of gravity waves is insignificant. It is the vertical inhomogeneity of molecular viscosity that causes the restriction of upward energy propagation of the gravity wave packet. Moreover, throughout propagation, the dominant vertical wavelength of the wave packet decreases with time, as it is affected by the joint actions of nonlinearity, background temperature, and dissipation. These results indicate that the molecular viscosity, especially the vertical inhomogeneity of molecular viscosity, plays an important role in the nonlinear propagation of gravity wave packets.

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The nonlinear effects on the characteristics of gravity wave packets: dispersion and polarization relations

Cited by 4 publications

References 16 publications

A numerical study on the propagation and evolution of resonant interacting gravity waves

A numerical study on the propagation and evolution of resonant interacting gravity waves

Numerical modeling of a gravity wave packet ducted by the thermal structure of the atmosphere

A numerical study of propagation characteristics of gravity wave packets propagating in a dissipative atmosphere

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