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Published byAlexis Allen Modified over 2 years ago

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Large-scale motions in the ocean and the atmosphere case of stable stratification (ocean, stratosphere)

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Characteristics of large-and meso-scale ocean flows ( 10 km < L < 6000 km ) : Thin layer of fluid: H << L Stable stratification Importance of Earths rotation T rot < T dyn Ro = = T rot / T dyn = U/2 L<1

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Apparent forces in a rotating frame with = z

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Navier-Stokes equations in a rotating frame with = z

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Navier-Stokes equations in a rotating frame with = z

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Navier-Stokes in a rotating frame with = z

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Boussinesq approximation

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Thin layer, stable stratification: hydrostatic approximation (L > 10 km)

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Incompressible, hydrostatic fluid: primitive equations

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Problem: A spherical Earth. Motion on a sphere: local tangent plane

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Incompressible, inviscid fluid on a local Cartesian plane at midlatitudes

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Problema: lapprossimazione geostrofica è diagnostica abbiamo bisogno di una approssimazione prognostica

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Primitive equations on a local Cartesian plane at midlatitudes

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Primitive equations on the beta plane

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Primitive equations on the beta plane

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