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Full-Text Articles in Physical Sciences and Mathematics
The Shallow Water Equations In Lagrangian Coordinates, J. L. Mead
The Shallow Water Equations In Lagrangian Coordinates, J. L. Mead
Jodi Mead
Recent advances in the collection of Lagrangian data from the ocean and results about the well-posedness of the primitive equations have led to a renewed interest in solving flow equations in Lagrangian coordinates. We do not take the view that solving in Lagrangian coordinates equates to solving on a moving grid that can become twisted or distorted. Rather, the grid in Lagrangian coordinates represents the initial position of particles, and it does not change with time. However, using Lagrangian coordinates results in solving a highly nonlinear partial differential equation. The nonlinearity is mainly due to the Jacobian of the coordinate …
Assimilation Of Simulated Float Data In Lagrangian Coordinates, J. L. Mead
Assimilation Of Simulated Float Data In Lagrangian Coordinates, J. L. Mead
Jodi Mead
We implement an approach for the accurate assimilation of Lagrangian data into regional general ocean circulation models. The forward model is expressed in Lagrangian coordinates and simulated float data are incorporated into the model via four dimensional variational data assimilation. We show that forward solutions computed in Lagrangian coordinates are reliable for time periods of up to 100 days with phase speeds of 1 m/s and deformation radius of 35 km. The position and depth of simulated floats are assimilated into the viscous, Lagrangian shallow water equations. The weights for the errors in the model and data are varied and …