A Universal Strouhal Law

A universal relationship between the frequency of oscillation induced in a restrained fluid body by an external free flow, the velocity of the latter, and a typical width of the body, is established. Evidence is offered of the accuracy of this “Strouhal law” in such phenomena as wing autorotation, intermittent formation of vortices behind weirs and orifices, jet flapping and puffing, wake vortex shedding, oscillation of shock waves, cavitation bubbles and vortex breakdowns. A corollary of the Strouhal law shows that travelling waves of a well‐defined length may associate with the fluid‐body oscillation. Corroborations are offered concerning the spacing of wind waves, internal waves and dunes and Taylor‐cell waves. The usefulness of the law as a heuristic tool is stressed.

[1]  J. R. Calvert,et al.  Experiments on the low-speed flow past cones , 1967, Journal of Fluid Mechanics.

[2]  Roddam Narasimha,et al.  The ‘bursting’ phenomenon in a turbulent boundary layer , 1971, Journal of Fluid Mechanics.

[3]  Owen M. Griffin.  A universal Strouhal number for the ‘locking-on’ of vortex shedding to the vibrations of bluff cylinders , 1978 .

[4]  H. Bossel,et al.  Vortex Breakdown Flowfield , 1969 .

[5]  E. Levi.  Longitudinal Streakings In Liquid Currents , 1965 .

[6]  V. Strouhal,et al.  Ueber eine besondere Art der Tonerregung , 1878 .

[7]  J. R. Calvert.  Some experiments on the flow past a sphere , 1972, The Aeronautical Journal (1968).

[8]  A. Roshko.  On the drag and shedding frequency of two-dimensional bluff bodies , 1954 .

[9]  E. Levi.  Oscillatory Model for Wall‐Bounded Turbulence , 1983 .

[10]  R. G. Jackson,et al.  Sedimentological and fluid-dynamic implications of the turbulent bursting phenomenon in geophysical flows , 1976, Journal of Fluid Mechanics.

[11]  Osami Okada,et al.  The stability and transition of an axisymmetric wake , 1966, Journal of Fluid Mechanics.

[12]  V. Goldschmidt,et al.  The Apparent Flapping Motion of a Turbulent Plane Jet—Further Experimental Results , 1980 .

[13]  A. Richter,et al.  Fluctuating forces on a rigid circular cylinder in confined flow , 1976, Journal of Fluid Mechanics.

[14]  S. A. Thorpe,et al.  Experiments on the instability of stratified shear flows: immiscible fluids , 1969, Journal of Fluid Mechanics.

[15]  S. Crow,et al.  Orderly structure in jet turbulence , 1971, Journal of Fluid Mechanics.

[16]  E. H. Smith.  Autorotating wings: an experimental investigation , 1971, Journal of Fluid Mechanics.

[17]  Sidney Leibovich,et al.  An experimental map of the internal structure of a vortex breakdown , 1978, Journal of Fluid Mechanics.

[18]  J. Rossiter.  Wind tunnel experiments on the flow over rectangular cavities at subsonic and transonic speeds , 1964 .

[19]  John K. Harvey,et al.  Some observations of the vortex breakdown phenomenon , 1962, Journal of Fluid Mechanics.

[20]  V. W. Goldschmidt,et al.  Flapping of a plane jet , 1973 .

[21]  D. Coles.  Transition in circular Couette flow , 1965, Journal of Fluid Mechanics.

[22]  Peter W. Bearman,et al.  On vortex street wakes , 1967, Journal of Fluid Mechanics.