Abstract
We study the interaction between a coherent structure (CS) and imposed external turbulence by employing direct numerical simulations (DNS) designed for unbounded flows with compact vorticity distribution. Flow evolution comprises (i) the reorganization of turbulence into finer-scale spiral filaments, (ii) the growth of wave-like perturbations within the vortex core, and (iii) the eventual arrest of production, leading to the decay of ambient turbulence. The filaments, preferentially aligned in the azimuthal direction, undergo two types of interactions: parallel filaments pair to form higher-circulation “threads”, and anti-parallel threads form dipoles that self-advect radially outwards. The consequent radial transport of angular momentum manifests as an overshoot of the mean circulation profile—a theoretically known consequence of faster-than-viscous vortex decay. It is found that while the resulting centrifugal instability can enhance turbulence production, vortex decay is arrested by the dampening of the instability due to the “turbulent mixing” caused by instability-generated threads. Ensemble-averaged turbulence statistics show strong fluctuations within the core; these are triggered by the external turbulence, and grow even as the turbulence decays. This surprising growth on a normal-mode-stable vortex results from algebraic amplification through “linear transient growth”. Transient growth is examined by initializing DNS with the “optimal” modes obtained from linear analysis. The simulations show that the growth of transient modes reproduces the prominent dynamics of CS-turbulence interaction: formation of thread-dipoles, growth of core fluctuations, and appearance of bending waves on the column’s core. At the larger Reynolds numbers prevailing in practical flows, transient growth may enable accelerated vortex decay through vortex column breakdown.
Preview
Unable to display preview. Download preview PDF.
References
Antkowiak A., Brancher P.: Transient growth for the Lamb-Oseen vortex. Phys. Fluids 16(1), L1–L4 (2004)
Cambon C., Scott J.F.: Linear and nonlinear models of anisotropic turbulence. Ann. Rev. Fluid Mech. 31, 1–54 (1999)
Davenport W.J., Rife M.C., Liapis S.I., Follin G.J.: The structure and development of a wing-tip vortex. J. Fluid Mech. 312, 67–106 (1996)
Govindaraju S.P., Saffman P.G.: Flow in a turbulent trailing vortex. Phys. Fluids 14(10), 2074–2080 (1971)
Hamilton J.M., Kim J., Waleffe F.: Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317–348 (1995)
Hoffman E.R., Joubert P.N.: Turbulent line vortices. J. Fluid Mech. 16(3), 395–411 (1963)
Jacquin L., Pantano C.: On the persistence of trailing vortices. J. Fluid Mech. 471, 159–168 (2002)
Kerswell R.R.: Elliptical instability. Ann. Rev. Fluid Mech. 34, 83–113 (2002)
Mansour N.N., Wray A.A.: Decay of isotropic turbulence at low Reynolds number. Phys. Fluids 6(2), 808–814 (1994)
Marshall, J.S., Beninati, M.L.: Turbulence evolution in vortex dominated flows. In: Debnath, L., Riahi, D.N. (eds.) Advances in Fluid Mechanics, vol. 25 (Nonlinear instability, chaos and turbulence II, p. 1), pp. 1–40. WIT Press, Southampton, England (2000)
Mayer E.W., Powell K.G.: Viscous and inviscid instabilities of a trailing vortex. J. Fluid Mech. 245, 91–114 (1992)
Melander M.V., Hussain F.: Coupling between a coherent structure and fine-scale turbulence. Phys. Rev. E 48(4), 2669–2689 (1993a)
Melander M.V., Hussain F.: Polarized vortex dynamics on a vortex column. Phys. Fluids A 5, 1992–2003 (1993b)
Phillips W.R.C., Graham J.A.H.: Reynolds-stress measurements in a turbulent trailing vortex. J. Fluid Mech. 147, 353–371 (1984)
Pradeep D.S., Hussain F.: Effects of boundary condition in numerical simulations of vortex dynamics. J. Fluid Mech. 516, 115–124 (2004)
Pradeep D.S., Hussain F.: Transient growth of perturbations in vortex column. J. Fluid Mech. 550, 251–288 (2006)
Ragab S., Sreedhar M.: Numerical simulation of vortices with axial velocity deficits. Phys. Fluids 7(3), 549–558 (1995)
Rennich S.C., Lele S.K.: Numerical method for incompressible vortical flows with two unbounded directions. J. Comput. Phys. 137, 101–129 (1997)
Saffman P.G.: Structure of turbulent line vortices. Phys. Fluids 16(8), 1182–1188 (1973)
Schoppa W., Hussain F.: Coherent structure generation in near-wall turbulence. J. Fluid Mech. 453, 57–108 (2002)
Spalart P.: Aircraft trailing vortices. Ann. Rev. Fluid Mech. 30, 107–138 (1998)
Sreedhar M., Ragab S.: Large eddy simulation of longitudinal stationary vortices. Phys. Fluids 6(7), 2501–2514 (1994)
Wallin S., Girimaji S.S.: Evolution of an isolated turbulent trailing vortex. AIAA J. 38(4), 657–665 (2000)
Zeman O.: The persistence of trailing vortices: a modeling study. Phys. Fluids 7(1), 135–143 (1995)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Additional information
Communicated by H. Aref
Rights and permissions
Copyright information
© 2010 Springer-Verlag
About this paper
Cite this paper
Pradeep, D.S., Hussain, F. (2010). Vortex dynamics of turbulence–coherent structure interaction. In: Aref, H. (eds) 150 Years of Vortex Dynamics. Iutam Bookseries, vol 20. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-8584-9_34
Download citation
DOI: https://doi.org/10.1007/978-90-481-8584-9_34
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-8583-2
Online ISBN: 978-90-481-8584-9
eBook Packages: Engineering (R0)