Roshko number

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

${\displaystyle \mathrm {Ro} ={fL^{2} \over \nu }=\mathrm {St} \,\mathrm {Re} }$

${\displaystyle \mathrm {St} ={fL \over U},}$

${\displaystyle \mathrm {Re} ={UL \over \nu }}$

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^[1] below from experiments on the flow of air around circular cylinders over range Re=50 to Re=2000:

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

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

Ormières and Provansal^[2] investigated vortex shedding in the wake of a sphere and found a relationship between Re and Ro in the range 280 < Re < 360.