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    Ekman Spiral, was: DR thread from Nov-Dec '04
    From: Trevor Kenchington
    Date: 2005 Jan 19, 10:49 -0400

    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{at}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
                          http://home.istar.ca/~gadus
    
    
    

       
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