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Roshko number

## Summary

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

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

where

## 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.

## Notes

1. ^ Roshko (1952) Figures 9 and 10
2. ^ Ormières and Provansal (1999), Figure 5

## 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.
• 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.