Driven Surface Waves Research Articles

Airflow measurements at a wavy air\u2013water interface using PIV and LIF

Physical phenomena at an air–water interface are of interest in a variety of flows with both industrial and natural/environmental applications. In this paper, we present novel experimental techniques incorporating a multi-camera multi-laser instrumentation in a combined particle image velocimetry and laser-induced fluorescence system. The system yields accurate surface detection thus enabling velocity measurements to be performed very close to the interface. In the application presented here, we show results from a laboratory study of the turbulent airflow over wind driven surface waves. Accurate detection of the wavy air–water interface further yields a curvilinear coordinate system that grants practical and easy implementation of ensemble and phase averaging routines. In turn, these averaging techniques allow for the separation of mean, surface wave coherent, and turbulent velocity fields. In this paper, we describe the instrumentation and techniques and show several data products obtained on the air-side of a wavy air–water interface.

Broadband spoof surface plasmon polariton couplers based on transmissive phase gradient metasurface

In this paper, we propose the design of broadband spoof surface plasmon polariton (SSPP) couplers based on transmissive phase gradient metasurfaces (TPGMs). Due to the large parallel phase gradient, transmitted waves through the TPGM are converted to driven surface waves (DSW). By placing the TPGM above a square patch array, the DSW can be coupled to an eigenmode SSPP in a broadband. High efficiency can be achieved since there is no initial reflection and SSPP decoupling effect in such SSPP couplers. A SSPP coupler was demonstrated in a microwave regime. Both the simulated and measured results show that the SSPP coupler can operate effectively in 7.0–9.9 GHz under normal incidence. Our finding may pave the way for broadband applications of SSPP.

Numerical simulation of Faraday waves oscillated by two-frequency forcing

We perform a numerical simulation of Faraday waves forced with two-frequency oscillations using a level-set method with Lagrangian-particle corrections (particle level-set method). After validating the simulation with the linear stability analysis, we show that square, hexagonal, and rhomboidal patterns are reproduced in agreement with the laboratory experiments [Arbell and Fineberg, “Two-mode rhomboidal states in driven surface waves,” Phys. Rev. Lett. 84, 654–657 (2000) and “Temporally harmonic oscillons in Newtonian fluids,” Phys. Rev. Lett. 85, 756–759 (2000)]. We also show that the particle level-set’s high degree of conservation of volume is necessary in the simulations. The numerical results of the rhomboidal states are compared with weakly nonlinear analysis. Difficulty in simulating other patterns of the two-frequency forced Faraday waves is discussed.

304 CIP有限体積法による風波乱流場の数値シミュレーション(OS3.CIP法とその関連手法(1),オーガナイズドセッション)

304 CIP有限体積法による風波乱流場の数値シミュレーション(OS3.CIP法とその関連手法(1),オーガナイズドセッション)

Effect of magnetic field on parametrically driven surface waves

Stability analysis of parametrically driven surface waves in liquid metals in the presence of a uniform vertical magnetic field is presented. Floquet analysis gives various subharmonic and harmonic instability zones. The magnetic field stabilizes the onset of parametrically excited surface waves. The minima of all the instability zones are raised by a different amount as the Chandrasekhar number is raised. The increase in the magnetic field leads to a series of bicritical points at a primary instability in thin layers of a liquid metal. The bicritical points involve one subharmonic and another harmonic solution of different wavenumbers. A tricritical point may also be triggered as a primary instability by tuning the magnetic field.

