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Home , Coriolis force, Ekman layer, Geostrophic current, Physical oceanography, Wind stress

Lecture 10: Circulation Basic Ocean Systems

Upper Ocean  -Driven Circulation surface circulation  , Transport, Pumping  Sverdrup Theory  Western

Deep Ocean

deep ocean circulation

ESS228 ESS228 Prof. Jin-Yi Yu (from “Is The Rising?”) Prof. Jin-Yi Yu

Global Surface Currents Thermohaline Conveyor Belt

(Figure from System Modeling) ESS200A (from Climate System Modeling) ESS228 Prof. Jin-Yi Yu Prof. Jin-Yi Yu

1 Six Great Current Circuits in the World Ocean Characteristics of the Gyres  5 of them are geostrophic gyres: (Figure from by Tom Garrison)  Currents are in geostropic balance  Each gyre includes 4 current components: two boundary currents: western and eastern two transverse currents: easteward and westward Western boundary current ( of ocean) the fast, deep, and narrow current moves warm Indian polarward (transport ~50 Sv or greater) Eastern boundary current the slow, shallow, and broad current moves cold  The 6th and the largest current: water equatorward (transport ~ 10-15 Sv) Circumpolr Current Trade wind-driven current the moderately shallow and broad westward (also called West Wind Drift) current (transport ~ 30 Sv) Westerly-driven current the wider and slower (than the trade wind-driven (Figure from Oceanography by Tom Garrison) Volume transport unit: current) eastward current 1 sv = 1 Sverdrup = 1 million m3/sec ESS228 ESS200A Prof. Jin-Yi Yu (the Amazon river has a transport of ~0.17 Sv) Prof. Jin-Yi Yu

Global Surface Currents Basic Systems

Upper Ocean surface circulation

Deep Ocean

deep ocean circulation

(from Climate System Modeling) ESS228 ESS228 Prof. Jin-Yi Yu (from “Is The Temperature Rising?”) Prof. Jin-Yi Yu

2 Wind-Driven (Upper Ocean) Circulation Frictional (Viscous) Surface Wind  Wind

Wind stress forcing = force + Drag force Ekman Theory

Ekman Spiral  Ekman Layer stress acting on the fluid below the box

Ekman Transport • Any real fluid is subject to internal • Stresses applied on a fluid element ()  • Force required to maintain this flow stress acting on the box from the fluid below Sverdrup Theory Sverdrup Curl  Variation in  Ekman Pumping  • Viscous force per unit due to stress

adding negative vorticity • For a layer of fluid at depth δZ, the force is   PGF (Ekman Pumping) = • Frictional force per unit mass in x-direction southward transport toward small f • Viscous force per unit area (shearing stress):  ESS228  ESS228 Geostrophic Currents; Conservation of PV  Sverdrup TransportProf. Jin-Yi Yu Prof. Jin-Yi Yu

Surface Wind Stress Step 1: Surface

Surface wind stress:

(Figure from Oceanography by Tom Garrison) ESS228 ESS228 Prof. Jin-Yi Yu Prof. Jin-Yi Yu

3 Step 2: Ekman Layer Step 3: (frictional force + Coriolis Force) ( Force + Corioils Foce)

NASA-TOPEX Observations of -Level Hight

(from Oceanography by Tom Garrison)

(Figure from Oceanography by Tom Garrison) ESS228 ESS228 Prof. Jin-Yi Yu Prof. Jin-Yi Yu

History / Wind-Driven Circulation

Step 4: Boundary Currents (from Robert H. Stewart’s book on “Introduction to ”)

30N 30N

(Figure from Oceanography by Tom Garrison) ESS228 ESS228 Prof. Jin-Yi Yu Eq Eq Prof. Jin-Yi Yu

4 Why an Angle btw Wind and Iceberg Directions? Step 1: Surface Winds

(Figure from Oceanography by Tom Garrison) ESS228 ESS228 Prof. Jin-Yi Yu (from Robert H. Stewart’s book on “Introduction to Physical OceanographyProf. Jin-Yi”) Yu

