Exact planetary waves and jet streams.

The article "Exact planetary waves and jet streams" delves into the study of nonlinear waves on surfaces resembling a rotating sphere for two-dimensional inviscid incompressible flow. It examines exact wave solutions in the Lagrangian reference frame within the β-plane and γ-approximation systems, showcasing non-trivial Lagrangian mean flow akin to polar jet streams. Through numerical experiments, the research investigates the temporal evolution of these waves and their connection to vorticity, shedding light on atmospheric dynamics and climate studies. The text also discusses the derivation of governing equations for two-dimensional flow on a sphere using stereographic coordinates and β and γ approximations, highlighting the stability and symmetry of vortex waves on the sphere. [Extracted from the article]