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Compressible vortex reconnection

Published online by Cambridge University Press:  26 April 2006

D. Virk ,
F. Hussain  and
R. M. Kerr
D. Virk
Affiliation:
Department of Mechanical Engineering, University of Houston, Houston, TX 77204-4792, USA
F. Hussain
Affiliation:
Department of Mechanical Engineering, University of Houston, Houston, TX 77204-4792, USA
R. M. Kerr
Affiliation:
Geophysical Turbulence Program, NCAR, Boulder, CO 80307-3000, USA
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Abstract

Reconnection of two antiparallel vortex tubes is studied as a prototypical coherent structure interaction to quantify compressibility effects in vorticity dynamics. Direct numerical simulations of the Navier-Stokes equations for a perfect gas are carried out with initially polytropically related pressure and density fields. For an initial Reynolds number (Re = Γ /v, circulation divided by the kinematic viscosity) of 1000, the pointwise initial maximum Mach number (M) is varied from 0.5 to 1.45. At M=0.5, not surprisingly, the dynamics are essentially incompressible. As M increases, the transfer of Γ starts earlier. For the highest M, we find that shocklet formation between the two vortex tubes enhances early Γ transfer due to viscous cross-diffusion as well as baroclinic vorticity generation. The reconnection at later times occurs primarily due to viscous cross-diffusion for all M. However, with increasing M, the higher early Γ transfer reduces the vortices’ curvature growth and hence the Γ transfer rate; i.e. for the Re case studied, the reconnection timescale increases with M. With increasing M, reduced vortex stretching by weaker ‘bridges’ decreases the peak vorticity at late times. Compressibility effects are significant in countering the stretching of the bridges even at late times. Our observations suggest significantly altered coherent structure dynamics in turbulent flows, when compressible.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 304 , 10 December 1995 , pp. 47 - 86
Copyright
© 1995 Cambridge University Press

