Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-23T20:55:06.732Z Has data issue: false hasContentIssue false

Separated rows structure of vortex streets behind triangular objects

Published online by Cambridge University Press:  10 January 2019

Ildoo Kim*
Affiliation:
School of Engineering, Brown University, Providence, RI 02912, USA
*
Email address for correspondence: ildoo.kim.phys@gmail.com

Abstract

We discuss two distinct spatial structures of vortex streets. The ‘conventional mushroom’ structure is commonly discussed in many experimental studies, and the exotic ‘separated rows’ structure is characterized by a thin layer of irrotational fluid between two rows of vortices. In a two-dimensional soap film channel, we generate the exotic vortex arrangement by using triangular objects. This setting allows us to vary the thickness of boundary layers and their separation distance independently. We find that the separated rows structure appears only when the boundary layer is thinner than 40 % of the separation distance. We also discuss two physical mechanisms of the breakdown of vortex structures. The conventional mushroom structure decays due to the mixing, and the separated rows structure decays because its arrangement is hydrodynamically unstable.

Type
JFM Papers
Copyright
© 2019 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Birkhoff, G. 1953 Formation of vortex streets. J. Appl. Phys. 24, 98103.Google Scholar
Choi, H., Jeon, W. & Kim, J. 2008 Control of flow over a bluff body. Annu. Rev. Fluid Mech. 40 (1), 113139.10.1146/annurev.fluid.39.050905.110149Google Scholar
Cimbala, J. M., Nagib, H. M. & Roshko, A. 1988 Large structure in the far wakes of two-dimensional bluff bodies. J. Fluid Mech. 190, 265298.10.1017/S0022112088001314Google Scholar
Dynnikova, G. Y., Dynnikov, Y. A. & Guvernyuk, S. V. 2016 Mechanism underlying Kármán vortex street breakdown preceding secondary vortex street formation. Phys. Fluids 28 (5), 054101.10.1063/1.4947449Google Scholar
Fey, U., Konig, M. & Eckelmann, H. 1998 A new Strouhal–Reynolds number relationship for the circular cylinder in the range 47. Phys. Fluids 10, 15471549.10.1063/1.869675Google Scholar
Georgiev, D. & Vorobieff, P. 2002 The slowest soap-film tunnel in the southwest. Rev. Sci. Instrum. 73 (3), 11771184.Google Scholar
Goldstein, S. 1938 Modern Development in Fluid Mechanics. Oxford University Press.Google Scholar
Hooker, S. G. 1936 On the action of viscosity in increasing the spacing ratio of a vortex street. Proc. R. Soc. Lond. A 154, 6791.Google Scholar
Inoue, O. & Yamazaki, T. 1999 Secondary vortex streets in two-dimensional cylinder wakes. Fluid Dyn. Res. 25, 118.10.1016/S0169-5983(98)00027-6Google Scholar
von Kármán, T. 1911 Uber den Mechanismus des Widerstandes, den ein bewegter Korper in einer Flussigkeit erfahrt. Gott. Nachr. Math.-Phys. Klasse 509517.Google Scholar
Kim, I. & Mandre, S. 2017 Marangoni elasticity of flowing soap films. Phys. Rev. Fluids 2 (8), 082001(R).10.1103/PhysRevFluids.2.082001Google Scholar
Kim, I. & Wu, X. L. 2015 Unified Strouhal–Reynolds number relationship for laminar vortex streets generated by different-shaped obstacles. Phys. Rev. E 92 (4), 043011.Google Scholar
Kumar, B. & Mittal, S. 2012 On the origin of the secondary vortex street. J. Fluid Mech. 711, 641666.10.1017/jfm.2012.421Google Scholar
Martin, B. & Wu, X.-L. 1995 Shear flow in a two-dimensional Couette cell: a technique for measuring the viscosity of free-standing liquid films. Rev. Sci. Instrum. 66, 56035608.10.1063/1.1146027Google Scholar
Prasad, V. & Weeks, E. R. 2009 Flow fields in soap films: relating viscosity and film thickness. Phys. Rev. E 80 (2), 026309.Google Scholar
Rivera, M., Vorobieff, P. & Ecke, R. E. 1998 Turbulence in flowing soap films: velocity, vorticity, and thickness fields. Phys. Rev. Lett. 81, 14171420.Google Scholar
Roushan, P. & Wu, X. L. 2005 Structure-based interpretation of the Strouhal–Reynolds number relationship. Phys. Rev. Lett. 94, 054504.10.1103/PhysRevLett.94.054504Google Scholar
Schlichting, H. 1979 Boundary Layer Theory. McGraw-Hill.Google Scholar
Taneda, S. 1959 Downstream development of the wakes behind cylinders. J. Phys. Soc. Japan 14, 843848.Google Scholar
Vivek, S. & Weeks, E. R. 2015 Measuring and overcoming limits of the Saffman–Delbrück model for soap film viscosities. PLoS ONE 10, e0121981.10.1371/journal.pone.0121981Google Scholar
Vorobieff, P. & Ecke, R. E. 1999 Cylinder wakes in flowing soap films. Phys. Rev. E 60, 29532956.Google Scholar
Vorobieff, P., Georgiev, D. & Ingber, M. S. 2002 Onset of the second wake: dependence on the Reynolds number. Phys. Fluids 14 (7), L53L56.10.1063/1.1486450Google Scholar
Wang, S., Tian, F., Jia, L., Lu, X. & Yin, X. 2010 Secondary vortex street in the wake of two tandem circular cylinders at low Reynolds number. Phys. Rev. E 81 (3), 036305.Google Scholar
Williamson, C. H. K. 1996 Vortex dynamics in the cylinder wake. Annu. Rev. Fluid Mech. 28, 477539.10.1146/annurev.fl.28.010196.002401Google Scholar
Williamson, C. H. K. & Brown, G. L. 1998 A series in 1/√Re to represent the Strouhal–Reynolds number relationship of the cylinder wake. J. Fluids Struct. 12, 10731085.10.1006/jfls.1998.0184Google Scholar
Williamson, C. H. K. & Prasad, A. 1993 Wave interactions in the far wake of a body. Phys. Fluids A 5, 18541856.10.1063/1.858810Google Scholar
Wu, X.-L., Martin, B., Kellay, H. & Goldburg, W. I. 1995 Hydrodynamic convection in a two-dimensional Couette cell. Phys. Rev. Lett. 75, 236239.10.1103/PhysRevLett.75.236Google Scholar