The effect of the Coriolis force on Faraday waves

Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Mondal Gour Chandra and Kumar Krishna 2004The effect of the Coriolis force on Faraday wavesProc. R. Soc. Lond. A.460897–908http://doi.org/10.1098/rspa.2003.1259SectionRestricted accessResearch articleThe effect of the Coriolis force on Faraday waves Gour Chandra Mondal Gour Chandra Mondal Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 Barrackpore Trunk Road, Kolkata 700108, India Google Scholar Find this author on PubMed Search for more papers by this author and Krishna Kumar Krishna Kumar Department of Physics and Meteorology, Indian Institute of Technology, Kharagpur 721302, India () Google Scholar Find this author on PubMed Search for more papers by this author Gour Chandra Mondal Gour Chandra Mondal Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 Barrackpore Trunk Road, Kolkata 700108, India Google Scholar Find this author on PubMed Search for more papers by this author and Krishna Kumar Krishna Kumar Department of Physics and Meteorology, Indian Institute of Technology, Kharagpur 721302, India () Google Scholar Find this author on PubMed Search for more papers by this author Published:08 March 2004https://doi.org/10.1098/rspa.2003.1259AbstractLinear stability of the free surface of a thin sheet of a viscous fluid on a vertically vibrated rigid plate, in the presence of a uniform and slow rigid body rotation about the vertical axis, is presented. The Coriolis force delays the onset of parametrically excited surface waves. The creation of Faraday waves is always possible by raising the acceleration amplitude above a critical value, if the angular frequency ωv of the vertical vibration is much larger than four times the angular velocity ωr of the rotating plate. The surface waves may be harmonic or superharmonic with the imposed vibration in a thin sheet of slowly rotating viscous fluids at small vibration frequencies. This leads to the possibility of a tri–critical point at the onset of the surface instability in thin layers of a viscous fluid. Subharmonic, harmonic and superharmonic waves with different wavenumbers may coexist at the instability onset in the presence of a small Coriolis force, which is a qualitatively new result. Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Tessier J, Castro-Folker N, Poulin F and Stastna M (2021) Anisotropy in Faraday instabilities of a shallow conducting fluid, EPL (Europhysics Letters), 10.1209/0295-5075/ac1779, 135:3, (34001), Online publication date: 1-Aug-2021. Guan X, Jia B, Yang L and Fu Q (2021) Linear instability of an annular liquid jet with gas velocity oscillations, Physics of Fluids, 10.1063/5.0049137, 33:5, (054110), Online publication date: 1-May-2021. Jia B, Xie L, Yang L, Fu Q and Cui X (2020) Energy budget of a viscoelastic planar liquid sheet in the presence of gas velocity oscillations, Physics of Fluids, 10.1063/5.0016311, 32:8, (083104), Online publication date: 1-Aug-2020. Jia B, Xie L, Yang L, Fu Q and Cui X (2019) Linear instability of viscoelastic planar liquid sheets in the presence of gas velocity oscillations, Journal of Non-Newtonian Fluid Mechanics, 10.1016/j.jnnfm.2019.104169, 273, (104169), Online publication date: 1-Nov-2019. Yang L, Jia B, Fu Q and Yang Q (2018) Stability of an air-assisted viscous liquid sheet in the presence of acoustic oscillations, European Journal of Mechanics - B/Fluids, 10.1016/j.euromechflu.2017.10.002, 67, (366-376), Online publication date: 1-Jan-2018. Stastna M and Poulin F (2014) The stochastic mode of the Faraday instability of shallow fluid layers, EPL (Europhysics Letters), 10.1209/0295-5075/106/44003, 106:4, (44003), Online publication date: 1-May-2014. Paul S and Kumar K (2006) Effect of magnetic field on parametrically driven surface waves, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 463:2079, (711-722), Online publication date: 8-Mar-2007. Mondal G and Kumar K (2006) Effect of Marangoni and Coriolis forces on multicritical points in a Faraday experiment, Physics of Fluids, 10.1063/1.2167994, 18:3, (032101), Online publication date: 1-Mar-2006. This Issue08 March 2004Volume 460Issue 2043 Article InformationDOI:https://doi.org/10.1098/rspa.2003.1259Published by:Royal SocietyPrint ISSN:1364-5021Online ISSN:1471-2946History: Published online08/03/2004Published in print08/03/2004 License: Citations and impact KeywordsFaraday WavesCoriolis ForceTri–Critical Point

Pattern formation at the bicritical point of the Faraday instability.