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References

Ashurst, W. T. & Meiron, D. I. 1987 Numerical study of vortex reconnection. Phys. Rev. Lett. 58, 1632–1635.Google Scholar
Baird, J. P. 1987 Supersonic vortex rings. Proc. R. Soc. Land. A, 409, 59–65.Google Scholar
Boratav, O. N., Pelz, R. B. & Zabusky, N. J. 1992 Reconnection in orthogonally interacting vortex tubes: Direct numerical simulations and quantifications. Phys. Fluids A 4, 581–605.Google Scholar
Bridges, J., Husain, H. S. & Hussain, F. 1989 Whither coherent structures? In Whither Turbulence? Turbulence at the Crossroads (ed. J. L. Lumley), 132–150. Springer.
Broadbent, E. G. & Moore, D. W. 1987 The interaction of a vortex ring and a coaxial supersonic jet. Proc. R. Soc. Land. A 409, 47–57.Google Scholar
Buntine, J. D. & Pullin, D. I. 1989 Merger and cancellation of strained vortices. J. Fluid Mech. 205, 263–295.Google Scholar
Crow, S. C. 1970 Stability theory for a pair of trailing vortices. AIAA J. 8, 2172–2179.Google Scholar
Erlebacher, G., Hussaini, M. Y., Kreiss, H. & Sarkar, S. 1990 The analysis and simulation of compressible turbulence. ICASE Rep. 90-15.
Feiereisen, W. J., Reynolds, W. C. & Ferziger, J. H. 1981 Numerical simulation of a compressible, homogeneous, turbulent shear flow. Rep. TF-13. Stanford University.
Fohl, T. & Turner, J. S. 1975 Colliding vortex rings. Phys. Fluids 18, 433–436.Google Scholar
Greene, J. M. 1988 Geometrical properties of three-dimensional reconnecting magnetic fields with nulls. J. Geophys. Res. 93, 8583–8590.Google Scholar
Heister, S. D., Mcdonough, J. M., Karagozian, A. R. & Jenkins, D. W. 1990 The compressible vortex pair. J. Fluid Mech. 220, 339–354.Google Scholar
Howard, L. N. & Matthews, D. L. 1956 On the vortices produced in shock diffraction. J. Appl. Phys. 26, 223–231.Google Scholar
Hussain, F. 1986 Coherent structures and turbulence. J. Fluid Mech. 173, 303–356.Google Scholar
Hussain, F. & Husain, H. S. 1989 Elliptic jets. Part 1. Characteristics of unexcited and excited jets. J. Fluid Mech. 208, 257–320.Google Scholar
Kambe, T. 1983 A class of exact solutions of two-dimensional viscous flow. J. Phys. Soc. Japan 52, 834–841.Google Scholar
Kerr, R. & Hussain, F. 1989 Simulation of vortex reconnection. Physica D 37, 474–484.Google Scholar
Kida, S. & Takaoka, M. 1987 Bridging in vortex reconnection. Phys. Fluids 30, 2911–2914.Google Scholar
Kida, S. & Takaoka, M. 1991 Breakdown of frozen motion of vorticity field and vortex reconnection. J. Phys. Soc. Japan 60, 2184–2196.Google Scholar
Kida, S. & Takaoka, M. 1994 Vortex reconnection. Ann. Rev. Fluid Mech. 60, 169–189.Google Scholar
Kida, S., Takaoka, M. & Hussain, F. 1989 Reconnection of two vortex rings. Phys. Fluids A 1, 630–632.Google Scholar
Kida, S., Takaoka, M. & Hussain, F. 1991a Collision of two vortex rings. J. Fluid Mech. 230, 583–646.Google Scholar
Kida, S., Takaoka, M. & Hussain, F. 1991b Formation of head-tail structure in two-dimensional straining flow. Phys. Fluids A 3, 2688–2697.Google Scholar
Lee, S., Lele, S. K. & Moin, P. 1991 Eddy shocklets in decaying compressible turbulence. Phys. Fluids A 3, 657–664.Google Scholar
Lim, T. T. 1989 An experimental study of a vortex ring interacting with an inclined wall. Exps. Fluids 7, 453–463.Google Scholar
Mandella, M. J. 1987 Experimental and analytical studies of compressible vortices. PhD thesis, Stanford University.
Meiron, D. I., Shelley, M. J., Ashurst, W. T. & Orszag, S. A. 1989 Numerical studies of vortex reconnection. In Mathematical Aspects of Vortex Dynamics (ed. R. Caflisch). SIAM.
Melander, M. V. & Hussain, F. 1988 Cut-and-connect of two antiparallel vortex tubes. CTR Rep. S-88, pp. 257–286 (referred to herein as MH 1988).
Melander, M. V. & Hussain, F. 1989 Cross-linking of two antiparallel vortex tubes. Phys. Fluids A 1, 633–636.Google Scholar
Melander, M. V. & Hussain, F. 1990 Topological aspects of vortex reconnection. In Topological Fluid Mechanics (ed. H.K. Moffatt & A. Tsinober), pp. 485–499. Cambridge University Press.
Melander, M. V. & Hussain, F. 1993 Coupling between a coherent structure and fine-scale turbulence. Phys. Rev. E 48, 2669–2689.Google Scholar
Melander, M. V. & Hussain, F. 1994a Topological vortex dynamics in axisymmetric viscous flows. J. Fluid Mech. 260, 57–80.Google Scholar
Melander, M. V. & Hussain, F. 1994b Core dynamics on a vortex column. Fluid Dvn. Res. 13, 1–37.Google Scholar
Meng, H. & Hussain, F. 1995 Instantaneous flow field in an unstable vortex ring measured by holographic particle velocimetry. Phys. Fluids 7, 9–11.Google Scholar
Moore, D. W. & Pullin, D. I. 1987 The compressible vortex pair. J. Fluid Mech. 185, 171–204.Google Scholar
Moser, R. D. & Rogers, M. M. 1993 The three-dimensional evolution of a plane mixing layer: pairing and transition to turbulence. J. Fluid Mech. 247, 275–320.Google Scholar
Oshima, Y. & Izutzu, N. 1988 Cross-linking of two vortex rings. Phys. Fluids 31, 2401.Google Scholar
Passot, T. & Pouquet, A. 1987 Numerical simulation of compressible homogeneous flows in the turbulent regime. J. Fluid Mech. 181, 441–466.Google Scholar
Pumir, A. & Siggia, E. 1990 Collapsing solutions to the three-dimensional Euler equations. Phys. Fluids A 2, 220–241.Google Scholar
Saffman, P. 1990 A model of vortex reconnection. J. Fluid Mech. 212, 395–402.Google Scholar
Schatzle, P. 1987 An experimental study of fusion of vortex rings. PhD thesis, California Institute of Technology.
Schoppa, W., Hussain, F. & Metcalfe, R. 1995 A new mechanism of small-scale transition in a plane mixing layer: core dynamics of span wise vortices. J. Fluid Mech. 298, 23–80Google Scholar
Shelley, M. J., Meiron, D. I. & Orszag, S. A. 1993 Dynamical aspects of vortex reconnection of perturbed anti-parallel vortex tubes. J. Fluid Mech. 246, 613–652.Google Scholar
Siggia, E. 1985 Collapse and amplification of a vortex filament. Phys. Fluids 28, 794–805.Google Scholar
Takaki, R. & Hussain, F. 1985 Recombination of vortex filaments and its role in aerodynamic noise. In Proc. 5th Symp. on Turbulent Shear Flows, pp. 3.19–3.25. Cornell University.
Thompson, P. A. 1984 Compressible-Fluid Dynamics. Mcgraw-Hill. Virk, D. 1993 Numerical studies of vortex dynamics: compressible reconnection and a polarized ring. PhD thesis, University of Houston.
Virk, D. & Hussain, F. 1993 Influence of initial conditions on compressible vorticity dynamics. Theor. Comput. Fluid Dyn. 5, 309–334.Google Scholar
Virk, D., Melander, M. V. & Hussain, F. 1994 Dynamics of a polarized vortex ring. J. Fluid Mech. 260, 23–55.Google Scholar
Wray, A. A. 1987 Very low storage time-advancement schemes. Internal Report. NASA Ames Research Center, Moffett Field, California.
Zabusky, N. J. & Melander, M. V. 1989 Three-dimensional vortex tube reconnection: morphology for orthogonally-offset tubes. Physica D 37, 555–562.Google Scholar
Zank, G. P. & Matthaeus, W. H. 1991 The equations of nearly incompressible fluids. I. Hydrodynamics, turbulence, and waves. Phys. Fluids A 3, 69–82.Google Scholar