Exact solutions of the vorticity equation on the sphere as a manifold

Abstract

RESUMENEl propósito de este trabajo es representar las soluciones exactas de la ecuación de vorticidad barotrópica sobre la esfera unitaria S 2 en rotación soluciones generalizadas llamadas modones. Se relacionan los métodos modernos de la teoría de funciones correcta, se esclarece la noción abstracta de mapa local, cambio de mapa y atlas. Uno de los objetivos de este trabajo es entender mejor la solución de la ecuación de vorticidad barotrópica sobre la variedad S 2 y su S 2 , g). Por lo tanto, estará disponible un tipo más general de espacio que también puede contener información geométrica y analítica sustancial sobre las soluciones a la ecuación de vorticidad barotrópica. ABSTRACTThe purpose of this paper is to represent the exact solutions of the barotropic vorticity equations (BVE) on the rotating unit sphere S 2 -ferentiable manifold. When the differentiable manifold S 2 is well understood, the abstract notion of local chart, change of chart, and atlases becomes evident. One of the aims of this paper is to better understand the solution of the barotropic vorticity equation on the manifold S 2 and its usefulness to identify the properties of the solutions on the Riemannian manifold (S 2 , g). Therefore, a more general type of space will be available, which can also contain substantial geometric and analytic information about solutions for the barotropic vorticity equation.

Connections in the development of tropical cyclone Mitch (1998): A tribute to the human loss in this calamity

“…where −ωμ is a solid body rotation and d is constant (Pérez-García, 2015). The following is a solution for Eq.…”

“…Using a grid of 5 × 5º on the local coordinate associated with the chart (λ', μ'), the Verkley (1984) modon was generated numerically (Pérez-García and Skiba, 1999;Pérez-García, 2015). This modon solution was built with the following parameters: k = 10, α = 10, α a = sin(66.14º), μ 0 = sin (10º), λ 0 = 270º and d 0 = 0.…”

Vorticity Gramian of Compact Riemannian Manifolds

“…It constructed numerical algorithms of covariant, anti-covariant metric tensor and Christoffel symbols of the first and second kinds in curvilinear coordinates. Similarly, Perez-Garcia [24] studied exact solutions of the vorticity equation on the sphere as a manifold. In the work of Peng and Yang [23], the existence of the curl operator on higher dimensional Euclidean space, R n , n > 3, was proved.…”