Top

Published in:

2013 | OriginalPaper | Chapter

Formation of Coherent Structures in a Class of Realistic 3D Unsteady Flows

Authors : Michel F. M. Speetjens, Herman J. H. Clercx

Published in: Fluid Dynamics in Physics, Engineering and Environmental Applications

Publisher: Springer Berlin Heidelberg

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

The formation of coherent structures in three-dimensional (3D) unsteady laminar flows in a cylindrical cavity is reviewed. The discussion concentrates on two main topics: the role of symmetries and fluid inertia in the formation of coherent structures and the ramifications for the Lagrangian transport properties of passive tracers. We consider a number of time-periodic flows that each capture a basic dynamic state of 3D flows: 1D motion on closed trajectories, (quasi-)2D motion within (approximately) 2D subregions of the flow domain and truly 3D chaotic advection. It is shown that these states and their corresponding coherent structures are inextricably linked to symmetries (or absence thereof) in the flow. Symmetry breaking by fluid inertia and the resulting formation of intricate coherent structures and (local) onset of 3D chaos is demonstrated. Finally, first experimental analyses on coherent structures and the underlying role of symmetries are discussed.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

previous chapter High Speed Shadowgraphy for the Study of Liquid Drops

next chapter Jets in Symbiotic Stars: The R Aqr Case

A space is termed convex if for any pair of points within the space, any point on the line joining them is also within the space.

The winding number \(W\) represents the number of revolutions around the axis of rotation required for completing a full loop on closed trajectories. The closed streamlines in Fig. 1b have unit winding number.

Alexandroff P (1961) Elementary concepts of topology. Dover, New York

Anderson PA, Galaktionov OS, Peters GWM, van de Vosse FN, Meijer HEH (1999) Analysis of mixing in three-dimensional time-periodic cavity flows. J Fluid Mech 386:149CrossRef

Anderson PA, Ternet TJ, Peters GWM, Meijer HEH (2006) Experimental/numerical analysis of chaotic advection in a three-dimensional cavity flow. Int Polym Process 4:412

Arnol’d VI (1978) Mathematical methods of classical mechanics. Springer, New York

Arnol’d VI, Khesin BA (1991) Topological methods in hydrodynamics. Springer, New York

Bennet A (2006) Lagrangian fluid dynamics. Cambridge University Press, CambridgeCrossRef

Biskamp D (1993) Nonlinear magnetohydrodynamics. Cambridge University Press, Cambridge

Cartwright JHE, Feingold M, Piro O (1996) Chaotic advection in three-dimensional unsteady incompressible laminar flow. J Fluid Mech 316:259CrossRef

Dombre T, Frisch U, Greene JM, Hénon M, Mehr A, Soward AM (1986) Chaotic streamlines in the ABC flows. J Fluid Mech 167:353CrossRef

Feingold M, Kadanoff LP, Piro O (1987) A way to connect fluid dynamics to dynamical systems: passive scalars. In: Hurd AJ, Weitz DA, Mandelbrot BB (eds) Fractal aspects of materials: disordered systems. Materials Research Society, Pittsburgh, pp 203–205

Feingold M, Kadanoff LP, Piro O (1988) Passive scalars, three-dimensional volume-preserving maps and chaos. J Stat Phys 50:529CrossRef

Franjione JG, Leong C-W, Ottino JM (1989) Symmetries within chaos: a route to effective mixing. Phys Fluids A 11:1772CrossRef

Gómez A, Meiss JD (2002) Volume-preserving maps with an invariant. Chaos 12:289CrossRef

Guckenheimer J, Holmes P (1983) Nonlinear oscillations, dynamical systems and bifurcations of vector fields. Springer, New York

Haller G, Mezić I (1998) Reduction of three-dimensional, volume-preserving flows by symmetry. Nonlinearity 11:319CrossRef

Luethi B, Tsinober A, Kinzelbach W (2005) Lagrangian measurement of vorticity dynamics in turbulent flow. J Fluid Mech 528:87CrossRef

