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

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

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

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

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

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

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.
• Note: Linear relation between Ro# and Re# from Roshko's Caltech Thesis (figures 9-10); tested in air [over range Re=50 to Re=2000]

  The kinematic viscosity of air at 15 °C is 1.48×10−5 m2/s. 
     at 20 °C, the kinematic viscosity is 1.525×10−5 m2/s.
     at 25 °C, the kinematic viscosity is 1.57×10−5 m2/s.

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.

External links

• On the Development of Turbulent Wakes From Vortex Streets PhD. Thesis by Anatol Roshko (hosted on Caltech Site).