scholarly journals Geostrophic Adjustment for Reversibly Staggered Grids

2005 ◽  
Vol 133 (5) ◽  
pp. 1119-1128 ◽  
Author(s):  
John L. McGregor
Keyword(s):  
Shallow Water ◽  
Gravity Wave ◽  
Shallow Water Equations ◽  
Geostrophic Adjustment ◽  
Staggered Grids ◽  
Dispersion Properties ◽  
Dispersion Behavior ◽  
Interpolation Procedure ◽  
Meteorological Modeling

Abstract A technique is presented for meteorological modeling in which all variables are held on an unstaggered grid, but the winds are transformed to a staggered C grid for the gravity wave calculations. An important feature is the use of a new reversible interpolation procedure for the staggering–unstaggering of the winds. This reversible procedure has excellent dispersion properties for geostrophic adjustment of the linearized shallow-water equations, being generally superior to those of the A, B, and C grids. Its dispersion behavior is generally similar to that of the unstaggered Z grid of Randall, which carries divergence and vorticity as primary variables. The scheme has fewer computational overheads than the Z grid.

scholarly journals A Finite-Volume Grid Using Multimoments for Geostrophic Adjustment

2006 ◽  
Vol 134 (9) ◽  
pp. 2515-2526 ◽  
Author(s):  
F. Xiao ◽  
X. D. Peng ◽  
X. S. Shen
Keyword(s):  
Shallow Water ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Shallow Water Equations ◽  
Control Volume ◽  
Numerical Dispersion ◽  
Geostrophic Adjustment ◽  
Simple Formulation ◽  
Volume Method

Abstract This paper presents a novel finite-volume grid that uses not only the volume-integrated average (VIA) like the traditional finite-volume method, but also the surface-integrated average (SIA) as the model variables. The VIA and SIA are generically called “moments” in the context used here and are carried forward in time separately as the prognostic quantities. With the VIA defined in the control volume while the SIA is on the surface of the control volume, the discretization based on VIA and SIA leads to some new features in the numerical dispersions. A simple formulation using both VIA and SIA for shallow-water equations is presented. The numerical dispersion of the resulting grid, which is denoted as the “M grid,” is discussed with comparisons to the existing ones.

scholarly journals Implicit and time reversible CABARET schemes for quasilinear shallow water equations

2016 ◽  
pp. 402-414
Author(s):  
В.М. Головизнин ◽  
Д.Ю. Горбачев ◽  
А.М. Колокольников ◽  
П.А. Майоров ◽  
П.А. Майоров ◽  
...  
Keyword(s):  
Difference Scheme ◽  
Numerical Solution ◽  
Shallow Water ◽  
Riemann Problem ◽  
Shallow Water Equations ◽  
Unconditionally Stable ◽  
One Dimensional ◽  
Dispersion Properties ◽  
The One ◽  
Stable Scheme

Предложена новая неявная безусловно устойчивая схема для одномерных уравнений мелкой воды, сохраняющая все особенности явной схемы Кабаре. Проведен анализ диссипативных и дисперсионных свойств новой схемы и предложен алгоритм ее численного решения. Приведены примеры решения задачи о распаде разрыва. A new implicit unconditionally stable scheme for the one-dimensional shallow water equations is proposed. This implicit scheme retains all the features of the explicit CABARET (Compact Accurately Boundary Adjusting-REsolution Technique) difference scheme. Dissipative and dispersion properties of this new scheme are analyzed; an algorithm of its numerical solution is discussed. Some examples of solving the Riemann problem are considered.

A Consistent Theory for Linear Waves of the Shallow-Water Equations on a Rotating Plane in Midlatitudes

2007 ◽  
Vol 37 (1) ◽  
pp. 115-128 ◽  
Author(s):  
Nathan Paldor ◽  
Shira Rubin ◽  
Arthur J. Mariano
Keyword(s):  
Dispersion Relation ◽  
Eigenvalue Problem ◽  
Shallow Water ◽  
Gravity Wave ◽  
Classical Theory ◽  
Shallow Water Equations ◽  
Phase Speed ◽  
Planetary Waves ◽  
Wave Phase ◽  
Linear Waves

Abstract The present study provides a consistent and unified theory for the three types of linear waves of the shallow-water equations (SWE) in a zonal channel on the β plane: Kelvin, inertia–gravity (Poincaré), and planetary (Rossby). The new theory is formulated from the linearized SWE as an eigenvalue problem that is a variant of the classical Schrödinger equation. The results of the new theory show that Kelvin waves exist on the β plane with vanishing meridional velocity, as is the case on the f plane, without any change in the dispersion relation, while the meridional structure of their height amplitude is trivially modified from exponential on the f plane to a one-sided Gaussian on the β plane. Similarly, inertia–gravity waves are only slightly modified in the new theory in comparison with their characteristics on the f plane. For planetary waves (which exist only on the β plane) the new theory yields a similar dispersion relation to the classical theory only for large gravity wave phase speed, such as those encountered in a barotropic ocean or an equivalent barotropic atmosphere. In contrast, for low gravity wave phase speed, for example, those in an equivalent barotropic ocean where the relative density jump at the interface is 10−3, the phase speed of planetary waves in the new theory is 2 times those of the classical theory. The ratio between the phase speeds in the two theories increases with channel width. This faster phase propagation is consistent with recent observation of the westward propagation of crests and troughs of sea surface height made by the altimeter aboard the Ocean Topography Experiment (TOPEX)/Poseidon satellite. The new theory also admits inertial waves, that is, waves that oscillate at the local inertial frequency, as a genuine solution of the eigenvalue problem.

MAPPING TIDAL CURRENTS AND RESIDUAL CURRENTS BY USE OF COASTAL ACOUSTIC TOMOGRAPHY

2017 ◽  
Author(s):  
Xiao-Hua Zhu ◽  
Xiao-Hua Zhu ◽  
Ze-Nan Zhu ◽  
Ze-Nan Zhu ◽  
Xinyu Guo ◽  
...  
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Mean Amplitude ◽  
Momentum Equation ◽  
Tidal Currents ◽  
Acoustic Tomography ◽  
Mean Values ◽  
Residual Currents ◽  
Water Depths ◽  
Deep Area

A coastal acoustic tomography (CAT) experiment for mapping the tidal currents in the Zhitouyang Bay was successfully carried out with seven acoustic stations during July 12 to 13, 2009. The horizontal distributions of tidal current in the tomography domain are calculated by the inverse analysis in which the travel time differences for sound traveling reciprocally are used as data. Spatial mean amplitude ratios M2 : M4 : M6 are 1.00 : 0.15 : 0.11. The shallow-water equations are used to analyze the generation mechanisms of M4 and M6. In the deep area, velocity amplitudes of M4 measured by CAT agree well with those of M4 predicted by the advection terms in the shallow water equations, indicating that M4 in the deep area where water depths are larger than 60 m is predominantly generated by the advection terms. M6 measured by CAT and M6 predicted by the nonlinear quadratic bottom friction terms agree well in the area where water depths are less than 20 m, indicating that friction mechanisms are predominant for generating M6 in the shallow area. Dynamic analysis of the residual currents using the tidally averaged momentum equation shows that spatial mean values of the horizontal pressure gradient due to residual sea level and of the advection of residual currents together contribute about 75% of the spatial mean values of the advection by the tidal currents, indicating that residual currents in this bay are induced mainly by the nonlinear effects of tidal currents.

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