Rossby Wave

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

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

3. Given plane wave solutions We have The dispersion relation is

4. 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=10-13 cm-1s-1, fo=10-4 s-1, H1+H2=4×105 cm, g*=0.002g=2 cm s-2 The phase speeds

7. Baroclinic Instability Consider a two-layer system with rigid lid and a mean slope interface H1. The vertical shear of the total velocity is Assume H1=H1(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, H1 outside derivatives can be replaced by its mean Hm

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

9. 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 Hm~ 800 m, we have λ1~ 50 km, λ2 ~ 100 km, the unstable eddies are in the scale of 100-200 km.

10. Meso-scale eddies

15. Energy Diagram of Rossby Wave

16. Reflection of Rossby Wave

19. Equatorial Dynamics

21. 1 and 1/2 layer model Y North X East

23. Equatorial Under Current

24. 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

28. Equatorial Waves

30. Tropical and subtropical connections

31. 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

32. Subduction 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.

33. 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 27.04 σt 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´.

34. The Ventilated ThermoclineLuyten, Pedlosky and Stommel, 1983

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

38. 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.