scholarly journals Shallow water gravity waves: A note on the particle orbits

1996 ◽  
Vol 52 (3) ◽  
pp. 353-357 ◽  
Author(s):  
Kern E. Kenyon
Keyword(s):  
Shallow Water ◽  
Gravity Waves ◽  
Particle Orbits

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.

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.

Simulation of resonant gravity waves in shallow water flows using a depth-averaged URANS model

2020 ◽  
pp. 1097-1103
Author(s):  
A. Navas-Montilla ◽  
C. Juez ◽  
M.J. Franca ◽  
J. Murillo
Keyword(s):  
Shallow Water ◽  
Gravity Waves ◽  
Water Flows ◽  
Shallow Water Flows

scholarly journals Internal Acoustic Gravity Waves

1968 ◽  
Vol 23 (10) ◽  
pp. 1459-1470
Author(s):  
Alden Mclellan ◽  
F. Winterberg
Keyword(s):  
Fluid Dynamics ◽  
Dispersion Relation ◽  
Gravity Waves ◽  
Wave Motion ◽  
Ideal Gas ◽  
Acoustic Gravity Waves ◽  
Dissipative Effects ◽  
Isothermal Medium ◽  
Particle Orbits ◽  
Penetration Depths

An exhaustive analysis of wave motion in a compressible isothermal medium under the influence of gravity is presented. The dispersion relation governing the wave propagation is derived from the linearized equations of fluid dynamics and thermodynamics, and it is arranged in a nondimensional form. Penetration depths, frequency cutoffs, and particle orbits are calculated under the assumption of an ideal gas. With the nondimensional form of the dispersion relation these data can be expressed in a form independent of the constants describing a particular atmosphere. The results can be conventiently displayed on a number of diagrams valid for monatomic and diatomic gases. Dissipative effects arising from viscosity and heat conduction are neglected.

scholarly journals Correction of shallow-water electromagnetic data for noise induced by instrument motion

Geophysics ◽  
2005 ◽  
Vol 70 (5) ◽  
pp. G127-G133 ◽  
Author(s):  
Pamela F. Lezaeta ◽  
Alan D. Chave ◽  
Rob L. Evans
Keyword(s):  
Shallow Water ◽  
Gravity Waves ◽  
Noise Source ◽  
Slave Craton ◽  
Electromagnetic Data ◽  
Lake Bottom ◽  
Correlation Noise ◽  
Hydrodynamic Effects ◽  
The Magnetic Field ◽  
Direct Induction

An unexpected noise source has been found in magnetic- and sometimes electric-field data recorded on the bottom of lakes in the Archean Slave craton (northwestern Canada) during warm seasons. The noise is the result of instrument motion and in some instances direct induction by wind-driven surface gravity waves when the lakes are not ice covered. The noise can be reduced or eliminated by prefiltering the data with an adaptive correlation noise-canceling filter using instrument tilt records prior to estimation of magnetotelluric (MT) response functions. Similar effects are to be expected in other shallow-water environments, and the adaptive correlation canceler is a suitable method to preprocess MT data to reduce motion-related noise in the magnetic field. This underscores the importance of ancillary tilt measurements in shallow-water MT surveys. In coastal or lake-bottom surveys, special efforts to reduce hydrodynamic effects on the instrument should also be pursued.

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