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Sverdrup relation in 1 and 1/2 layer model

Explore the Sverdrup relation in a 1 and 1/2 layer model for the western boundary layer. Understand the role of upper layer thickness, geostrophic flow, reduced gravity, and wind stress forcing. Analyze the impact of boundary layer dynamics on transport and potential vorticity conservation.

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Sverdrup relation in 1 and 1/2 layer model

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  1. Sverdrup relation in 1 and 1/2 layer model Where D is the upper layer thickness v1 is the geostrophic flow in the upper layer g’ is the reduced gravity

  2. Integrating over the basin outside the western boundary layer Under an anticyclone wind stress forcing (independent of y) and assume The magnitude of Do is determined by 

  3. Inertial western Boundary Layer Assume that a western boundary layer extends from x=0, where D=Db~0, to x=W, where D=D0, the total transport should be

  4. Outside the boundary layer Inside the boundary layer  The conservation of potential vorticity requires Rossby radius of deformation

  5. Let We have These parameters are in right magnitudes  

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