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Re: [ferret_users] how to calculate the streamfunction and velocity potential

Yes, thank you Ryo. I should have said that. The streamfunction exists only when the flow is nondivergent, typically when u and v are integrated from the ocean bottom to the surface.

Another use is a vertical streamfunction, valid for a zonal, coast-to- coast integral. That is easier to calculate, because w is identically zero at the surface:

let streamfn=v[x=@din,z=@iin]   ! where v is in a single, bounded basin

And a velocity potential is valid only when the flow is irrotational (curl(v)=0), which is unlikely to be the case in the ocean. In the atmosphere, it can be used to describe the upper-level circulation which is predominantly zonal.

Billy K

On Aug 8, 2007, at 6:46 PM, Ryo Furue wrote:

Hi Billy and Hanh,

| ! compute the horizontal streamfunction from vertically integrated u
| ! and v fields
| ! note that u and v must occur on the same spatial points (B-grid)
| ! arg1=variable name for u
| ! arg2=variable name for v
| ! arg1=x0 (must be on a gridpoint or set mode interp)
| ! arg2=y0 (likewise)
| ! psi=int(y0,y)u(x,y)dy - int(x0,x)v(x,y0)dx
| ! u=d(psi)/dy, v=-d(psi)/dx

I guess this gives you a correct streamfunction only
when du/dx + dv/dy = 0, right?  (There's no function satisfying
both u=d(psi)/dy and v=-d(psi)/dx when du/dx + dv/dy is nonzero.)

Hanh mentioned velocity potential, which suggests that a Helmholz
decomposition is required:

  (u,v) = grad(phi) + k x grad(psi)

To obtain phi(x,y) and psi(x,y), you need to solve these Poisson equations

  div grad (phi) = div(u,v)
  div grad (psi) = curl(u,v)

with some (probably arbitrary) boundary conditions.

I myself haven't done this, but a colleague of mine uses the method
described by:

  Watterson, I., 2001. Decomposition of global ocean currents using a
  simple iterative method. J. Atmos. Oceanic Tech., 18, 691–703.

Hope this helps,

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