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George wrote:

> I remember taking a short course on oceanography, 50 years ago, and one of
> the topics that has stuck in my mind ever since is the Ekman theory of wind
> drift, developed just 100 yearss ago, and using some ferocious (to me then)
> maths. Ekman deduced that in the Northern hemisphere the current at the
> surface was 45 degrees to the right of the wind, and deeper down it was
> further still around, to the right. The mechanism is similar to that which
> makes the wind spin in circles in storms and depressions, and is due to the
> rotation of the Earth. There is a return current, which allows the water
> that's shifted by the surface current, to flow back the other way at a
> deeper level, deeper even than Doug's ships. It's satisfying to think that
> Ekman's academic work is now saving fuel on the World's oceans.

Ekman's theory (which actually works, in deep ocean away from
complicating factors, if the wind blows steadily for long enough) was
that the surface drift is directed to the right (in the northern
hemisphere) of the wind direction, with the movement of the next layer
down being displaced still further to the right, and so on reaching ever
deeper into the sea. These are not, however, really separate layers
(with thermoclines between) but really infinitely-thin "layers", such
that the vectors of the water movements describe a spiral -- the "Ekman
Spiral".

Meanwhile, the velocities decrease from layer to layer, such that the
deep flow running upwind is very much slower than the surface flow,
running almost downwind. Integrating over the whole spiral, the combined
effect is water transport at right angles to wind direction (again: to
the right in the northern hemisphere). Where that transport is away from
a landmass, deep water upwells to replace the water driven away -- which
is the mechanism that generates the huge productivity of the Humboldt
Current ecosystem off Peru and northern Chile (except when El Nino
events shut the thing down). Hence the Peruvian anchoveta fishery, the
largest the world has ever seen and likely ever will. Hence also the old
guano trade from the Chincha islands.

However, for the navigators of ships in that, or any other trade
(excluding submarine operations -- "The Trade" as RN submariners once
termed their business), the only part of the Ekman Spiral that has any
direct relevance is the surface drift itself. Doug's 40 degrees to the
right of the wind (in the northern hemisphere) and 2% of wind speed
seems to be the accepted generalized average for navigational use. The
real set and drift will depend on how long the wind has been blowing
with its present strength and direction, the recent history of strengths
and directions, the depth of the seabed, nearby land masses or shoal
water, any shallow thermoclines, and anything which affects the
ocean/atmosphere coupling (a swell from distant winds? a thin surface
slick of light oil, as from biological activity? winds so extreme as to
break the sea surface into foam?) and maybe a bunch of other factors
that I can't think of right now.

Also: Although we gaily talk of "to the right in the northern hemisphere
and to the left in the south", the reality is that there is no such
deflection in an Equatorial belt, where the horizontal component of the
Coriolis force is negligible (actually zero right on the Equator). I
have never heard just how wide that belt may be. Oddly enough, it seems
that Ekman Spirals are not affected by latitude, so long as it is great
enough for them to form. I guess if I had understood the equations, back
when I did undergrad oceanography, I would know why but I didn't, so I
don't.


Trevor Kenchington


--
Trevor J. Kenchington PhD                         Gadus@iStar.ca
Gadus Associates,                                 Office(902) 889-9250
R.R.#1, Musquodoboit Harbour,                     Fax   (902) 889-9251
Nova Scotia  B0J 2L0, CANADA                      Home  (902) 889-3555

                     Science Serving the Fisheries
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