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

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Fluid Dynamics in Physics, Engineering and Environmental Applications

Part of the book series: Environmental Science and Engineering ((ENVENG))

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.

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Notes

  1. 1.

    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.

  2. 2.

    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.

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Energy Technology and J.M. Burgers Center for Fluid Dynamics, P.O. Box 513, 5600, Eindhoven, The Netherlands

    Michel F. M. Speetjens

  2. Department of Applied Physics, Fluid Dynamics Laboratory and J.M. Burgers Center for Fluid Dynamics, P.O. Box 513, 5600, Eindhoven, The Netherlands

    Herman J. H. Clercx

Authors
  1. Michel F. M. Speetjens
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  2. Herman J. H. Clercx
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Corresponding author

Correspondence to Michel F. M. Speetjens .

Editor information

Editors and Affiliations

  1. Nucleares, Instituto Nacional des Investigaciones, La Marquesa, Ocoyoacac, Carretera Mexico-Toluca S/N, Mexico, 52750, Mexico

    Jaime Klapp

  2. Metropolitana-Azcapotzalco, Departamento de Ciencias Básicas, Unviersidat Autonóma, Avenida San Pablo 180, Mexico City, 02200, Mexico

    Abraham Medina

  3. Instituto de Astronomia y Meteorologia, Vallarta 2602, Guadalajara, 44100, Mexico

    Anne Cros

  4. Metropolitana-Azcapotzalco, Departamento de Ciencias Básicas, Universidad Autonóma, Avenida San Pablo 180, Mexico City, 02200, Mexico

    Carlos A. Vargas

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Speetjens, M.F.M., Clercx, H.J.H. (2013). Formation of Coherent Structures in a Class of Realistic 3D Unsteady Flows. In: Klapp, J., Medina, A., Cros, A., Vargas, C. (eds) Fluid Dynamics in Physics, Engineering and Environmental Applications. Environmental Science and Engineering(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27723-8_9

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