ATOC 5051 INTRODUCTION TO PHYSICAL OCEANOGRAPHY Lecture 23: STG & westward intensification Learning objectives: Science: observed strong western boundary current - westward intensification, why? Approach: What approach have we used in order to know “why”? 1. Interior solution (continue) 2. Western boundary current: a) Scaling equations of motion in WB region; b) Solutions in WB region, WBC; c) Major physical difference between interior & WB region. Previous class: Observed STG & Westward intensification

Westward intensification!

STG Previous class: Derived Sverdrup balance (ocean interior: away from wester boundary) � − ������ ��������

= �� � = �� Schematic: Observed Surface wind pattern

�� � = ��� = , () �� �� � = ��� = − () �� Zonal wind stress Observations: Pedlosky 1987 15N-45N, STG region: + <0 - EQ y 45N

30N

15N - + <0 <0

45N

Maximum

15N y 45N L

30N

15N 0 y=L 45N

30N y=0 15N X=0 x= y

westerly

easterly 65N

45N

Question: In polar front area, surface wind stress are shown as red and blue vectors. Use the Sverdrup balance, to discuss the vertically integrated interior ocean circulation (clockwise or counter clockwise; why?). >0 >0 Schematic diagram: wind-driven circulation in the ocean interior Summary: STG interior circulation Wind-driven ocean circulation in the NH subtropical region: Interior solution y=L 45N

30N

15N y=0 (a) Scale analysis the equations of motion: with Ro<<1, E<<1 & steady state circulation; (b) Obtain vorticity equation; (obtain Sverdrup relation) (c) Vertically integrate the vorticity equation; (obtain Sverdrup balance) Observations: Western boundary current

SST in the Western N. Atlantic •Interior: large zonal scale, slow current; •Western boundary: narrow, swift current; •The strongest Western Boundary Current (WBC): off the coast! 2. Western boundary current: westward intensification

Steady state, vertically averaged:

4a

4b

Linear 4c Obtain general vorticity equation: Bottom drag: added

(Fun exercise: derive this at home) General vorticity equation:

We have: What assumptions do we make to obtain the vorticity equation for ocean interior?

Ex=Ey<<1 & bottom drag=0 Scale analysis for western boundary region: * *

*

To the lowest order:

Local wind forcing: negligible Solution: Western boundary current (WBC)

(i) Stommel’s solution (1948): H. Stommel, The Westward Intensification of Wind-Driven Ocean Currents, Transactions American Geophysical Union: Vol. 29, 1948

Solution: Subject to boundary conditions:

WBC: 45N

30N (a) Vmax: @ x=0 (b) When 15N 45N =0

No westward Symmetric! 30N Intensification!

15N Stommel’s solution: Constant f varying f β ≠ 0

From Stommel, 1948 β ≠ 0 Is required for No westward Westward intensification! Intensification! Questions • Westward intensification requires β ≠ 0 ; Physically, what does this indicate?

• For Stommel’s solution, which part do you think is unreasonable? Observations

Pedlosky 1987

SST in the Western N. Atlantic

•The strongest Western Boundary Current (WBC): off the coast! Question

• What are the physical reason for us to integrate the Sverdrup balance equation from the eastern boundary westward, by assuming Ψ=0 at the eastern boundary?