Vertical Velocity

[nikeshnarayan]

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.

[vinu]

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

[nikeshnarayan]

Yeah it really helped.