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This reading explores the concepts of advection, transport budgets, and flux in the context of heat and salt transport in the ocean. Topics covered include the surface heat balance, Gulf Stream advection, diffusion by eddies, continuity, and conservation of volume, salt, and freshwater. Adapted from Dr. Lynne Talley’s SIO class notes.
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MAST602: Advection, transports, budgets Reading: Knauss Chapter 4 Flux, transport Radiation, Advection, Diffusion Conservation of volume Continuity Conservation of salt Freshwater transport Heat budget Heat transport Adapted from Dr. Lynne Talley’s SIO class notes
Transport processes In lieu of an animation, pretend that this is animated. (1) The surface heat balance, including radiation, makes the ocean warmer to the south. (2) The Gulf Stream flows northward, advectting warm water. (3) Eddies diffuse the heat.
Transport Velocity times concentration integrated (summed) over area normal to the velocity (same as Flux normal to an area integrated over that area.) Flux of a property Velocity times concentration (same as Transport per unit area) Flux and transport
Transport definitions • Volume = integral of velocity v m3/sec • Mass = integral of density x velocity v kg/sec • Heat = integral of heat x velocity cpTv J/sec=W • Salt = integral of salt x velocity Sv kg/sec • Freshwater = integral of Fwater x velocity (1-S)v kg/sec • Chemical tracers = integral of tracer x velocity Cv moles/sec • Where “integral” is the over the area normal to the velocity • Flux is just these quantities per unit area
Conservation of volume, salt and freshwater • (1) Mass conservation: oVo - i Vi = (R + AP) - AE F • (2) Salt conservation: Vii Si = Vo o So • (3) F = i Vi (Si /So - 1) or F = o Vo (1 – So /Si ) • (4) Also from (2), Vii Si /Sm = Vo o So / Sm where Sm is a mean salinity, so • (5) F = i Vi (1- Si /Sm ) - o Vo (1 - So / Sm) which is useful if we have to assume that i Vi ~ o Vo given error in observations
Mediterranean and Black Seas Evaporative basin Runoff/precipitation