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curl

Compute curl and angular velocity of vector field

Syntax

[curlx,curly,curlz,cav] = curl(X,Y,Z,U,V,W)
[curlx,curly,curlz,cav] = curl(U,V,W)
[curlz,cav]= curl(X,Y,U,V)
[curlz,cav]= curl(U,V)
[curlx,curly,curlz] = curl(...)
[curlx,curly] = curl(...)
cav = curl(...)

Description

[curlx,curly,curlz,cav] = curl(X,Y,Z,U,V,W) computes the curl (curlx, curly, curlz) and angular velocity (cav) perpendicular to the flow (in radians per time unit) of a 3-D vector field U, V, W.

The arrays X, Y, and Z, which define the coordinates for U, V, and W, must be monotonic, but do not need to be uniformly spaced. X, Y, and Z must have the same number of elements, as if produced by meshgrid.

[curlx,curly,curlz,cav] = curl(U,V,W) assumes X, Y, and Z are determined by the expression

[X Y Z] = meshgrid(1:n,1:m,1:p)

where [m,n,p] = size(U).

[curlz,cav]= curl(X,Y,U,V) computes the curl z-component and the angular velocity perpendicular to z (in radians per time unit) of a 2-D vector field U, and V.

The arrays X and Y, which define the coordinates for U and V, must be monotonic, but do not need to be uniformly spaced. X and Y must have the same number of elements, as if produced by meshgrid.

[curlz,cav]= curl(U,V) assumes X and Y are determined by the expression

[X Y] = meshgrid(1:n,1:m)

where [m,n] = size(U).

[curlx,curly,curlz] = curl(...), [curlx,curly] = curl(...) returns only the curl.

cav = curl(...) returns only the curl angular velocity.

Examples

collapse all

Use colored slice planes to display the curl angular velocity at specified locations in the vector field.

cav = curl(x,y,z,u,v,w);
h = slice(x,y,z,cav,[90 134],59,0);
daspect([1 1 1]);
axis tight
colormap(hot(16));
camlight
set([h(1),h(2)],'ambientstrength',.6);

Display the curl angular velocity in one plane of the volume. Then plot the velocity vectors in the same plane.

k = 4;
x = x(:,:,k);
y = y(:,:,k);
u = u(:,:,k);
v = v(:,:,k);
cav = curl(x,y,u,v);
pcolor(x,y,cav);
hold on
quiver(x,y,u,v,'y');
hold off
colormap('copper');