1. The Role of Canyons, Promontories and Topography in DOES
Susan Allen, Department of Earth & Ocean Science University of British Columbia Vancouver, Canada

2. Outline Some definitions Limitation of shelf-break exchange
Eddy shedding and instability: capes and promontories
Advection effects : canyons and ridges
Mixing effects: canyons, banks and deep channels

3. Ocean & the Shelf
Exchange: it is not enough to simply bring ocean water inside the shelf- break line but it needs also to “upwell” to shelf depths

4. Deep Channels
However, deep channels can be extremely important in bringing ocean water into shelf regions where mixing or other processes can bring water to shelf-depth.
DFO

5. “Exchange” Water onto the shelf ≠ Water off the shelf
Bottom topography: water onto the shelf
Capes/promontories: water off the shelf

6. Limitations of Flow over the Shelf-break
Purely geostrophic flow is constrained to follow the isobaths near the bottom
“Near the bottom” is given by the scale depth NL/f where N is the Brunt- Vaisala frequency, f is the Coriolis parameter and L is an appropriate horizontal length scale for the flow.
Geostrophy: ρfv = dp/dx ρfu = -dp/dy
Conserv. Volume: ∇∙ū= Implies dw/dz = 0
But w=0 at the surface and as the bottom condition is: w = -u dh/dx - v dh/dy flow at the bottom must follow the isobaths
Furthermore, using the density equation, Brink (1998) shows that the flow must follow the isobaths upto a depth where the flow is zero.

7. Breaking the Constraints
In order to move deep water over the shelf-break, one needs to break the constraints of geostrophy:
Time-dependence
Advection
Friction
(turbulence)
Bottom boundary layers probably play a smaller role than I originally thought in canyon upwelling.
Slopes are steep and the water is stratified. On a slope of 0.02 and a with a stratification of s-1, the bottom boundary layer will arrest on a timescale of 0.9 days. (MacCready and Rhines, 1992)
S =( N sin(theta)/fcos(theta))^2
tau = 1/S^2 f cos(theta)
if s=0.01 theta = 0.01, sin(theta) = 0.01, cos(theta)=1
S = N^2 s^2/f^2
= (10^-3)^2 (10^-2)^2/(10^-4)^2
= (10^-1)^2
= 10^-2
tau = 1/S^2 f
= 1/(10^-2)^2 10^-4
=10^8 s
==> 3 years
if s=0.02 N = 5e-3 then
S = 1
tau = 10000
==>1/10 of a day
or N=3e-3 gives 0.9 day

8. Topography breaking the Constraints
Decreased L:
Flows on the scale of the topography
Induced instabilities
Increased U:
Converging isobaths
Mixing:
Internal wave breaking
Enhanced shear
Advection: governed by the Rossby Number Ro = U/Lf. Topography usually works by decreasing L but can also increase U.
Turbulent Mixing: Topography can induce increased mixing.

9. Capes and Promontories
Capes cause:
Separation and instabilities
Increased flow due to isobath convergence
COAS

10. Capes : Separation in Eastern Boundary Currents
For eastern boundary currents, - effect is destabilizing.
For anti-cyclonic currents, stretching is destabilizing. (Marshall & Tansley, 2001)
Shelf-current off Oregon/California is “inherently unstable”. Probably kept stable by winds increasing to the south.
Flow can re-attach or eddies become trapped by the topographic slope and not actually lead to exchange.
J. Gower

11. Isobath Convergence
If near-bottom geostrophic flow follows the isobaths, if the isobaths converge the flow accelerates.
Flow that was initially low Ro number can have elevated Ro numbers and cross-isobaths.
Allen, 2000

12. Reduced Ro number
Any topography that has a length scale small compared to the along- shelf current or the shelf width will increase the Rossby number.
If the Rossby number is sufficiently large, cross- isobath flow will occur
F. Shepard

13. Advection driven exchange over Canyons
Allen, 2004

14. Observations from Astoria Canyon
Hickey 1997
6.5°C water advected into the canyon and onto the shelf.

15. Advection driven exchange over Canyons
Ro =U/fR
Allen & Hickey

16. Flux Estimate (Astoria Canyon)
Flux through canyon
Surface Ekman flux
Mirshak & Allen 2005
Using laboratory experiments and theory we can formulate an estimate for upwelling flux through the canyon based on the incoming flow

17. Draining through Canyons
Canyons can guide deep shelf water out to the open ocean
Chapman (2000) shows limitations on water created near the shelf actually getting into the canyon
Wahlin, 2002

18. Exchange due to Rough Slope
We looked at diffusion of a tracer from the coast to the open ocean in a homogeneous fluid.
Topography included a shelf, slope and deep ocean with significant small scale topography on the slope

19. Exchange due to Rough Slope
Tracer contours are packed near shelf- break but are obviously less packed than they would be without the roughness
Exchange is advective with flow shoreward in the canyons and oceanward over the ridges

20. Enhanced Mixing due to Topography
Canyons,ridges and banks have been shown to be regions of enhanced mixing due to breaking internal waves, boundary layer separation and hydraulic processes.
However, mixing in many of these cases do not lead directly to exchange.
Klymak & Gregg, 2004

21. Canyons
Carter & Gregg, 2002
Extremely large values of diapycnal mixing have been seen over canyons, in particular Monterey Canyon.
Deep ocean water can be advected into the canyon and then mixed up into the water column and advected onto the shelf

22. Head of Laurentian Channel
The deep Laurentian channel carries oceanic water toward the Saguenay region.
Here intense tidal mixing pumps deep water and the associated nutrients toward the surface
Saucier, 2000

23. San Juan/Gulf Islands
The Juan de Fuca canyon and Strait of Juan de Fuca similar give a deep channel from the Pacfic toward the Strait of Georgia
In the Gulf/San Juan islands intense tidal mixing between the deep inflowing water and the surface buoyant water of the Strait of Georgia form a new high nutrient water mass
Griffin & LeBlond, 1990

24. San Juan/Gulf Islands
Griffin & LeBlond, 1990
This mixed water both fills the Strait of Georgia with nutrient rich water but also flows seaward and provides up to 2/3 of the nutrients to the productive West Vancouver Island shelf. (Crawford & Dewey, 1989)

25. Summary
Topography can induce cross-shelf exchange by increasing the Rossby number leading to flow separation/instabilities or advective crossing of isobaths.
Topography can induce cross-shelf exchange by a combination of delivering deep water into the shelf area through canyons or deep channels and then by enhancing mixing.
Topography can also act in tandem with other exchange process to enhance them: for example time dependent flows.