Malyuga VS, Meleshko VV, Speetjens M (2002) Mixing in the Stokes flow in a cylindrical container. Proc R Soc Lond A 458:1867CrossRef

MacKay RS (1994) Transport in 3D volume-preserving flows. J Nonlinear Sci 4:329CrossRef

Meier SW, Lueptow RM, Ottino JM (2007) A dynamical systems approach to mixing and segregation of granular materials in tumblers. Adv Phys 56:757CrossRef

Meleshko VV, Peters GWM (1996) Periodic points for two-dimensional Stokes flow in a rectangular cavity. Phys Lett A 216:87CrossRef

Mezić I, Wiggins S (1994) On the integrability and perturbation of three-dimensional fluid flows with symmetry. J Nonlinear Sci 4:157CrossRef

Mezić I (2001) Break-up of invariant surfaces in action-angle-angle maps and flows. Physica D 154:51CrossRef

Moffatt HK, Zaslavsky GM, Comte P, Tabor M (1992) Topological aspects of the dynamics of fluids and plasmas. Kluwer Academic Publishers, Dordrecht

Mullowney P, Julien K, Meiss JD (2008) Blinking rolls: chaotic advection in a three-dimensional flow with an invariant. SIAM J Appl Dyn Sys 4:159186

Mullowney P, Julien K, Meiss JD (2008) Chaotic advection and the emergence of tori in the Küppers–Lortz state. Chaos 18:033104CrossRef

Ottino JM (1989) The kinematics of mixing: stretching, chaos and transport. Cambridge University Press, Cambridge

Ottino JM, Jana SC, Chakravarthy VS (1994) From Reynolds stretching and folding to mixing studies using horseshoe maps. Phys Fluids 6:685CrossRef

Pouransari Z, Speetjens MFM, Clercx HJH (2010) Formation of coherent structures by fluid inertia in three-dimensional laminar flows. J Fluid Mech 654:5CrossRef

Shankar PN (1997) Three-dimensional eddy structure in a cylindrical container. J Fluid Mech 342:97CrossRef

Speetjens MFM (2001) Three-Dimensional chaotic advection in a cylindrical domain. PhD thesis, Eindhoven University of Technology, The Netherlands

Speetjens MFM, Clercx HJH, van Heijst GJF (2004) A numerical and experimental study on advection in three-dimensional Stokes flows. J Fluid Mech 514:77CrossRef

Speetjens MFM, Clercx HJH, van Heijst GJF (2006) Inertia-induced coherent structures in a time-periodic viscous mixing flow. Phys Fluids 18:083603CrossRef

Speetjens MFM, Clercx HJH, van Heijst GJF (2006) Merger of coherent structures in time-periodic viscous flows. Chaos 16:043104CrossRef

Sturman R, Ottino JM, Wiggins S (2006) The mathematical foundation of mixing. Cambridge University Press, Cambridge

Sturman R, Meier SW, Ottino JM, Wiggins S (2008) Linked twist map formalism in two and three dimensions applied to mixing in tumbled granular flows. J Fluid Mech 602:129CrossRef

Voth GA, Haller G, Gollub JP (2002) Experimental measurements of stretching fields in fluid mixing. Phys Rev Lett 88:254501CrossRef

Wiggins S (2010) Coherent structures and chaotic advection in three dimensions. J Fluid Mech 654:1CrossRef

Znaien JG, Speetjens MFM, Trieling RR, Clercx HJH (2012) On the observability of periodic lines in 3D lid-driven cylindrical cavity flows. Phys Rev E 85(6):066320–1/14CrossRef

Title: Formation of Coherent Structures in a Class of Realistic 3D Unsteady Flows
Authors: Michel F. M. Speetjens
Herman J. H. Clercx
Publisher: Springer Berlin Heidelberg
Book: Fluid Dynamics in Physics, Engineering and Environmental Applications
Print ISBN: 978-3-642-27722-1

Electronic ISBN: 978-3-642-27723-8

Copyright Year: 2013
DOI: https://doi.org/10.1007/978-3-642-27723-8_9