In numerical model simulations of global-scale circulations, it is often more convenient to express the governing equati
Posted: Wed May 18, 2022 4:37 pm
- In Numerical Model Simulations Of Global Scale Circulations It Is Often More Convenient To Express The Governing Equati 1 (225.9 KiB) Viewed 46 times
In numerical model simulations of global-scale circulations, it is often more convenient to express the governing equations in spherical coordinates. When doing so, the surface of the Earth becomes a coordinate surface. However, when viewing motions on the spherical coordinate surface, the (x,y,z) system of coordinates is no longer Cartesian because the unit vectors, i, j, k are not constant. When the changes in the unit vectors are accounted for, additional curvature terms arise in the momentum equations. Show that the components of the motion equation in spherical coordinates take the following form: du uvtang 1 др UW + a +fv – 222wcose + Fr dt a рдх 1 др dy u2tanº + + dt VW = a - fu+F, a рду dw u2 + y2 1 dp = - 8 + 292ucoso + F, - dt a p dz