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 p and  surfaces are parallel

Barotropic flow:.  p and  surfaces are parallel. For a barotropic flow, we have. is geostrophic current. Since. . Given a barotropic and hydrostatic conditions,. and. Therefore,. By definition,   and  t are both constant in barotropic flow. And. So.

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 p and  surfaces are parallel

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  1. Barotropic flow:  p and  surfaces are parallel For a barotropic flow, we have is geostrophic current. Since  Given a barotropic and hydrostatic conditions, and Therefore, By definition,  and t are both constant in barotropic flow And So (≈0 in Boussinesq approximation) The slope of isopycnal is small and undetectable (as isobar) for V=0.1 m/s, slope~10-6, i.e., 0.1m height change in 100 km

  2. Relations between isobaric and isopycnal surfaces and currents Baroclinic Flow: and There is no simple relation between the isobars and isopycnals. slope of isobar is proportional to velocity slope of isopycnal is proportional to vertical wind shear. With a barotropic of mass the water may be stationary but with a baroclinic field, having horizontal density gradients, such as situation is not possible In the ocean, the barotropic case is most common in deep water while the baroclinic case is most common in the upper 1000 meters where most of the faster currents occur.

  3. 1 and 1/2 layer flow Simplest case of baroclinic flow: Two layer flow of density 1 and 2. The sea surface height is =(x,y) (In steady state, =0). The depth of the upper layer is at z=d(x,y)<0. The lower layer is at rest. For z > d, For z ≤ d, If we assume  The slope of the interface between the two layers (isopycnal)= times the slope of the surface (isobar). The isopycnal slope is opposite in sign to the isobaric slope.

  4. σt A B diff 26.8 50m --- >50m 27.0 130m 280m -150m 27.7 579m 750m -180m Isopycnals are nearly flat at 100m Isobars ascend about 0.13m between A and B for upper 150m Below 100m, isopycnals and isobars slope in opposite directions with 1000 times in size.

  5. Relation between fluctuations of SSH () and thermocline depth (h) 20oC isotherm anomalies (m) COLA ODA December,1997-February, 1998 SSH anomalies (cm) TOPEX/Poseidon

  6. Example: sea surface height and thermocline depth

  7. Comments on the geostrophic equation • If the ocean is in “real” geostrophy, there is no water parcel acceleration. No other forces acting on the parcel. Current should be steady • Present calculation yields only relative currents and the selection of an appropriate level of no motion always presents a problem • One is faced with a problem when the selected level of no motion reaches the ocean bottom as the stations get close to shore • It only yields mean values between stations which are usually tens of kilometers apart • Friction is ignored • Geostrophy breaks down near the equator (within 0.5olatitude, or ±50km) • The calculated geostrophic currents will include any long-period transient current

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