Step 2: Ekman Layer In the (frictional force + Coriolis Force) For a steady state, homogeneous Coriolis force balances boundary layer frictional force

viscosity

(Figure from Oceanography by Tom Garrison) ESS228 ESS228 Prof. Jin-Yi Yu Prof. Jin-Yi Yu

5 Frictional (Viscous) Force Surface Wind Stress

stress acting on the fluid below the box

• Any real fluid is subject to internal friction • Stresses applied on a fluid element (viscosity)  • Force required to maintain this flow stress acting on the box from the fluid below Surface wind stress:  • Viscous force per unit mass due to stress

• For a layer of fluid at depth δZ, the force is   • Frictional force per unit mass in x-direction • Viscous force per unit area (shearing stress):   ESS228 ESS228 Prof. Jin-Yi Yu Prof. Jin-Yi Yu

How Deep is the Ekman Layer? Ekman Transport

(from Climate System Modeling)  D  (/f)1/2

or  = vertical diffusivity of f = Coriolis parameter = 2sin

The thickness of the Ekman layer is arbitrary because the Ekman currents decrease (Figure from The System) exponentially with depth. Ekman proposed that the thickness be the depth DE at which the current is opposite the velocity at the surface, which occurs at a depth DE = π/a ESS228 ESS228 (from Robert H. Steward) Prof. Jin-Yi Yu Prof. Jin-Yi Yu

6 Ekman Transport and Ekman Pumping Ekman Transport  Convergence/Divergence

(Figure from The Earth System) Surface wind + Coriolis Force

Ekman Transport

Convergence/divergence (in the center of the gyre)

(from Talley 2011) Pressure Gradient Force (from The Earth System)

Geostrophic Currents

ESS228 ESS228 Prof. Jin-Yi Yu Prof. Jin-Yi Yu

Step 3: Geostrophic Current (Pressure Gradient Force + Corioils Foce) Geostrophic Current

NASA-TOPEX Geostrophic Gyre Currents Observations of Sea-Level Hight

(from Oceanography by Tom Garrison)

(Figure from The Earth System)

ESS228 ESS228 Prof. Jin-Yi Yu Prof. Jin-Yi Yu

7 Characteristics of the Gyres Ekman Transport  Convergence/Divergence (Figure from Oceanography by Tom Garrison)  Currents are in geostropic balance (Figure from The Earth System) Surface wind + Coriolis Force  Each gyre includes 4 current components: two boundary currents: western and eastern two transverse currents: easteward and westward Ekman Transport Western boundary current (jet stream of ocean) the fast, deep, and narrow current moves warm water polarward (transport ~50 Sv or greater) Convergence/divergence Eastern boundary current Thermocline (in the center of the gyre) the slow, shallow, and broad current moves cold water equatorward (transport ~ 10-15 Sv) Trade wind-driven current the moderately shallow and broad westward Pressure Gradient Force current (transport ~ 30 Sv) Westerly-driven current the wider and slower (than the trade wind-driven Volume transport unit: current) eastward current Geostrophic Currents 1 sv = 1 Sverdrup = 1 million m3/sec ESS200A ESS228 (the Amazon river has a transport of ~0.17 Sv) Prof. Jin-Yi Yu Prof. Jin-Yi Yu

Theories that Explain the Wind-Driven Ocean Circulation Sverdrup’s Theory of the Oceanic Circulation

. Harald Sverdrup (1947) showed that the circulation in the upper kilometer or so of the ocean is directly related to the curl of the wind stress if the Coriolis force varies with . . (1948) showed that the circulation in oceanic . The , or Sverdrup gyres is asymmetric also because the Coriolis force varies with relation, is a theoretical latitude. relationship between the wind stress exerted on the surface of the . (1950) added viscosity and calculated the open ocean and the vertically circulation of the upper layers of the Pacific. integrated meridional (north-south) . Together the three oceanographers laid the foundations for a transport of ocean water. modern theory of ocean circulation. . Positive wind stress curl  Northward mas transport Negative wind stress curl  Southward mass transport ESS228 ESS228 (from Robert H. Stewart’s book on “Introduction to Physical OceanographyProf. Jin-Yi”) Yu Prof. Jin-Yi Yu

