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
R o = f L 2 ν = S t R e {\displaystyle \mathrm {Ro} ={fL^{2} \over \nu }=\mathrm {St} \,\mathrm {Re} }
S t = f L U , {\displaystyle \mathrm {St} ={fL \over U},}
R e = U L ν {\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 below from experiments on the flow of air around circular cylinders over range Re=50 to Re=2000:
R o = 0.212 R e − 4.5 {\displaystyle \mathrm {Ro} =0.212\mathrm {Re} -4.5} valid over [ 50 <= Re < 200]
R o = 0.212 R e − 2.7 {\displaystyle \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.
Notes
References Olim, A. M.; Riethmuller, M. L.; Gameiro da Silva, M. C. (2002). "Flowfield characterisation in the wake of a low-velocity heated sphere anemometer". Exp. Fluids. 32 (6): 645–651. Bibcode:2002ExFl...32..645O. doi:10.1007/s00348-001-0403-6. S2CID 119624650. Ormieres, D.; Provansal, M. (1999). "Transition to turbulence in the wake of a sphere". Phys. Rev. Lett. 83 (1): 80–83. Bibcode:1999PhRvL..83...80O. doi:10.1103/PhysRevLett.83.80. Roshko, Anatol (1952). On the development of turbulent wakes from vortex streets (Ph.D.). California Institute of Technology. doi:10.7907/4WDN-9807.