how to convert u(r,z) (axisymmetric) data to u(x,y,z)??

I have an axisymmetric velocity vector field in cylindrical coordinate system (r,z), where r is the radius (sqrt(x^2+y^2)) and z is the axis.

theta is the angle between the radius and x-axis and actually revolves around z-axis.

My question is:

if u(r,z) is the velocity vector in cylindrical coordinate system, then

how to convert u(r,z) (axisymmetric) data to u(x,y,z)??

Answer 1

[Roger Stafford]

Probably I don't understand your question, but it would seem that the following is the obvious answer, where uppercase 'U' is the function of x, y, and z and lowercase 'u' is the function of 'r' and 'z':

U(x,y,z) = u(sqrt(x^2+y^2),z)

[Udit Srivastava]

sqrt(x^2+y^2) may not be an integer and I think fractional indexing is not possible in MATLAB.