Example for curl and div of a 2D vector field
Contents
You need to download new m-files.
Download the files vectorfield.m, ezpcolor.m, colorposneg.m
(1) Plot a 2D vector field
Plot the 2D vector field F = ( cos(x+2*y), sin(x-2*y) ) for x,y in [-2,2].
syms x y z real F = [ cos(x+2*y), sin(x-2*y) ]; vectorfield(F,-2:.25:2,-2:.25:2)
(2) Find G = curl(F) and plot G_3 together with vector field
G = curl([F,0],[x y z]) % need vector field of 3 components for curl vectorfield(F,-2:.25:2,-2:.25:2); hold on ezpcolor(G(3),[-2.5 2.5 -2.5 2.5]); hold off colorbar; colorposneg title('colors show curl: blue is clockwise, red is counterclockwise')
G =
0
0
cos(x - 2*y) + 2*sin(x + 2*y)
(3) Find div(F) and plot it together with vector field
g = divergence(F,[x y]) % find divergence vectorfield(F,-2:.25:2,-2:.25:2); hold on ezpcolor(g,[-2.5 2.5 -2.5 2.5]); hold off colorbar; colorposneg title('colors show divergence: blue is sink, red is source')
g = - 2*cos(x - 2*y) - sin(x + 2*y)
