The Subtropical Gyres: setting the stage for generating a more realistic gyre Ekman used an ideal, infinite ocean, no slopes in sea level, or variations in salinity Western Boundary Currents fast, deep, narrow, warm Gulf Stream, Kuroshio O(100 km) width, u = 2 m/s Eastern Boundary Currents slow, shallow, broad, cool Canary, California O(1000 km) width, u = 0.25 m/s

Dynamic Systems: conservation of momentum (linear and angular) Conservation of a tendency to rotate Conservation of vorticity Current shear – change in the velocity in the direction perpendicular to the flow direction. Current shear will induce a tendency to rotate in a water parcel. Positive Vorticity: anticlockwise Negative Vorticity: clockwise

All rotating objects on the Earth possess: relative vorticity: rotation in relation the surface of the Earth – ζ Planetary vorticity: vorticity associated with the rotation of the Earth – f VORTICITY is a measurement of the rotation of a small air/water parcel. It has vorticity when the parcel spins as it moves along its path. Although the axis of the rotation can extend in any direction, meteorologists/oceanographers are primarily concerned with the rotational motion about an axis that is perpendicular to the earth's surface. If it does not spin, it is said to have zero vorticity. In the Northern Hemisphere, the vorticity is positive when the parcel has a counterclockwise, or cyclonic, rotation. It is negative when the parcel has clockwise, or anticyclonic, rotation.

Conservation of Vorticity: relative to fixed space Absolute Vorticity = relative + planetary vorticity Absolute vorticity of a parcel of fluid (its vorticity as a result of being on the Earth plus any vorticity relative to the Earth) must remain constant in the absence of any of external forces such as wind stress and friction (f +  ) X

For much of the ocean (away from coastal boundaries and large current shear) f >>  This results in ‘topographic steering’. Conservation of Vorticity  Conservation of Potential Vorticity (f +  )/D D Q4.5

1948: Henry Stommel onto the problem of the Gulf Stream Considered the effects of a symmetrical wind field on a rectangular basin for three different scenarios: 1.non rotating Earth 2.rotating with constant Coriolis parameter f 3.rotating and Coriolis parameter varies with latitude Stommel added friction – Sverdrup did not have it equilibrium achieved so forces must balance (steady state) ‘lines’ of wind

1.non rotating Earth 2.rotating with constant Coriolis parameter f 3.rotating and Coriolis parameter varies with latitude Stommel’s Results

Munk: extends Stommel’s domain up to 60 N, and improves the representation of both wind and friction. Considered friction with boundaries and friction associated with both lateral and vertical current shear (eddy viscosity in both horizontal and vertical dimensions; Ah and Az) Result: reproduced more realistic ocean circulation features