Rossby Wave Two-layer model with rigid lid η=0, p s ≠0 The pressures for the upper and lower layers are The perturbations are 

Potential vorticity conservation in upper and lower layers: Linearize with respect to a rest state using i=1,2 We have

Given plane wave solutions We have The dispersion relation is

The two solutions are  A=B, barotropic or external mode  Out of phase between the upper and lower layers, baroclinic or internal mode Let β= cm -1 s -1, f o =10 -4 s -1, H 1 +H 2 =4×10 5 cm, g*=0.002g=2 cm s -2 The phase speeds

Baroclinic Instability Consider a two-layer system with rigid lid and a mean slope interface H 1. The vertical shear of the total velocity is Assume H 1 =H 1 (x) only and the lower layer is at rest, we have Where V is mean meridional current in the upper layer The linearized potential vorticity equations are For simplicity, H 1 outside derivatives can be replaced by its mean H m

Using the symbols we have used before, we have Consider wave solutions as where

The dispersion relation is It can be shown that, if, the equation has complex solution The instability relation can also be written as Take n=1 and k=0, we get minimum criteria as Take H m ~ 800 m, we have λ 1 ~ 50 km, λ 2 ~ 100 km, the unstable eddies are in the scale of km.

Meso- scale eddies

Energy Diagram of Rossby Wave

Reflection of Rossby Wave

Equatorial Dynamics

1 and 1/2 layer model Y North X East

Equatorial Under Current

Core close to the equator, ~1m/s Below mixed layer Thickness ~ 100 m Half-width 1-2 degrees (Rossby radius at the equator) Forced by zonal pressure gradient established by equatorial easterlies

Equatorial Waves

Tropical and subtropical connections

Vertical structure of the ocean: Large meridional density gradient in the upper ocean, implying significant vertical shear of the currents with strong upper ocean circulation

Water mass formation by subduction occurs mainly in the subtropics. Water from the bottom of the mixed layer is pumped downward through a convergence in the Ekman transport Water “sinks” slowly along surfaces of constant density. Subduction

Sketch of water mass formation by subduction First diagram: Convergence in the Ekman layer (surface mixed layer) forces water downward, where it moves along surfaces of constant density. The σ t surface, given by the TS-combination 8°C and 34.7 salinity, is identified. Second diagram: A TS- diagram along the surface through stations A ->D is identical to a TS-diagram taken vertically along depths A´ - D´.

The Ventilated Thermocline Luyten, Pedlosky and Stommel, 1983

Interaction between the Subtropical and Equatorial Ocean Circulation: The Subtropical Cell

The permanent thermocline and Central Water The depth range from below the seasonal thermocline to about 1000 m is known as the permanent or oceanic thermocline. It is the transition zone from the warm waters of the surface layer to the cold waters of great oceanic depth The temperature at the upper limit of the permanent thermocline depends on latitude, reaching from well above 20°C in the tropics to just above 15°C in temperate regions; at the lower limit temperatures are rather uniform around 4 - 6°C depending on the particular ocean. The water of the permanent thermocline is named as the Central Water, which is formed by subduction in the subtropics.