Plotting a given velocity field (vortex flow)

Hi all,

I am trying to plot following u_x and u_y functions, which are the x and y components of a velocity field.

The results should look like a vortex, as can be seen in the attached picture which I took from "wolframalpha.com" when I tried to compare my results.

However, instead such a simle 2D vortex I get complex velocity field which is also attached here.

I suspect it is due to wrong initialiazing the domain or wrong usage domain values in the "for loop", which is shown in the end of this message.

Could you please suggest me any possible solution.

I appreciate your time.

[darova]

You code works ok. Just try this

plot(u_x,u_y)

[Mammadbaghir Baghirzade]

Thank you for your reply.

I did plot these functions, however, I got complex result as in the attached.

But instead I need to get something like following. And I can not get such simple vortex flow.

Answer 1

[Ameer Hamza]

try this

x = 0:0.1:3;
y = 0:0.1:3;

[X,Y] = meshgrid(x,y);
Psi = (1/pi)*sin(pi*X).^2.*sin(pi*Y).^2;

u_x =  2*(sin(pi*X).^2).*(sin(pi*Y)).*(cos(pi*Y));   
u_y = -2*(sin(pi*Y).^2).*(sin(pi*X)).*(cos(pi*X)); 

figure;
contourf(X,Y,Psi)
title('velocity field intensity')

figure;
quiver(X,Y,u_x,u_y)
title('velocity field direction')

[Mammadbaghir Baghirzade]

I appreciare, thank you very much.

Is there anyway of getting it's x and y components as u_x and u_y?

[Ameer Hamza]

Check the updated answer.

[Mammadbaghir Baghirzade]

Thank you, I appreciate.

It works as I needed.

[Ameer Hamza]

I am glad to be of help.

[Monisha Srabanti]

Hi, I have a similar problem where I made hemodynamic 3d atlases and I want to calculate and plot the vortex in that atlas. How can I do that? Can anyone help me with that? I have the velocity fields of MRI images and have the atlas as .fig