Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-25T07:23:42.306Z Has data issue: false hasContentIssue false
  • English
  • Français

Bound-state formation in interfacial turbulence: direct numerical simulations and theory

Published online by Cambridge University Press:  28 January 2013

M. Pradas ,
S. Kalliadasis ,
P.-K. Nguyen  and
V. Bontozoglou
M. Pradas
Affiliation:
Department of Chemical Engineering, Imperial College London, London SW7 2AZ, UK
S. Kalliadasis*
Affiliation:
Department of Chemical Engineering, Imperial College London, London SW7 2AZ, UK
P.-K. Nguyen
Affiliation:
Department of Mechanical Engineering, University of Thessaly, Pedion Areos, GR-38334 Volos, Greece
V. Bontozoglou
Affiliation:
Department of Mechanical Engineering, University of Thessaly, Pedion Areos, GR-38334 Volos, Greece
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We examine pulse interaction and bound-state formation in interfacial turbulence using the problem of a falling liquid film as a model system. We perform direct numerical simulations (DNSs) of the full Navier–Stokes equations and associated wall and free-surface boundary conditions and we examine both analytically and numerically a low-dimensional (LD) model for the film. For a two-pulse system, DNSs reveal the existence of very rich and complex pulse interactions, characterized by either overdamped, underdamped or self-sustained oscillating behaviours, all of them found to be in excellent agreement with LD results. Having demonstrated the reliability of the LD model for two-pulse systems/smaller domains, we use it to investigate larger domains with many interacting pulses, where DNSs are computationally expensive. We demonstrate that such systems are likely to be dominated by a self-sustained oscillatory dynamics.

JFM classification

Instability: Instability Interfacial Flows (free surface): Interfacial Flows (free surface) Interfacial Flows (free surface): Thin films
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 716 , 10 February 2013 , R2
Copyright
©2013 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Balmforth, N. J. 1995 Solitary waves and homoclinic orbits. Annu. Rev. Fluid Mech. 27, 335–373.CrossRefGoogle Scholar
Chang, H.-C. & Demekhin, E. 2002 Complex Wave Dynamics on Thin Films. Springer.Google Scholar
Chang, H.-C., Demekhin, E. & Kalaidin, E. 1995 Interaction dynamics of solitary waves on a falling film. J. Fluid Mech. 294, 123–154.CrossRefGoogle Scholar
Demekhin, E. A., Kalaidin, E. N., Kalliadasis, S. & Vlaskin, S. Yu. 2007 Three-dimensional localized coherent structures of surface turbulence. I. Scenarios of two-dimensional–three-dimensional transition. Phys. Fluids 19, 114103.Google Scholar
Duprat, C., Giorgiutti-Dauphiné, F., Tseluiko, D., Saprykin, S. & Kalliadasis, S. 2009 Liquid film coating a fiber as a model system for the formation of bound states in active dispersive–dissipative nonlinear media. Phys. Rev. Lett. 103, 234501.Google Scholar
Kalliadasis, S., Ruyer-Quil, C., Scheid, B. & Velarde, M. G. 2012 Falling Liquid Films. Springer Series on Applied Mathematical Sciences , vol. 176 Springer.CrossRefGoogle Scholar
Krishnamurti, R. 1970 On the transition to turbulent convection. Part 1. The transition from two- to three-dimensional flow. J. Fluid Mech. 42, 295–307.Google Scholar
Liu, J., Paul, J. D. & Gollub, J. P. 1993 Measurements of the primary instabilities of film flows. J. Fluid Mech. 250, 69–101.Google Scholar
Malamataris, N. A., Vlachogiannis, M. & Bontozoglou, V. 2002 Solitary waves on inclined films: flow structure and binary interactions. Phys. Fluids 14, 1082–1094.CrossRefGoogle Scholar
Manneville, P. 1990 Dissipative Structure and Weak Turbulence. Academic Press.Google Scholar
Miles, J. & Henderson, D. 1990 Parametrically forced surface waves. Annu. Rev. Fluid Mech. 22, 143.CrossRefGoogle Scholar
Pradas, M., Tseluiko, D. & Kalliadasis, S. 2011 Rigorous coherent-structure theory for falling liquid films: Viscous dispersion effects on bound-state formation and self-organization. Phys. Fluids 23, 044104.Google Scholar
Pradas, M., Kalliadasis, S. & Tseluiko, D. 2012 Binary interactions of solitary pulses in falling liquid films. IMA J. Appl. Maths 77, 408–419.Google Scholar
Ruyer-Quil, C. & Manneville, P. 1998 Modelling film flows down inclined planes. Eur. Phys. J. B 6, 277–292.Google Scholar
Ruyer-Quil, C. & Manneville, P. 2000 Improved modelling of flows down inclined planes. Eur. Phys. J. B 15, 357–369.Google Scholar
Ruyer-Quil, C. & Manneville, P. 2002 Further accuracy and convergence results on the modeling of flows down inclined planes by weighted-residual approximations. Phys. Fluids 14, 170–183.Google Scholar
Scheid, B., Ruyer-Quil, C. & Manneville, P. 2006 Wave patterns in film flows: modelling and three-dimensional waves. J. Fluid Mech. 562, 183–222.Google Scholar
Shkadov, V. Ya. 1967 Wave modes in the flow of thin layer of a viscous liquid under the action of gravity. Izv. Akad. Nauk SSSR Mekh. Zhidk. Gaza 1967 (1), 43–50.Google Scholar
Shkadov, V. Ya. 1977 Solitary waves in a layer of viscous liquid. Izv. Akad. Nauk SSSR Mekh. Zhidk. Gaza 1977 (1), 63–66.Google Scholar
Turaev, D., Vladimirov, A. G. & Zelik, S. 2012 Long-range interactions and synchronization of oscillating dissipative solitons. Phys. Rev. Lett. 108, 263906.Google Scholar
Vlachogiannis, M. & Bontozoglou, V. 2001 Observations of solitary wave dynamics of film flows. J. Fluid Mech. 435, 191–215.CrossRefGoogle Scholar

Pradas et al. supplementary movie

Self-sustained oscillatory dynamics in a system compound of 7 pulses that are sufficiently close to each other (initially separated by ℓ0 = 29).

Download Pradas et al. supplementary movie(Video)
Video 11.3 MB