(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A velocity field is given byv= ui+ vj

where:

u = cos(x)sin(y)

v = -sin(x)cos(y)

x = y = [-pi/2,pi/2]

the stream function psi is:

psi = cos(x)cos(y)

Matlab function:

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function[X,Y,psi] = streamfun(n)

if nargin < 1;

n=20;

end

x=linspace(-0.5*pi,0.5*pi,n);

[X,Y] = meshgrid(x,x);

psi=cos(X).*cos(Y);

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2. Relevant equations

calculate the velocity numerically with [tex]\nabla[/tex]psi

3. The attempt at a solution

I am starting with the assumption, the velocity is [tex]\nabla[/tex]psi, is this correct?

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[x,y,psi] = streamfun(20)

[u,v] = gratient(20)

quiver(x,y,u,v)

and I get numfield.jpg, see attachment, but this is not the same as my velocityfield.jpg

which I got from:

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x = linspace(-0.5*pi,0.5*pi,n);

[x,y] = meshgrid(x,x);

u = cos(x).*sin(y);

v = -sin(x).*cos(y);

quiver(x,y,u,v)

----------------------------------------------------------

Can someone please help me and tell me what I am doing wronge.

Edit:

nabla*psi = -sin(x)cos(y)i- cos(x)*sin(y)j

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# Velocityfield and stream function

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