**To**:**Ryo Furue <furue@xxxxxxxxxx>, nguyen@xxxxxxxxxx****Subject**:**Re: [ferret_users] how to calculate the streamfunction and velocity potential****From**:**"William S. Kessler" <William.S.Kessler@xxxxxxxx>**- Date: Wed, 08 Aug 2007 21:13:56 -0700
- Cc: Ferret users <oar.pmel.ferret_users@xxxxxxxx>
- In-reply-to: <20070808.154623.46607072.furue@xxxxxxxxxx>
- References: <Pine.LNX.4.58.0708090246390.6707@xxxxxxxxxxxxxxxxxx> <46100.169.226.43.169.1186610221.squirrel@xxxxxxxxxxxxxxxxxx> <72CABF42-4A5A-4EAD-BAC9-CF8FDAEB8C22@xxxxxxxx> <20070808.154623.46607072.furue@xxxxxxxxxx>
- Sender: owner-ferret_users@xxxxxxxx

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

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 Poissonequationsdiv 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, Ryo

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**References**:**Re: [ferret_users] how to convert decimal date to date and time***From:*Jaison Kurian

**[ferret_users] how to calculate the streamfunction and velocity potential***From:*nguyen

**Re: [ferret_users] how to calculate the streamfunction and velocity potential***From:*william s. kessler

**Re: [ferret_users] how to calculate the streamfunction and velocity potential***From:*Ryo Furue

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