Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgments
- 1 Introduction
- 2 Eulerian and Lagrangian Fundamentals
- 3 Objectivity of Transport Barriers
- 4 Barriers to Chaotic Advection
- 5 Lagrangian and Objective Eulerian Coherent Structures
- 6 Flow Separation and Attachment Surfaces as Transport Barriers
- 7 Inertial LCSs: Transport Barriers in Finite-Size Particle Motion
- 8 Passive Barriers to Diffusive and Stochastic Transport
- 9 Dynamically Active Barriers to Transport
- Appendix
- References
- Index
5 - Lagrangian and Objective Eulerian Coherent Structures
Published online by Cambridge University Press: 20 February 2023
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgments
- 1 Introduction
- 2 Eulerian and Lagrangian Fundamentals
- 3 Objectivity of Transport Barriers
- 4 Barriers to Chaotic Advection
- 5 Lagrangian and Objective Eulerian Coherent Structures
- 6 Flow Separation and Attachment Surfaces as Transport Barriers
- 7 Inertial LCSs: Transport Barriers in Finite-Size Particle Motion
- 8 Passive Barriers to Diffusive and Stochastic Transport
- 9 Dynamically Active Barriers to Transport
- Appendix
- References
- Index
Summary
Here, we take our first step to discover barriers to transport outside the idealized setting of temporally recurrent (steady, periodic or quasiperiodic) velocity fields. While we can no longer hope for even approximately recurring material surfaces in this general setting, we can certainly look for material surfaces that remain coherent. We perceive a material surface to be coherent if it preserves the spatial integrity without developing smaller scales. Those smaller scales would manifest themselves as protrusions from either side of the material surface without a break-up of that surface. In other words, using the terminology of the Introduction, we seek advective transport barriers in nonrecurrent flows as Lagrangian coherent structures (LCS). We will refer to this instantaneous limit of LCSs as objective Eulerian coherent structures (OECSs). These Eulerian structures act as LCSs over infinitesimally short time scales and hence their time-evolution is not material. Despite being nonmaterial, OECSs have advantages and important applications in unsteady flow analysis, as we will discuss separately.
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- Information
- Transport Barriers and Coherent Structures in Flow DataAdvective, Diffusive, Stochastic and Active Methods, pp. 141 - 241Publisher: Cambridge University PressPrint publication year: 2023