Physics: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

[math]\displaystyle{ \mathrm{Ro} = {f L^{2}\over \nu} =\mathrm{St}\,\mathrm{Re} }[/math]

[math]\displaystyle{ \mathrm{St}= {f L\over U}, }[/math]

[math]\displaystyle{ \mathrm{Re} = {U L\over \nu} }[/math]

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:

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

[math]\displaystyle{ \mathrm{Ro} = 0.212 \mathrm{Re} - 2.7 }[/math] 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.

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. doi:10.1007/s00348-001-0403-6. Bibcode: 2002ExFl...32..645O. 
• Ormieres, D.; Provansal, M. (1999). "Transition to turbulence in the wake of a sphere". Phys. Rev. Lett. 83 (1): 80–83. doi:10.1103/PhysRevLett.83.80. Bibcode: 1999PhRvL..83...80O. 
• Roshko, Anatol (1952). On the development of turbulent wakes from vortex streets (Ph.D.). California Institute of Technology. doi:10.7907/4WDN-9807.