A general numerical method for the solution of gravity wave problems. Part 1: 2D steep gravity waves in shallow water

1991 ◽  
Vol 12 (8) ◽  
pp. 727-745 ◽  
Author(s):  
S. J. Liao
Keyword(s):  
Shallow Water ◽  
Numerical Method ◽  
Gravity Wave ◽  
Gravity Waves ◽  
Wave Problems

Cyclone–anticyclone asymmetry in gravity wave radiation from a co-rotating vortex pair in rotating shallow water

2015 ◽  
Vol 772 ◽  
pp. 80-106 ◽  
Author(s):  
Norihiko Sugimoto ◽  
K. Ishioka ◽  
H. Kobayashi ◽  
Y. Shimomura
Keyword(s):  
Shallow Water ◽  
Gravity Wave ◽  
Gravity Waves ◽  
Water System ◽  
Local Maximum ◽  
Vortex Pair ◽  
Wave Radiation ◽  
Earth’S Rotation ◽  
Far Field ◽  
Earth's Rotation

Cyclone–anticyclone asymmetry in spontaneous gravity wave radiation from a co-rotating vortex pair is investigated in an $f$-plane shallow water system. The far field of gravity waves is derived analytically by analogy with the theory of aeroacoustic sound wave radiation (Lighthill theory). In the derived form, the Earth’s rotation affects not only the propagation of gravity waves but also their source. While the results correspond to the theory of vortex sound in the limit of $f\rightarrow 0$, there is an asymmetry in gravity wave radiation between cyclone pairs and anticyclone pairs for finite values of $f$. Anticyclone pairs radiate gravity waves more intensely than cyclone pairs due to the effect of the Earth’s rotation. In addition, there is a local maximum of intensity of gravity waves from anticyclone pairs at an intermediate $f$. To verify the analytical solution, a numerical simulation is also performed with a newly developed spectral method in an unbounded domain. The novelty of this method is the absence of wave reflection at the boundary due to a conformal mapping and a pseudo-hyperviscosity that acts like a sponge layer in the far field of waves. The numerical results are in excellent agreement with the analytical results even for finite values of $f$ for both cyclone pairs and anticyclone pairs.

scholarly journals Influence of the cloud-level neutral layer on the vertical propagation of topographically generated gravity waves on Venus

2019 ◽  
Vol 71 (1) ◽  
Author(s):  
Takeru Yamada ◽  
Takeshi Imamura ◽  
Tetsuya Fukuhara ◽  
Makoto Taguchi
Keyword(s):  
Layer Thickness ◽  
Gravity Wave ◽  
Local Time ◽  
Gravity Waves ◽  
Analytical Approach ◽  
Wave Activity ◽  
Neutral Layer ◽  
Low Latitudes ◽  
Vertical Propagation ◽  
The Waves

AbstractThe reason for stationary gravity waves at Venus’ cloud top to appear mostly at low latitudes in the afternoon is not understood. Since a neutral layer exists in the lower part of the cloud layer, the waves should be affected by the neutral layer before reaching the cloud top. To what extent gravity waves can propagate vertically through the neutral layer has been unclear. To examine the possibility that the variation of the neutral layer thickness is responsible for the dependence of the gravity wave activity on the latitude and the local time, we investigated the sensitivity of the vertical propagation of gravity waves on the neutral layer thickness using a numerical model. The results showed that stationary gravity waves with zonal wavelengths longer than 1000 km can propagate to the cloud-top level without notable attenuation in the neutral layer with realistic thicknesses of 5–15 km. This suggests that the observed latitudinal and local time variation of the gravity wave activity should be attributed to processes below the cloud. An analytical approach also showed that gravity waves with horizontal wavelengths shorter than tens of kilometers would be strongly attenuated in the neutral layer; such waves should originate in the altitude region above the neutral layer.