We present measurements on parametrically driven surface waves (Faraday waves) performed in the vicinity of a bicritical point in parameter space, where modes with harmonic and subharmonic time dependence interact. The primary patterns are squares in the subharmonic and hexagons in the harmonic regime. If the primary instability is harmonic we observe a hysteretic secondary transition from hexagons to squares without a perceptible variation of the fundamental wavelength. The transition is understood in terms of a set of coupled Landau equations and related to other canonical examples of phase transitions in nonlinear dissipative systems. Moreover, the subharmonic-harmonic mode competition gives rise to a variety of new superlattice states. These structures are interpreted as mediator modes involved in the transition between patterns of fourfold and sixfold rotational symmetry.

Parametrically driven surface waves in surfactant–covered liquids

Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Kumar Satish and Matar Omar K. 2002Parametrically driven surface waves in surfactant–covered liquidsProc. R. Soc. Lond. A.4582815–2828http://doi.org/10.1098/rspa.2002.1017SectionRestricted accessResearch articleParametrically driven surface waves in surfactant–covered liquids Satish Kumar Satish Kumar Department of Chemical Engineering and Materials Science, University of Minnesota, 151 Amundson Hall, 421 Washington Ave. SE, Minneapolis, MN 55455, USA Google Scholar Find this author on PubMed Search for more papers by this author and Omar K. Matar Omar K. Matar Department of Chemical Engineering and Chemical Technology, Imperial College of Science, Technology and Medicine, London SW7 2BY, UK Google Scholar Find this author on PubMed Search for more papers by this author Satish Kumar Satish Kumar Department of Chemical Engineering and Materials Science, University of Minnesota, 151 Amundson Hall, 421 Washington Ave. SE, Minneapolis, MN 55455, USA Google Scholar Find this author on PubMed Search for more papers by this author and Omar K. Matar Omar K. Matar Department of Chemical Engineering and Chemical Technology, Imperial College of Science, Technology and Medicine, London SW7 2BY, UK Google Scholar Find this author on PubMed Search for more papers by this author Published:08 November 2002https://doi.org/10.1098/rspa.2002.1017AbstractVertical vibration will excite standing waves on a liquid free surface. We perform a linear–stability analysis for viscous and viscoelastic liquids of arbitrary depth to determine the role that insoluble surfactants play in the formation of these parametrically driven surface waves. We find that in order to obtain time–periodic solutions which involve Marangoni forces in a non–trivial way, it is necessary to consider the high–Peclet number limit of the surfactant transport equation. Floquet theory is applied to the linearized governing equations to obtain a recursion relation for the temporal modes of the free–surface deflection. The recursion relation is then solved numerically to obtain the critical vibration amplitude needed to excite the surface waves, and the corresponding wavenumber. The results show that the presence of surfactants raises or lowers the critical amplitude and wavenumber depending on the spatial phase shift between the surfactant–concentration variations and surface deflections. Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited bySamanta A (2020) Effect of porous layer on the Faraday instability in viscous liquid, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 476:2239, Online publication date: 1-Jul-2020. Jia B, Xie L, Yang L, Fu Q and Cui X (2020) Energy budget of a viscoelastic planar liquid sheet in the presence of gas velocity oscillations, Physics of Fluids, 10.1063/5.0016311, 32:8, (083104), Online publication date: 1-Aug-2020. Zhu Z, Song Y, Liu X, Xiao D, Yang L and Huang L (2019) Observation of alternately localized Faraday waves in a narrow tank, Physical Review Fluids, 10.1103/PhysRevFluids.4.014807, 4:1 Mikishev A, Friedman B and Nepomnyashchy A (2016) Generation of transverse waves in a liquid layer with insoluble surfactant subjected to temperature gradient, Fluid Dynamics Research, 10.1088/0169-5983/48/6/061403, 48:6, (061403), Online publication date: 1-Dec-2016. Ibrahim R (2015) Recent Advances in Physics of Fluid Parametric Sloshing and Related Problems, Journal of Fluids Engineering, 10.1115/1.4029544, 137:9, Online publication date: 1-Sep-2015. Strickland S, Shearer M and Daniels K (2015) Spatiotemporal measurement of surfactant distribution on gravity–capillary waves, Journal of Fluid Mechanics, 10.1017/jfm.2015.352, 777, (523-543), Online publication date: 25-Aug-2015. This Issue08 November 2002Volume 458Issue 2027 Article InformationDOI:https://doi.org/10.1098/rspa.2002.1017Published by:Royal SocietyPrint ISSN:1364-5021Online ISSN:1471-2946History: Published online08/11/2002Published in print08/11/2002 License: Citations and impact Keywordsviscoelasticitywavesinstabilitysurfactantfree surface

