A Spectral Numerical Solution of Navier-Stokes Equations in a 3-Dimensional Spherical Coordinate System

Aiming at numerically studying the global nonlinear propagation of atmospheric tides,a new fully nonlinear numerical model in a three dimensional spherical coordinates is established.In the construction of the numerical model,the spectral allocation method was used to numerically resolve the Navier-Stokes equations,which was taking as the governing equations.In the specification of the boundary conditions,periodic and projected characteristic line boundaries are chosen as the zonal and vertical boundaries,respectively;moreover,the polar boundary are also carefully specified.For the purpose of examining our newly established model,the global nonlinear propagation of a gravity-wave packet with large scales is simulated and compared with a previou simulation.The calculation result exhibits the essential characteristics of the nonlinear propagation of a gravity-wave packet in atmosphere:the whole wave packet propagates upward and the wave-associated disturbance velocity increases with the increasing height,which is quantitatively consistent with the previous simulation.These suggested that our numerical model and the nonlinear simulation are reliable.