Abyssal circulation/ Stommel-Arons (1960) theory:
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MOTIVATION:
* Objective: large-scale abyssal circulation, below 2 km depth.
* Video of lab experiment (Marshall, MIT).
* Heuristic explanation: upwelling, "angular momentum" conservation on a beta plane.

BASICS, VORTICITY:
* derivation and interpretation of terms in linear vorticity equation for a one layer model on a beta plane: 
         \zeta_t+\beta v=-r\zeta+f w_z  
* vorticity: brief reminder and intuitive explanation 
* steady interior vorticity budget: beta v = f w_z, 

INTERIOR CIRCULATION AWAY FROM WESTERN BOUNDARY:
* large-scale deep upwelling fed by deep water formation, and the interior abyssal transport it drives
* need for a boundary current
(2-notes-vorticity-eqn-and-Abyssal-circulation.pdf) [use Acrobat to open this, not Mac's preview]

INTERIOR CIRCULATION AND EXPECTED BOUNDARY TRANSPORT ON A SPHERE:
* Stommel Arons picture in spherical coordinates: combining calculating both interior transport and boundary transport from source strength.
(3-Stommel-Arons-from-Pedlosky-circulation-book.pdf, pages 396-top paragraph of p 399; then figure on page 404)

OBSERVATIONS:
* observational verification of predicted deep western boundary current
(4-Swallow-Worthington-1961.pdf, page 9 of the pdf, showing section VIII, March 29-31)

WESTERN BOUNDARY DYNAMICS:
* solving for the western boundary: 
  (1) boundary layer approximation: an ODE example, use of stretched coordinates
      (5-notes-singular-perturbation.pdf)
  (2) using the boundary layer method to solve for the western boundary layer



HOMEWORK:

1) Consider a basin on a sphere bounded by two meridians $\phi_1$ and $\phi_2$ and extending from the equator ($\theta=0$) to the south pole ($\theta=-\pi/2$).  A bottom water source of magnitude $S_0$ is located at $\theta=30S$.  Calculate and schematically draw the corresponding interior abyssal circulation and the transport of the western boundary circulation as function of latitude.  Substitute $S_0=20Sv$, $\phi_1=0$, $\phi_2=\pi/4$ and plot the boundary current transport $T_w(\theta)$.