How to plot a velocity field

I want to plot a velocity field defined in polar coodinates as Vr = -10/r and Vt=10/r (radial and tangent coordinates, respectively), but im having some troubles, below the code that i made.

x = -4:0.3:4;
y = x;
[X, Y] = meshgrid(x,y);

Vr = -10./sqrt(X.^2 + Y.^2);
Vt = 10./sqrt(X.^2 + Y.^2);
quiver(x, y, Vr,Vt)

How can i plot it correctly?

Answer 1

[Divyajyoti Nayak]

Hi Andres,

I see that you are trying to plot a velocity field defined in polar coordinates using the ‘quiver’ function. The ‘quiver’ function however requires the velocity to be defined in cartesian coordinates. Here’s a documentation link for the ‘quiver’ function:

https://www.mathworks.com/help/releases/R2019b/matlab/ref/quiver.html?searchHighlight=quiver&s_tid=doc_srchtitle

To plot the velocity field, convert the velocity components from polar coordinates to cartesian coordinates. Here’s a sample code that might help:

clear
clc
x = linspace(-4,4,27);
y = x;
[X, Y] = meshgrid(x,y);

r = sqrt(X.^2 + Y.^2); % r in function of (x, y)
theta = atan2(Y,X); % theta in function of (x, y)

Vr = -10./r;
Vt = 10./r;

u = Vt.*sin(theta) + Vr .* cos(theta);
v = Vt.*cos(theta) - Vr.*sin(theta);
figure
quiver(X, Y, u,v)