MAST602: Advection, transports, budgets

Flux, transport

Radiation, Advection, Diffusion

Conservation of volume

Continuity

Conservation of salt

Freshwater transport

Heat budget

Heat transport

Reading: Knauss Chapter 4

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.

Continuity

Flux and transport

• 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)

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: Vi i Si = Vo o So

• (3) F = i Vi (Si /So - 1) or F = o Vo (1 – So /Si )

• (4) Also from (2), Vi i 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