Roshko number

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

: $\mathrm{Ro} = {f L^{2}\over \nu} =\mathrm{St}\,\mathrm{Re}$

: $\mathrm{St}= {f L\over U},$

: $\mathrm{Re} = {U L\over \nu}$

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 correlationRoshko (1952) Figures 9 and 10 below from experiments on the flow of air around circular cylinders over range Re=50 to Re=2000:

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

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

Ormières and ProvansalOrmières and Provansal (1999), Figure 5 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

{{cite journal |last1=Olim |first1=A. M. |last2=Riethmuller |first2=M. L. |last3=Gameiro da Silva |first3=M. C. |year=2002 |title=Flowfield characterisation in the wake of a low-velocity heated sphere anemometer |journal=Exp. Fluids |volume=32 |issue=6 |pages=645–651 |doi=10.1007/s00348-001-0403-6 |bibcode = 2002ExFl...32..645O |s2cid=119624650 }}
{{cite journal |last1=Ormieres |first1=D. |last2=Provansal |first2=M. |year=1999 |title=Transition to turbulence in the wake of a sphere |journal=Phys. Rev. Lett. |volume=83 |issue=1 |pages=80–83 |doi=10.1103/PhysRevLett.83.80 |bibcode = 1999PhRvL..83...80O }}
{{cite thesis |last=Roshko |first=Anatol |author-link=Anatol Roshko|date=1952 |title= On the development of turbulent wakes from vortex streets |type=Ph.D. |publisher=California Institute of Technology |url=http://resolver.caltech.edu/CaltechETD:etd-10302003-144124 |doi=10.7907/4WDN-9807}}

Category:Dimensionless numbers of fluid mechanics

Category:Fluid dynamics