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Integration of the Nondivergent Barotropic Vorticity Equation with AN Icosahedral-Hexagonal Grid for the SPHERE1
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In this paper, a finite difference scheme was developed for numerical integration of the nonsmooth barotropic vorticity equation with an icosahedral-hexagonal grid covering the sphere. But the grid is made by dividing the 20 triangular faces of the icosahedron into smaller triangles, the vertices of which are the grid points.Abstract:
A finite difference scheme is developed for numerical integration of the nondivergent barotropic vorticity equation with an icosahedral-hexagonal grid covering the sphere. The grid is made by dividing the 20 triangular faces of an icosahedron into smaller triangles, the vertices of which are the grid points. Each grid point is surrounded by six neighboring points, except the 12 vertices of the icosahedron which are surrounded by five points. The difference scheme for the advection of vorticity exactly conserves total vorticity, total square vorticity, and total kinetic energy. A numerical test is made, with a stationary Neamtan wave as the initial condition, by integrating over 8 days with 1-hr. time steps and a grid of 1002 points for the sphere. There is practically no distortion of the waves over the 8 days, but there is a phase displacement error of about 1° of long. per day toward the west.read more
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References
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Journal ArticleDOI
Computational Design for Long-Term Numerical Integration of the Equations of Fluid Motion
TL;DR: In this article, it was shown that the derived form of the finite difference Jacobian can prevent nonlinear computational instability and thereby permit long-term numerical integrations, which is not the case in finite difference analogues of the equation of motion for two-dimensional incompressible flow.
Journal ArticleDOI
On the computational stability of numerical solutions of time-dependent non-linear geophysical fluid dynamics problems
TL;DR: In this article, the conservation and stability properties of the spatial differencing methods devised by Arakawa are investigated by means of spectral analysis of the stream function into finite Fourier modes.
Journal ArticleDOI
Numerical Integration of the Primitive Equations on a Spherical Grid
TL;DR: In this paper, a new spherical grid system whose grid density on the globe is almost homogeneous is proposed, and the elementary rules of finite differencing on the grid system are defined so that a desirable condition for numerical area integration is satisfied.
Journal ArticleDOI
The motion of harmonic waves in the atmosphere
TL;DR: In this article, harmonic wave solutions of the complete vorticity equation were obtained both for the plane and for the sphere, with the assumption of nondivergent horizontal flow, and these solutions yield, for the velocity of propagation of the waves, formulae which are identical in form with those obtained by Haurwitz from an approximate linearized form of the vortivity equation.
Journal ArticleDOI
A Study of Numerical Errors in the Integration of Barotropic Flow on a Spherical Grid
TL;DR: In this paper, the barotropic vorticity equation for horizontal non-ivergent flow is integrated numerically over the northern hemisphere on a spherical grid and compared with the known analytic solution for harmonic initial conditions.
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