Nonlinear wave dynamics in Faraday instabilities

Nonlinear wave dynamics in parametrically driven surface waves are studied in numerical simulations of the two-dimensional Navier-Stokes equation, with an emphasis on the evolution and interaction between different wave number modes. The dynamics are found to be closely correlated with the single-mode nonlinear saturated wave amplitudes. Modulating behavior of primary wave modes in a particular parameter range and in time scales much longer than the underlining wave periods is observed.

Parametric instability of a liquid sheet

Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Kumar Sathish 2001Parametric instability of a liquid sheetProc. R. Soc. Lond. A.4571315–1326http://doi.org/10.1098/rspa.2000.0724SectionRestricted accessResearch articleParametric instability of a liquid sheet Sathish Kumar Sathish Kumar Department of Chemical Engineering, University of Michigan, 2300 Hayward, 3074 H. H. Dow Building, Ann Arbor, MI 481097–2136, USA [email protected] Google Scholar Find this author on PubMed Search for more papers by this author Sathish Kumar Sathish Kumar Department of Chemical Engineering, University of Michigan, 2300 Hayward, 3074 H. H. Dow Building, Ann Arbor, MI 481097–2136, USA [email protected] Google Scholar Find this author on PubMed Search for more papers by this author Published:08 June 2001https://doi.org/10.1098/rspa.2000.0724AbstractWhen a liquid sheet is subject to vertical vibration, parametric instabilities may occur and give rise to standing waves. The present work develops the linear theory of this phenomenon for inviscid, Newtonian and viscoelastic liquids. Floquet theory is applied to the governing equations to obtain recursion relations for the temporal modes of the deformations of the free surfaces. In contrast to the case where there is no vibration, we find that the symmetric and antisymmetric deformations of the liquid sheet are coupled to each other. For the inviscid case, the recursion relations are shown to be equivalent to a pair of coupled Mathieu equations. For the Newtonian and viscoelastic cases, the recursion relations are converted into an eigenvalue problem which is solved numerically to obtain the critical vibration amplitude needed to excite the instability, along with the corresponding critical wavenumber. The results display behaviour which is similar in several ways to that of the classic Faraday instability. The parametric instabilities studied here may be an important mechanism in the initial stages of foam destruction by ultrasound, as well as in several other practical applications. Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Guan X, Jia B, Yang L and Fu Q (2021) Linear instability of an annular liquid jet with gas velocity oscillations, Physics of Fluids, 10.1063/5.0049137, 33:5, (054110), Online publication date: 1-May-2021. Liu L and Yang L (2018) Nonlinear wave evolution of shear-thinning Carreau liquid sheets, Journal of Fluid Mechanics, 10.1017/jfm.2018.810, 859, (659-676), Online publication date: 25-Jan-2019. Vegad C, Kumar A and Chakravarthy S (2019) Dynamics of free-surface mutually perpendicular twin liquid sheets and their atomization characteristics, Physics of Fluids, 10.1063/1.5109828, 31:8, (082103), Online publication date: 1-Aug-2019. Yang L, Jia B, Fu Q and Yang Q (2018) Stability of an air-assisted viscous liquid sheet in the presence of acoustic oscillations, European Journal of Mechanics - B/Fluids, 10.1016/j.euromechflu.2017.10.002, 67, (366-376), Online publication date: 1-Jan-2018. Pototsky A and Bestehorn M (2016) Faraday instability of a two-layer liquid film with a free upper surface, Physical Review Fluids, 10.1103/PhysRevFluids.1.023901, 1:2 Shevtsova V, Gaponenko Y, Yasnou V, Mialdun A and Nepomnyashchy A (2016) Two-scale wave patterns on a periodically excited miscible liquid–liquid interface, Journal of Fluid Mechanics, 10.1017/jfm.2016.222, 795, (409-422), Online publication date: 25-May-2016. Vécsei M, Dietzel M and Hardt S (2014) Coupled self-organization: Thermal interaction between two liquid films undergoing long-wavelength instabilities, Physical Review E, 10.1103/PhysRevE.89.053018, 89:5 Stastna M and Poulin F (2014) The stochastic mode of the Faraday instability of shallow fluid layers, EPL (Europhysics Letters), 10.1209/0295-5075/106/44003, 106:4, (44003), Online publication date: 1-May-2014. Mulmule A, Tirumkudulu M and Ramamurthi K (2010) Instability of a moving liquid sheet in the presence of acoustic forcing, Physics of Fluids, 10.1063/1.3290745, 22:2, (022101), Online publication date: 1-Feb-2010. Kumar S and Matar O (2004) On the Faraday instability in a surfactant-covered liquid, Physics of Fluids, 10.1063/1.1629128, 16:1, (39-46), Online publication date: 1-Jan-2004. Kumar S and Matar O (2002) Parametrically driven surface waves in surfactant–covered liquids, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 458:2027, (2815-2828), Online publication date: 8-Nov-2002. This Issue08 June 2001Volume 457Issue 2010 Article InformationDOI:https://doi.org/10.1098/rspa.2000.0724Published by:Royal SocietyPrint ISSN:1364-5021Online ISSN:1471-2946History: Published online08/06/2001Published in print08/06/2001 License: Citations and impact Keywordsinstabilityviscoelasticliquid sheetfree surface

