The development of a Lagrangian Particle Method (LPM) for geophysical applications is discussed for various problems including tracer transport, vor- ticity dynamics in rotating flow, and shallow water gravity waves. The LPM is based on Vortex Methods, numerical techniques developed for incompressible flow that rely on the point vortex approximation. A Poisson equation relates the stream function to vorticity and is solved using a Green’s function integral. Velocity is computed from the related Biot-Savart integral and a quadrature scheme on a finite set of moving particles (point vortices). A new remapping procedure is applied at regular time intervals to maintain spatial accuracy and minimize error due to particle distortion. Particles are inserted and removed adaptively to maintain resolution of the flow as small-scale features develop. The challenge of extending these techniques to flows with nonzero velocity di- vergence using Particle Strength Exchange (PSE) is discussed. Examples and solutions are presented for planar and spherical geometries and include trans- port in deformational flow, Rossby-Haurwitz waves, Gaussian vortices, and the interaction of gravity waves with topography.

 

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