8 Global Surface Currents Sverdrup Transport

vertical integration from surface (z=0) to a depth of no (z=-D).

d/dy ( ) – d/dx ( ) and use

(from Climate System Modeling) ESS228 ESS228 Prof. Jin-Yi Yu Prof. Jin-Yi Yu

Sverdrup, Geostrophic, and Ekman Transports Sverdrup, Geostrophic, and Ekman Transports

• Continuity equation for an incompressible flow: • Continuity equation for an incompressible flow: • Integrate the equation from the bottom of the upper ocean (Dw) to the bottom of the Ekman layer (DE): assume zero Ekman layer pumping  vertical depth decreases • Assume the horizontal flows are geostrophic:  move equatorward to conserve absolute • Assume the horizontal flows are geostrophic: vorticity. • Ekman pumping (ѡE) is related to the convergence of the Ekman transport: • Replace the geostrophic flow pressure gradients: • Replace the geostrophic flow pressure gradients:

• Therefore, we obtain:

Ekman layer suction  vertical depth increases • The continuity equation becomes: • The continuity equation becomes: geostrophic Sverdrup -(Ekman  move poleward to conserve absolute vorticity. transport transport Transport) • Therefore, ESS228 ESS228 Prof. Jin-Yi Yu Sverdrup transport = Geostrophic transportProf. + Jin-YiEkman Yu transport

9 Ekman and Sverdrup Transports Ekman Pumping and Thermocline Eq E W E 90N

Ekman Layer

Ekman Pumping Ekman Suction (w<0) (w>0)

Equatorward Poleward Sverdrup Transport Sverdrup Transport

ESS228 ESS228 Subtropical Gyre Subpolar Gyre Prof. Jin-Yi Yu (from John Marshall and R. Alan Plumb’s , Ocean and Climate : An IntroductoryProf. Jin-Yi Text) Yu

Stommel’s Theory of Western Boundary Currents Step 4: Boundary Currents

Stommel’s Theory added bottom friction into the same equations used by Svedrup.

(Figure from Oceanography by Tom Garrison) ESS228 surface stress bottom stress ESS228 Prof. Jin-Yi Yu Prof. Jin-Yi Yu (from Robert H. Stewart’s book on “Introduction to Physical Oceanography”)

10 Munk’s Theory of Western Boundary Currents Why Strong Boundary Currents? A Potential Vorticity View

(Figure from The Earth System)

surface stress lateral friction

mass-transport stream function Ψ

. Munk (1950) built upon Sverdrup’s theory, adding lateral eddy viscosity, Goal: Maintain the “steady state” of the negative vorticity induced by wind stress curve to obtain a solution for the circulation within an ocean basin. . To simplify the equations, Munk used the mass-transport stream function. ξ- = ξ- plus ξ+ ξ- = ξ+ plus ξ+ ESS228 ESS228 (from Robert H. Stewart’s book on “Introduction to Physical OceanographyProf. Jin-Yi”) Yu friction has to be big  strong boundary currentProf. Jin-Yi Yu

Gulf Stream Characteristics of the Gyres A river of current (Figure from Oceanography by Tom Garrison)  Currents are in geostropic balance  Each gyre includes 4 current components: Jet stream in the ocean two boundary currents: western and eastern two transverse currents: easteward and westward Western boundary current (jet stream of ocean) the fast, deep, and narrow current moves warm water polarward (transport ~50 Sv or greater) Eastern boundary current . = 2 m/sec the slow, shallow, and broad current moves cold water equatorward (transport ~ 10-15 Sv) . Depth = 450 m Trade wind-driven current . Width = 70 Km the moderately shallow and broad westward current (transport ~ 30 Sv) . Color: clear and blue Westerly-driven current the wider and slower (than the trade wind-driven Volume transport unit: current) eastward current 1 sv = 1 Sverdrup = 1 million m3/sec ESS200A (Figure from Oceanography by Tom Garrison) ESS228 (the Amazon river has a transport of ~0.17 Sv) Prof. Jin-Yi Yu Prof. Jin-Yi Yu

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