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
\( \mathrm{Ro} = {f L^{2}\over \nu} =\mathrm{St}\,\mathrm{Re} \)
\( \mathrm{St}= {f L\over U}, \)
\( {\displaystyle \mathrm {Re} ={UL \over \nu }} \)
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.
Notes
Roshko (1952) Figures 9 and 10
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". Physical Review Letters 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.
vte
Dimensionless numbers in fluid mechanics
Archimedes Atwood Bagnold Bejan Biot Bond Brinkman Capillary Cauchy Chandrasekhar Damköhler Darcy Dean Deborah Dukhin Eckert Ekman Eötvös Euler Froude Galilei Graetz Grashof Görtler Hagen Iribarren Kapitza Keulegan–Carpenter Knudsen Laplace Lewis Mach Marangoni Morton Nusselt Ohnesorge Péclet Prandtl
magnetic turbulent Rayleigh Reynolds
magnetic Richardson Roshko Rossby Rouse Schmidt Scruton Sherwood Shields Stanton Stokes Strouhal Stuart Suratman Taylor Ursell Weber Weissenberg Womersley
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