Does anyone know the non dimensional group assocaited with vorticity.

I derived the following, via Non Dimensional Analysis, but @ present I am not to sure if its correct. (Is Rads already Non Dimensional????)

Vorticity*=Vorticity*Char_lenght^2*kinematic viscoity/free stream circulation^2.

Also can anyone give me a decent definition of Rossby number.

Again thanks for the advice.

(1). In fluid dynamics, the free stream condition is normally taken as a reference state. (there are other parameters one can use, such as the wall states)(2). It is convenient, because one can get a feeling about the change of the fluid states downstream of the inlet state. (3). The free stream reference state can be taken as U_free, P_free, T_free, Vorticity_free, etc... (4). In this case, the flow variable become, u/U_free, p/P_free, t/T_free, vorticity/Vorticity_free, etc... (5). One can also express Vorticity_free in terms of other free stream variables through its definition. (6). When the length is involved, the characteristic length, such as the inlet diameter, of the length of the body can be used. (7). I think, it is important to recognize that, the purpose of doing this is to make the variation of the flow field variable easier to understand. I mean the distance between the reference state and the local state. Otherwise, even if the final variable is dimensionless, it is hard to understand the behavior. Thus, it becomes useless.