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Two-vortex equilibrium in the flow past a flat plate at incidence

Published online by Cambridge University Press:  14 August 2014

Luca Zannetti  and
Alexandre Gourjii
Luca Zannetti*
Affiliation:
DIMEAS, Politecnico di Torino, C.so Duca degli Abruzzi 24, 10129 Torino, Italy
Alexandre Gourjii
Affiliation:
National Technical University of Ukraine‘KPI’, 37 Pobedy av., 03056 Kiev, Ukraine
*
†Email address for correspondence: luca.zannetti@polito.it
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Abstract

The two-dimensional inviscid incompressible steady flow past an inclined flat plate is considered. A locus of asymmetric equilibrium configurations for vortex pairs is detected. It is shown that the flat geometry has peculiar properties compared to other geometries: (i) in order to satisfy the Kutta condition at both edges, which ensures flow regularity, the total circulation and the force acting on the plate must be zero; and (ii) the Kutta condition and the free vortex equilibrium conditions are not independent of each other. The non-existence of symmetric equilibrium configurations for an orthogonal plate is extended to more general asymmetric flows.

JFM classification

Vortex Flows: Vortex Flows Vortex Flows: Vortex instability Wakes/Jets: Wakes/Jets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 755 , 25 September 2014 , pp. 50 - 61
Copyright
© 2014 Cambridge University Press 

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References

Arnold, V. I. 1991 Mathematical Methods of Classical Mechanics. Springer.Google Scholar
Batchelor, G. K. 1956 A proposal concerning laminar wakes behind bluff bodies at large Reynolds number. J. Fluid Mech. 1, 388–398.CrossRefGoogle Scholar
Cai, J., Liu, F. & Luo, S. 2003 Stability of symmetric vortices in two dimensions and over three-dimensional slender conical bodies. J. Fluid Mech. 480, 65–94.CrossRefGoogle Scholar
Clements, R. R. 1973 An inviscid model of two-dimensional vortex shedding. J. Fluid Mech. 57, 321–336.CrossRefGoogle Scholar
Crowdy, D. G. & Marshall, J. S. 2005 Analytical formulae of the Kirchhoff–Routh path function in multiply connected domains. Proc. R. Soc. Lond. A 461 (2060), 2477–2501.Google Scholar
Elcrat, A., Ferlauto, M. & Zannetti, L. 2014 Models for inviscid wakes past bluff bodies. Fluid Dyn. Res. 46, 031407.CrossRefGoogle Scholar
Elcrat, A., Forneberg, B., Horn, M. & Miller, K. 2000 Some steady vortex flows past a circular cylinder. J. Fluid Mech. 409, 13–27.CrossRefGoogle Scholar
Gallizio, F., Iollo, A., Protas, B. & Zannetti, L. 2010 On continuation of inviscid vortex patches. Physica D 239, 190–201.CrossRefGoogle Scholar
Gantmacher, F. R. 1966 Théorie des Matrices. Dunod.Google Scholar
Iosilevskii, G. & Seginer, A. 1994 Asymmetric vortex pair in the wake of a circular cylinder. AIAA J. 32, 1999–2003.CrossRefGoogle Scholar
Joukowskii, N. E. 1907 On annexed bounded vortices. Trudy Otd. Fiz. Nauk. Mosk. Obshch. Lyub. Estest. Antr. Etn. 13 (2), 12–25 (in Russian).Google Scholar
Katz, J. & Plotkin, A. 2001 Low-speed Aerodynamics. Cambridge University Press.CrossRefGoogle Scholar
Lin, C. C. 1941 On the motion of vortices in two dimensions-I existence of the Kirchoff–Routh function, -II some further investigations on the Kirchoff–Routh function. Proc. Natl Acad. Sci. USA 27, 570–577.CrossRefGoogle Scholar
Lugt, H. J. 1985 Vortex flow and maximum principles. Am. J. Phys. 53 (7), 649–653.CrossRefGoogle Scholar
Meleshko, V. V. & Aref, H. 2007 A bibliography of vortex dynamics 1858–1956. Adv. Appl. Mech. 41, 197–292.Google Scholar
Newton, P. K. 2000 The N-Vortex Problem. Springer.Google Scholar
Saffman, P. G. 1992 Vortex Dynamics. Cambridge University Press.Google Scholar
Saffman, P. G. & Sheffield, J. S. 1977 Flow over a wing with an attached free vortex. Stud. Appl. Maths 57, 107–117.CrossRefGoogle Scholar
Smith, J. H. B. & Clark, R. W. 1975 Non-existence of stationary vortices behind a two-dimensional normal plate. AIAA J. 13 (8), 1114–1115.CrossRefGoogle Scholar
Vasconcelos, G. L., Moura, N. M. & Schakel, A. M. J. 2011 Vortex motion around a circular cylinder. Phys. Fluids 23, 123601.CrossRefGoogle Scholar
Zannetti, L. 2006 Vortex equilibrium in the flow past bluff bodies. J. Fluid Mech. 562, 151–171.CrossRefGoogle Scholar
Zannetti, L. & Franzese, P. 1994 The non-integrability of the restricted problem of two vortices in closed domains. Physica D 76, 99–109.CrossRefGoogle Scholar