Skip to main content
×
Home
    • Aa
    • Aa

Streaming patterns in Faraday waves

  • Nicolas Périnet (a1), Pablo Gutiérrez (a1) (a2), Héctor Urra (a3), Nicolás Mujica (a1) and Leonardo Gordillo (a4)...
Abstract

Wave patterns in the Faraday instability have been studied for decades. Besides the rich wave dynamics observed at the interface, Faraday waves hide elusive flow patterns in the bulk – streaming patterns – which have not been studied experimentally. The streaming patterns are responsible for a net circulation in the flow, which is reminiscent of the circulation in convection cells. In this article, we analyse these streaming flows by conducting experiments in a Faraday-wave set-up using particle image velocimetry. To visualise the flows, we perform stroboscopic measurements to both generate trajectory maps and probe the streaming velocity field. We identify three types of patterns and experimentally show that identical Faraday waves can mask streaming patterns that are qualitatively very different. Next, we consider a three-dimensional model for streaming flows in quasi-inviscid fluids, whose key is the complex coupling occurring at all of the viscous boundary layers. This coupling yields modified boundary conditions in a three-dimensional Navier–Stokes formulation of the streaming flow. Numerical simulations based on this framework show reasonably good agreement, both qualitative and quantitative, with the velocity fields of our experiments. The model highlights the relevance of three-dimensional effects in the streaming patterns. Our simulations also reveal that the variety of streaming patterns is deeply linked to the boundary condition at the top interface, which may be strongly affected by the presence of contaminants.

Copyright
Corresponding author
Email address for correspondence: leonardo.gordillo@usach.cl
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

G. K. Batchelor 2000 An Introduction to Fluid Dynamics. Cambridge University Press.

P. Chen , Z. Luo , S. Güven , S. Tasoglu , A. V. Ganesan , A. Weng  & U. Demirci 2014 Microscale assembly directed by liquid-based template. Adv. Mater. 26 (34), 59365941.

A. J. Chorin 1968 Numerical solution of the Navier–Stokes equations. Math. Comput. 22, 745762.

D. Coles 1965 Transition in circular Couette flow. J. Fluid Mech. 21, 385425.

S. Douady 1990 Experimental study of the Faraday instability. J. Fluid Mech. 221, 383409.

G. Falkovich , A. Weinberg , P. Denissenko  & S. Lukaschuk 2005 Surface tension: floater clustering in a standing wave. Nature 435 (7045), 10451046.

M. Faraday 1831 On a peculiar class of acoustical figures; and on certain forms assumed by groups of particles upon vibrating elastic surfaces. Phil. Trans. R. Soc. Lond. A 121, 299340.

H. J. van Gerner , K. van der Weele , M. A. van der Hoef  & D. van der Meer 2011 Air-induced inverse Chladni patterns. J. Fluid Mech. 689, 203220.

L. Gordillo  & N. Mujica 2014 Measurement of the velocity field in parametrically excited solitary waves. J. Fluid Mech. 754, 590604.

P. Gutiérrez  & S. Aumaître 2016 Clustering of floaters on the free surface of a turbulent flow: an experimental study. Eur. J. Mech. B 60, 2432.

D. Henderson  & J. W. Miles 1994 Surface wave damping in a circular cylinder with a fixed contact line. J. Fluid Mech. 275, 285299.

M. Higuera  & E. Knobloch 2006 Nearly inviscid Faraday waves in slightly rectangular containers. Prog. Theor. Phys. Supp. 161, 5367.

M. Higuera , J. M. Vega  & E. Knobloch 2002 Coupled amplitude–streaming flow equations for nearly inviscid Faraday waves in small aspect ratio containers. J. Nonlinear Sci. 12 (5), 505551.

M. S. Longuet-Higgins 1953 Mass transport in water waves. Phil. Trans. R. Soc. Lond. A 245, 535.

E. Martin , C. Martel  & J. M. Vega 2002 Drift instability of standing Faraday waves. J. Fluid Mech. 467, 5779.

E. Martin  & J. M. Vega 2005 The effect of surface contamination on the drift instability of standing Faraday waves. J. Fluid Mech. 546, 203225.

C. D. Meinhart , S. T. Wereley  & J. G. Santiago 2000 A PIV algorithm for estimating time-averaged velocity fields. Trans. ASME J. Fluids Engng 122 (2), 285289.

J. W. Miles 1967 Surface-wave damping in closed basins. Proc. R. Soc. Lond. A 297, 459.

J. W. Miles 1976 Nonlinear surface waves in closed basins. J. Fluid Mech. 75, 419448.

J. W. Miles  & D. Henderson 1990 Parametrically forced surface waves. Annu. Rev. Fluid Mech. 22, 143165.

J. A. Nicolás  & J. M. Vega 2000 A note on the effect of surface contamination in water wave damping. J. Fluid Mech. 410, 367373.

J. A. Nicolás  & J. M. Vega 2003 Three-dimensional streaming flows driven by oscillatory boundary layers. Fluid Dyn. Res. 32 (4), 119139.

M. Raffel , C. E. Willert , S. T. Wereley  & J. Kompenhans 2007 Particle Image Velocimetry: A Practical Guide, 2nd edn. Springer.

N. Riley 2001 Steady streaming. Annu. Rev. Fluid Mech. 33, 4365.

P. H. Wright  & J. R. Saylor 2003 Patterning of particulate films using Faraday waves. Rev. Sci. Instrum. 74 (9), 4063.

J. Wu , R. Keolian  & I. Rudnick 1984 Observation of a nonpropagating hydrodynamic soliton. Phys. Rev. Lett. 52 (1), 14211424.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords:

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 3
Total number of PDF views: 114 *
Loading metrics...

Abstract views

Total abstract views: 397 *
Loading metrics...

* Views captured on Cambridge Core between 21st April 2017 - 21st September 2017. This data will be updated every 24 hours.