Website owner: James Miller
FUNCTIONAL REPRESENTATION OF PROBLEMS IN PHYSICS
Functional representation of the trajectory of a particle in a moving, turbulent fluid. The functional representation of the position of a particle as a function of time within a moving, turbulent fluid can be expressed in any of the following equivalent ways:
x = f1(x0, y0, z0, t)
1] y = f2(x0, y0, z0, t)
z = f3(x0, y0, z0, t)
where (x0, y0, z0) is the position of the particle at some initial time t0 and (x, y, z) is the position of the particle at time t.
x = x(x0, y0, z0, t)
2] y = y(x0, y0, z0, t)
z = z(x0, y0, z0, t)
5] X = x(x0, y0, z0, t) i + y(x0, y0, z0, t) j + z(x0, y0, z0, t) k
where i, j and k are unit vectors along the coordinate axes.