Velocityfield and stream function

[MaxManus]

Homework Statement

A velocity field is given by v = 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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Homework Equations

calculate the velocity numerically with $$\nabla$$psi

The Attempt at a Solution

I am starting with the assumption, the velocity is $$\nabla$$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

 

[MaxManus]

One more question:

A velocity field is given by v = ui + vj
where:
u = cos(x)sin(y)
v = -sin(x)cos(y)

Draw stream vectors along the x and y axes.

What is a stream vector?
Is it just like arrows with magnitude and direction v?