Hostname: page-component-76fb5796d-wq484 Total loading time: 0 Render date: 2024-04-26T22:20:00.934Z Has data issue: false hasContentIssue false
  • English
  • Français

The rollup of a vortex layer near a wall

Published online by Cambridge University Press:  26 April 2006

Javier Jiménez  and
Paolo Orlandi
Javier Jiménez
Affiliation:
School of Aeronautics, U. Politécnica, Pl. Cardenal Cisneros 3, 28040 Madrid, Spain Centre for Turbulence Research, Standford University, CA 94305, USA and NASA Ames Research Centre, CA 94035, USA
Paolo Orlandi
Affiliation:
Dipartimento di Meccanica e Aeronautica, Università ‘La Sapienza’, Via Eudossiana 16, 00184, Roma, Italy Centre for Turbulence Research, Standford University, CA 94305, USA and NASA Ames Research Centre, CA 94035, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The behaviour of an inviscid vortex layer of non-zero thickness near a wall is studied, both through direct numerical simulation of the two-dimensional vorticity equation at high Reynolds numbers, and using an approximate ordinary nonlinear integro-differential equation which is satisfied in the limit of a thin layer under long-wavelength perturbations. For appropriate initial conditions the layer rolls up and breaks into compact vortices which move along the wall at constant speed. Because of the effect of the wall, they correspond to equilibrium counter-rotating vortex dipoles. This breakup can be related to the disintegration of the initial conditions of the approximate nonlinear dispersive equation into solitary waves. The study is motivated by the formation of longitudinal vortices from vortex sheets in the wall region of a turbulent channel.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 248 , March 1993 , pp. 297 - 313
Copyright
© 1993 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

Benjamin, T. B. 1967 Internal waves of permanent form in fluids of great depth. J. Fluid Mech. 29, 559– 592.Google Scholar
Broadbent, E. G. & Moore, D. W. 1985 Waves of extreme form on a layer of uniform vorticity. Phys. Fluids 28, 1561– 1563.Google Scholar
Deem, G. S. & Zabusky, N. J. 1978 Vortex waves: stationary V-states, interactions, recurrence and breaking. Phys. Rev. Lett 40 859– 862.Google Scholar
Dritschel, D. G. 1988 The repeated filamentation of two-dimensional vorticity interface. J. Fluid Mech. 194, 511– 547.Google Scholar
Goldstein, M. E., Leib, S. J. & Cowley, S. J. 1992 Distortion of a flat plate boundary layer by a free stream vorticity normal to the plate. J. Fluid Mech. 237, 231– 260.Google Scholar
Higuera, F. & Jiménez, J. 1992 Solitary waves on planar and axisymmetric vorticity layers. J. Fluid Mech. (submitted).Google Scholar
Jiménez, J. & Moin, P. 1991 The minimal flow unit in near wall turbulence. J. Fluid Mech. 225, 213– 240.Google Scholar
Kim, H. T., Kline, S. J. & Reynolds, W. C. 1971 The production of turbulence near a smooth wall in a turbulent boundary layers. J. Fluid Mech. 50, 133– 160.Google Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133– 166.Google Scholar
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.
Lin, S. J. & Corcos, G. M. 1984 The mixing layer: deterministic models of a turbulent flow. Part 3. The effect of plane strain on the dynamics of streamwise vortices. J. Fluid Mech. 141, 139– 178.CrossRefGoogle Scholar
Lundgren, T. S. 1982 Strained spiral vortex model for turbulent fine structure. Phys. Fluids 25, 2193– 2203.Google Scholar
Melander, M. V., McWilliams, J. C. & Zabusky, N. J. 1987 Axisymmetrisation and vorticity gradient intensification of isolated two dimensional vortices through filamentation. J. Fluid Mech. 178, 137– 159.Google Scholar
Neu, J. 1984 The dynamics of stretched vortices. J. Fluid Mech. 143, 253– 276.Google Scholar
Orlandi, P. 1989 Numerical simulation of vortices motion in presence of solid boundaries. In Proc 8th GAMM Conf. on Numerical Methods in Fluid Mechanics (ed. P. Weeseling) pp. 436– 441. Vieweg, Braunschweig.
Orlandi, P. & Jiménez, J. 1991 A model for bursting of near wall vortical structures in boundary layers. In 8th Symp. Turbulent Shear Flows, Munich, Sept. 9-11, 1991, pp. 28.1.1– 28.1.6.
Pierrehumbert, R. T. 1980 A family of steady, translating vortex pairs with distributed vorticity. J. Fluid Mech. 99, 129– 144 (and Corrigendum. J. Fluid Mech. 102, 478).Google Scholar
Polvani, L. M. & Flierl, G. R. 1986 Generalised Kirchhoff vortices. Phys. Fluids 29, 2376– 2379.Google Scholar
Pullin, D. I. 1981 The nonlinear behaviour of a constant vorticity layer at a wall. J. Fluid Mech. 108, 401– 421.Google Scholar
Rayleigh, Lord 1887 On the stability or instability of certain fluid motions, II. Scientific Papers, vol 3, pp. 17– 23. Cambridge University Press. Also Proc. Lond. Math. Soc. 19, 67–74.
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Ann. Rev. Fluid Mech. 23, 601– 639.Google Scholar
Sadovskii, K. S. 1971 Vortex regions in a potential stream with a jump of Bernouilli's constant at the boundary. Prik. Matem. Mekh. 35, 773– 779.Google Scholar
Saffman, P. G. & Szeto, R. 1980 Equilibrium shapes of a pair of equal uniform vortices. Phys. Fluids 23, 2339– 2342.Google Scholar
Saffman, P. G. & Tanveer, S. 1982 The touching pair of equal and opposite uniform vortices. Phys. Fluids 25, 1929– 1930.Google Scholar
Sendstad, O. 1992 Mechanics of three dimensional boundary layers. PhD thesis, Stanford University.
Spalart, P. R. 1988 Direct numerical simulation of a turbulent boundary layer up to Rθ = 1410. J. Fluid Mech. 187, 61– 98.Google Scholar
Stern, M. E. & Paldor, N. 1983 Large amplitude long waves in shear flow. Phys. Fluids 26, 906– 919.Google Scholar
Stern, M. E. & Pratt, L. J. 1985 Dynamics of vorticity fronts. J. Fluid Mech. 161, 513– 532.Google Scholar
Whitham, G. B. 1974 Linear and Nonlinear Waves. John Wiley.