how can set up the inital field velocity for the fluid?

Hello

I want to simulate the motion of a nano ball in the liquid. the liquid has a stale field velocity, angular velocity W(r) and has nothing with the angle theta due to symmetry. I would how to set up the inital field velocity. since there is only Ux and Uy. here, the U(x)~ r*w*sin(w*t) and U(y)~r*w*cos(w*t). there w is the angluar velocty and t is the time.
but t is the a variable.

I atttched the picture of this modle. The big circule is the confined space for computation.


Thanks for your time.