Shock wave criterion for propagating solitary states in driven surface waves.

Highly localized solitary states are observed to propagate along the surface of a thin two-dimensional fluid layer. The states are driven by means of a spatially uniform, temporally periodic, vertical acceleration (Faraday experiment) in a highly dissipative fluid. These states are shown to be formed by coupled fronts that propagate, periodically, as shock waves. A criterion for their formation based on shock initiation is presented. Both the characteristic form and interaction dynamics of the solitary states can be understood in this picture.

Parametric Bragg resonances in waves on a shallow fluid over a periodically drilled bottom.

Bragg resonances involving strong interactions among Fourier wave components of a periodically drilled bottom and parametrically driven surface waves on a shallow liquid are experimentally shown to break down the secular dispersion relation of surface waves. When the fluid is sufficiently shallow, wave components that match reciprocal wave vectors of the bottom topography are dominant. Experimental evidence of band-gap phenomena in these surface waves are also shown. Moreover, the prevalence of Bragg resonances is so strong that one of them is excited anomalously within the band gap.

Two-mode rhomboidal states in driven surface waves

Two-mode rhomboid patterns are generated experimentally via two-frequency parametric forcing of surface waves. These patterns are formed by the simple nonlinear resonance: k-->'2-k-->(2) = k-->(1) where k(1) and k(2)( = k(')(2)) are concurrently excited eigenmodes. The state possesses a direction-dependent time dependence described by a superposition of the two modes, and a dimensionless scaling delineating the state's region of existence is presented. We also show that 2n-fold quasipatterns naturally arise from these states when the coupling angle between k-->(2) and k-->'2 is 2pi/n.

