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Thread: Vertical Velocity

  1. #1
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    Vertical Velocity

    Hi all,

    We all know that we can calculate the surface geostrophic currents from the SSHA data. But is it advisable to use the u and v velocity calculated by the above way can be used in the equation of continuty to calculate the vertical velocity.
    NIKESH NARAYAN
    CENTRE FOR ATMOSPHERIC AND OCEANIC STUDIES(CAOS)
    INDIAN INSTITUTE OF SCIENCE(IISC)
    BANGALORE-12 ccasion5

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    I think, In many ways, the answer is 'No, it is not possible in your case'.

    (1) First of all, geostrophic relation is non-convergent in f-plane.
    If one follow the geostrophic relation,

    -f.v = -dp/dx
    f.u = -dp/dy and take the 'curl' of this equation (i.e. d/dy of first
    equation and d/dx of second and subtract each other),
    one may end up with du/dx + dv/dy = 0. That means
    geostrohpic flow is non-convergent or non-divergent. or, dw/dz = 0.
    You may not find vertical velocity from this assumption.

    (2) Inorder to attain a convergence or divergence (i.e. a vertical
    movement) the geostrophic relation should deviate a little bit. This is
    called Quasi-geostrophy. In quasi-geostrophic flow
    a convergence is achieved from the first order departure of
    geostrophic velocity. i.e. u = u0 + u1, where u0 is zeroth order geostrophic flow
    and u1 is its first order departure or 'ageostrphic flow'. Thus if one
    has u0 and v0 from geostrophic relation, its divergence should
    be equal to zero. IF it is not zero, that is contributed from
    the 'ageostrophic flow' and 'w' is possible to find out from
    mass conservation equation.

    In this case, you need a boudary condition for 'w' to integrate du/dx + dv/dy
    vertically to find 'w' at each level. At the level of no-motion,
    w=0 boundary condition may be applicable. But, I think, in this case
    one should take horizontal convergence along the pressure surfaces
    or density surfaces (i.e. not along the constant depths).

    (3) But in your case, you are asking for SSHA derived geostrophic currents which
    is only at the surface. You cannot find currents below the surface (say below
    10 m or more) to reach level of no-motion. In this case you cannot use
    quasi-geostrophic assumption to find vertical velocity.

    More details can be found in some Ocean dynamics books.

    Hope this helps

    -Vinu

  3. #3
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    Thanks Vinu

    Yeah it really helped.
    NIKESH NARAYAN
    CENTRE FOR ATMOSPHERIC AND OCEANIC STUDIES(CAOS)
    INDIAN INSTITUTE OF SCIENCE(IISC)
    BANGALORE-12 ccasion5

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