Scaling of streamwise vortices in wakes

In this Letter, we demonstrate the coexistence of two distinct systems of streamwise vortices in a bluff body wake. It appears that there exist conditions to amplify streamwise vorticity in bluff body wakes, by vortex stretching, in both the separating shear layers from the sides of the body and also in the vortex street wake. The length scale governing the streamwise vortices in the shear layer has a 1/√Re dependence, whereas the scale of such structures in the wake is independent of Reynolds number, Re (over a large range of Re). The proposition that there should exist two distinct, and possibly disparate, spanwise length scales in the cylinder wake is well supported by compiled measurements, particularly those of Williams and co‐workers (Mansy et al. [J. Fluid Mech. 270, 277 (1994)]), as well as those from Chyu and Rockwell (submitted to J. Fluid Mech.).

[1]  C. Williamson The natural and forced formation of spot-like ‘vortex dislocations’ in the transition of a wake , 1992, Journal of Fluid Mechanics.

[2]  G. Corcos,et al.  The mixing layer: deterministic models of a turbulent flow. Part 2. The origin of the three-dimensional motion , 1984, Journal of Fluid Mechanics.

[3]  Patrick Chassaing,et al.  Prediction of large‐scale transition features in the wake of a circular cylinder , 1990 .

[4]  M. Bloor,et al.  The transition to turbulence in the wake of a circular cylinder , 1964, Journal of Fluid Mechanics.

[5]  AN EXPERIMENTAL INVESTIGATION OF STREAMWISE VORTICES IN THE WAKE OF A BLUFF BODY , 1994 .

[6]  Donald Rockwell,et al.  Cinematographic system for high-image-density particle image velocimetry , 1994 .

[7]  A. Michalke On spatially growing disturbances in an inviscid shear layer , 1965, Journal of Fluid Mechanics.

[8]  M. Thompson,et al.  Longitudinal vortex structures in a cylinder wake , 1994 .

[9]  Eckart Meiburg,et al.  Experimental and numerical investigation of the three-dimensional transition in plane wakes , 1988, Journal of Fluid Mechanics.

[10]  C. Williamson The Existence of Two Stages in the Transition to Three-Dimensionality of a Cylinder Wake , 1988 .

[11]  Patrick Chassaing,et al.  Nonlinear interaction and the transition to turbulence in the wake of a circular cylinder , 1987, Journal of Fluid Mechanics.

[12]  C. R. Smith,et al.  Secondary vortices in the wake of circular cylinders , 1986, Journal of Fluid Mechanics.

[13]  David R. Williams,et al.  Quantitative measurements of three-dimensional structures in the wake of a circular cylinder , 1994 .

[14]  J. Gerrard The wakes of cylindrical bluff bodies at low Reynolds number , 1978, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[15]  Luis P. Bernal,et al.  Streamwise vortex structure in plane mixing layers , 1986, Journal of Fluid Mechanics.