Parametrically driven surface waves in viscoelastic liquids

When a container of liquid is subject to vertical sinusoidal oscillation, the free surface becomes unstable at a critical driving acceleration and gives rise to standing waves. Here, we consider containers of finite depth, neglect the influence of lateral boundaries, and perform a linear stability analysis for viscoelastic liquids. Floquet theory is applied to transform the linearized governing equations into a recursion relation for the temporal modes of the free surface deformation. In the absence of external forcing, the recursion relation yields the dispersion equation for free surface waves on viscoelastic liquids. In the presence of external forcing, the recursion relation is studied both numerically and analytically for the case where the polymer stresses are described by a single-mode Maxwell model. When surface tension forces are sufficiently strong relative to elastic forces, the numerical results show that the standing waves respond subharmonically to the driving frequency. However, the instability threshold increases less rapidly with the driving frequency than that for a Newtonian liquid of the same zero-shear viscosity. When elastic forces become sufficiently strong relative to surface tension forces, the standing waves can respond harmonically within certain ranges of the driving frequency if the product of the driving frequency and the liquid relaxation time is not too large or too small. Dramatic changes are seen in the behavior of the neutral stability curves, dispersion relations, and instability thresholds. In the case where the viscous boundary layer thickness is much less than the disturbance wavelength, the viscoelastic recursion relation is simplified to yield a Mathieu equation which is nonlocal in time. The method of multiple scales is then applied to determine the instability threshold analytically. The results of this study indicate that the behavior of parametrically driven surface waves is very sensitive to the liquid relaxation time, and suggest that such waves may serve as a useful tool for the measurement of rheological properties.

Erratum: Spatial and Temporal Dynamics of Two Interacting Modes in Parametrically Driven Surface Waves [Phys. Rev. Lett. 81, 4384 (1998)

Erratum: Spatial and Temporal Dynamics of Two Interacting Modes in Parametrically Driven Surface Waves [Phys. Rev. Lett. 81, 4384 (1998)

Spatial and Temporal Dynamics of Two Interacting Modes in Parametrically Driven Surface Waves

Nonlinear waves with basic wave numbers, ${k}_{1}$ and ${k}_{2}$, are simultaneously excited via two-frequency parametric excitation of a fluid surface. Three new multiwave states are observed: (1) A superlattice state composed of ${k}_{1}$ and ${k}_{2}$ whose relative orientation is governed by a temporal resonance condition, (2) a superlattice built entirely of wave numbers ${k}_{1}$ and ${k}_{1}/2$, and (3) a state composed of wave numbers of lengths ${k}_{1}$ and ${k}_{2}$ that are uncorrelated in both space and time. The three states exhibit interesting temporal as well as spatial behavior and are observed in a variety of frequency combinations.

Coherent Structures in Convection and Parametrically Driven Surface Wavesa

Abstract: A system maintained outside of thermodynamic equilibrium often develops complex spatial structures and, in some cases, persistent dynamics. The amplitude equation formalism has been widely used to study pattern formation in the weakly nonlinear regime (slightly beyond onset of instability from some stationary reference state.) Application of the formalism is briefly discussed for Rayleigh‐Benard convection, and at some length for parametrically driven surface waves (Faraday waves).

Numerical study of pattern formation in weakly damped parametric surface waves

We present a numerical study of parametrically driven surface waves in fluids of low viscosity. The equations governing fluid motion in the bulk and the appropriate boundary conditions at the free surface are approximated by a nonlocal set of equations involving surface coordinates alone, thus allowing the numerical analysis of the large aspect ratio limit (the aspect ratio being the ratio between the size of the system and the wavelength of the waves). The numerical calculation supports the predictions of a previously given multi-scale asymptotic analysis, yielding stable patterns of square symmetry above onset in the capillary dominated regime. In the case of mixed capillary-gravity waves, patterns of eight-fold symmetry are obtained, again in agreement with the predictions of the asymptotic expansion. These calculations provide indirect evidence about the stability of such patterns, analysis that is too involved to be carried out analytically.

Scaling of the transition to parametrically driven surface waves in highly dissipative systems

We present an experimental study of the onset of the Faraday instability in highly dissipative fluids. In this regime of high viscosity and shallow fluid depth, we find that the critical acceleration for the transition to parametrically excited surface waves scales as a function of two dimensionless parameters corresponding to the ratios of the critical driving amplitude height and viscous boundary layer depth to the fluid depth. This scaling, which exists over a wide range of fluid parameters, identifies the proper characteristic scales and indicates that a Rayleigh-Taylor type mechanism drives the instability in this regime.

Comment on “Pressure‐pulse driven surface waves at the magnetopause: A rebuttal” by D. G. Sibeck and P. T. Newell

Comment on “Pressure‐pulse driven surface waves at the magnetopause: A rebuttal” by D. G. Sibeck and P. T. Newell