contour plot of stream function for a tornado

I have a stream function for a tornado and I watned to plot it using contour function, but it's not working:

m1=-3000;
m2 = 5800;%strength
[r,theta] = meshgrid(-20:1:20,0:0.1:2*pi);
psi = (m1/(2*pi))*theta + (m2/(2*pi))*log(r);
contour(r,theta,psi); 

How should I fix it so the plot looks something like this:

I also want to plot a circle in the middle with radius r = a constant value

Answer 1

[Alan Stevens]

More like this?

m1=-3000;
m2 = 5800;%strength
R = 0:0.1:20; 
THETA = linspace(0,2*pi,numel(R));
[r,theta] = meshgrid(R,THETA);

psi = m1/(2*pi)*theta + (m2/(2*pi))*log(r);
contour(r.*cos(theta),r.*sin(theta),psi,20,'b--'); 

[Randy Chen]

yes that's great!

by the way how should I add a circle with a constant radius? should I still use contour? i'm not sure how to do that

[Alan Stevens]

Like so

m1=-3000;
m2 = 5800;%strength
R = 0:0.1:20; 
THETA = linspace(0,2*pi,numel(R));

[r,theta] = meshgrid(R,THETA);
psi = m1/(2*pi)*theta + (m2/(2*pi))*log(r);

contour(r.*cos(theta),r.*sin(theta),psi,20,'b--'); 
hold on
rc = 10; 
plot(rc*cos(THETA), rc*sin(THETA),'k')
axis equal