Roshko number

In fluid mechanics, the Roshko number (Ro) is a dimensionless number describing oscillating flow mechanisms. It is named after the American Professor of Aeronautics Anatol Roshko. It is defined as


 * $$ \mathrm{Ro} = {f L^{2}\over \nu} =\mathrm{St}\,\mathrm{Re} $$


 * $$ \mathrm{St}= {f L\over U}, $$


 * $$ \mathrm{Re} = {U L\over \nu} $$

where
 * St is the dimensionless Strouhal number;
 * Re is the Reynolds number;
 * U is mean stream velocity;
 * f is the frequency of vortex shedding;
 * L is the characteristic length (for example hydraulic diameter);
 * ν is the kinematic viscosity of the fluid.

Correlations
Roshko determined the correlation below from experiments on the flow of air around circular cylinders over range Re=50 to Re=2000:


 * $$ \mathrm{Ro} = 0.212 \mathrm{Re} - 4.5$$ valid over [ 50 <= Re < 200]
 * $$ \mathrm{Ro} = 0.212 \mathrm{Re} - 2.7$$ valid over [200 <= Re < 2000]

Ormières and Provansal investigated vortex shedding in the wake of a sphere and found a relationship between Re and Ro in the range 280 < Re < 360.