Semi-Lagrangian exponential time-integration method for the shallow water equations on the cubed sphere grid

2020 ◽  
Vol 35 (6) ◽  
pp. 355-366
Author(s):  
Vladimir V. Shashkin ◽  
Gordey S. Goyman
Keyword(s):  
Shallow Water ◽  
Gravity Waves ◽  
Shallow Water Equations ◽  
Time Integration ◽  
Standard Test ◽  
Integration Scheme ◽  
Test Problems ◽  
Cubed Sphere ◽  
Lagrangian Scheme ◽  
Inertia Gravity Waves

AbstractThis paper proposes the combination of matrix exponential method with the semi-Lagrangian approach for the time integration of shallow water equations on the sphere. The second order accuracy of the developed scheme is shown. Exponential semi-Lagrangian scheme in the combination with spatial approximation on the cubed-sphere grid is verified using the standard test problems for shallow water models. The developed scheme is as good as the conventional semi-implicit semi-Lagrangian scheme in accuracy of slowly varying flow component reproduction and significantly better in the reproduction of the fast inertia-gravity waves. The accuracy of inertia-gravity waves reproduction is close to that of the explicit time-integration scheme. The computational efficiency of the proposed exponential semi-Lagrangian scheme is somewhat lower than the efficiency of semi-implicit semi-Lagrangian scheme, but significantly higher than the efficiency of explicit, semi-implicit, and exponential Eulerian schemes.

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

2000 ◽  
Vol 18 (10) ◽  
pp. 1316-1324 ◽  
Author(s):  
S.-D. Zhang ◽  
F. Yi ◽  
J.-F. Wang
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
Middle Atmosphere ◽  
Wave Packets ◽  
Nonlinear Effects ◽  
Wave Theory ◽  
Nonlinear Propagation ◽  
Waves And Tides ◽  
Time Variations ◽  
Isothermal Atmosphere

Abstract. By analyzing the results of the numerical simulations of nonlinear propagation of three Gaussian gravity-wave packets in isothermal atmosphere individually, the nonlinear effects on the characteristics of gravity waves are studied quantitatively. The analyses show that during the nonlinear propagation of gravity wave packets the mean flows are accelerated and the vertical wavelengths show clear reduction due to nonlinearity. On the other hand, though nonlinear effects exist, the time variations of the frequencies of gravity wave packets are close to those derived from the dispersion relation and the amplitude and phase relations of wave-associated disturbance components are consistent with the predictions of the polarization relation of gravity waves. This indicates that the dispersion and polarization relations based on the linear gravity wave theory can be applied extensively in the nonlinear region.Key words: Meteorology and atmospheric dynamics (middle atmosphere dynamics; waves and tides)

scholarly journals GRAVITY-WAVE DETECTORS AS PROBES OF EXTRA DIMENSIONS

2005 ◽  
Vol 14 (12) ◽  
pp. 2347-2353 ◽  
Author(s):  
CHRIS CLARKSON ◽  
ROY MAARTENS
Keyword(s):  
Black Holes ◽  
String Theory ◽  
Gravity Wave ◽  
Gravity Waves ◽  
Extra Dimensions ◽  
State Of The Art ◽  
Three Dimensional ◽  
Observable Universe ◽  
Dimensional Spacetime ◽  
Higher Dimensional

If string theory is correct, then our observable universe may be a three-dimensional "brane" embedded in a higher-dimensional spacetime. This theoretical scenario should be tested via the state-of-the-art in gravitational experiments — the current and upcoming gravity-wave detectors. Indeed, the existence of extra dimensions leads to oscillations that leave a spectroscopic signature in the gravity-wave signal from black holes. The detectors that have been designed to confirm Einstein's prediction of gravity waves, can in principle also provide tests and constraints on string theory.

Asymptotic stability of a polar vortex perturbed by harmonic waves describing atmospheric gravity waves circulating in an equatorial plane of a spherical planet

2018 ◽  
Vol 13 (4) ◽  
pp. 36
Author(s):  
Ranis Ibragimov ◽  
Pirooz Mohazzabi ◽  
Rebecca Roembke ◽  
Justin Van Ee
Keyword(s):  
Shallow Water ◽  
Gravity Waves ◽  
Equatorial Plane ◽  
Polar Vortex ◽  
Water Model ◽  
Large Radius ◽  
Atmospheric Gravity Waves ◽  
Nonstationary Motion ◽  
Two Parameters ◽  
Atmospheric Gravity

We examine stability of the vortex that represents one particular class of exact solution of a a nonlinear shallow water model describing atmospheric gravity waves circulating in an equatorial plane of a spherical planet. The mathematical model is represented by a two-dimensional free boundary Cauchy–Poisson problem on the nonstationary motion of a perfect uid around a solid circle with a sufficiently large radius so that the gravity is directed to the center of the circle. It is shown that the model admits two functionally independent nonlinear systems of shallow water equations. Two essential parameters that control stability of the vortex for both systems are identified. The order of their importance is analyzed and it is shown that one of the systems is more resistant to small perturbations and remains stable for larger range of these two parameters.

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