Recent studies have elucidated the possibility of solitary wave behavior in Marangoni–Bénard instability flows. The present paper takes a look at experiments in both heat‐transfer‐ and mass‐transfer‐driven Marangoni systems to discern nonlinear behavior of the type associated with solitary wave interactions. Direct observation of phase shifts incurred by two Marangoni waves having undergone a head‐on collision are reported. Analysis of experiments exhibiting wave reflection at a solid wall and obliquely interacting waves in Marangoni instability flows also show remarkable similarities with nonlinear behavior in Korteweg–de Vries systems.
REFERENCES
1.
M. G.
Velarde
, X.-L.
Chu
, and A. N.
Garazo
, “Onset of possible solitons in surface tension-driven convection
,” Phys. Scr.
T35
, 71
(1991
).2.
X.-L.
Chu
and M. G.
Velarde
, “Korteweg-de Vries soliton excitation in Bénard-Marangoni convection
,” Phys. Rev. A
43
, 1094
(1991
).3.
C. V.
Sternling
and L. E.
Scriven
, “Interfacial turbulence: Hydrodynamic instability and the Marangoni effect
,” AIChE J.
5
, 514
(1959
).4.
J.
Lucassen
, “Longitudinal capillary waves. Part 1. Theory
,” Trans. Faraday Soc.
64
, 2221
(1968
);J.
Lucassen
, “Longitudinal capillary waves. Part 2. Experiment
,” Trans. Faraday Soc.
64
, 2230
(1968
).5.
A. Sanfeld, A. Steinchen, M. Hennenberg, P. M. Bisch, D. Van Lamsweerde-Gallez, and W. Dalle-Vedove, “Mechanical, chemical, and electrical constraints and hydrodynamic interfacial instability,” in Lecture Notes in Physics: Dynamics and Instability of Fluid Interfaces, edited by T. S. Sorensen (Springer-Verlag, Berlin, 1979), Vol. 105, pp. 168–204.
6.
J.
Reichenbach
and H.
Linde
, “Linear perturbation analysis of surface-tension-driven convection at a plane interface (Marangoni instability)
,” J. Colloid Interface Sci.
84
, 433
(1981
).7.
X.-L.
Chu
and M. G.
Velarde
, “Sustained transverse and longitudinal waves at the open surface of a liquid
,” PhysicoChem. Hydrodyn.
10
, 727
(1988
).8.
X.-L.
Chu
and M. G.
Velarde
, “Transverse and longitudinal waves induced and sustained by surfactant gradients at liquid-liquid interfaces
,” J. Colloid Interface Sci.
131
, 471
(1989
).9.
A. N.
Garazo
and M. G.
Velarde
, “Dissipative Korteweg-de Vries description of Marangoni-Bénard oscillatory convection
,” Phys. Fluids A
3
, 2295
(1991
).10.
H.
Linde
and K.
Loeschcke
, “Rollzellen und Oszillation beim Warmeubergang zwischen Gas und Flussigkeit
,” Chem. Ing. Tech. (GDR)
39
, 65
(1966
).11.
H.
Linde
, E.
Schwarz
, and K.
Groger
, “Zum Auftreten des Oszillatoris-chen Regimes der Marangoni-instabilitat beim Stoffubergang
,” Chem. Eng. Sci.
22
, 823
(1967
).12.
H.
Linde
and M.
Kunkel
, “Some new qualitative observations in the oscillatory regime of the Marangoni instability
,” Warme-Stoffubertr.
2
, 60
(1969
).13.
H. Linde, P. Schwartz, and H. Wilke, “Dissipative structures and nonlinear kinetics of the Marangoni-instability,” in Ref. 5, pp. 75–119.
14.
H. Linde, “Marangoni Instabilities,” in Convective Transport and Instability Phenomena, edited by J. Zierep and H. Oertel, Jr. (Braun, Karlsruhe, 1982), pp. 265–296.
15.
16.
M.
Oikawa
and N.
Yajima
, “Interactions of solitary waves: A perturbation approach to nonlinear systems
,” J. Phys. Soc. Jpn.
34
, 1093
(1973
).17.
T.
Maxworthy
, “Experiments on collisions between solitary waves
,” J. Fluid Mech.
76
, 177
(1976
).18.
J. W.
Miles
, “Obliquely interacting solitary waves
,” J. Fluid Mech.
79
, 171
(1977
).19.
P. H. Perroud, The solitary reflection along a straight vertical wall at oblique incidence,” Ph.D. thesis, University of California, Berkeley, 1957.
20.
J. W.
Miles
, “Obliquely interacting solitary waves
,” J. Fluid Mech.
79
, 157
(1977
).21.
T.
Maxworthy
, “On the formation of nonlinear internal waves from the gravitational collapse of mixed regions in two and three dimensions
,” J. Fluid Mech.
96
, 47
(1980
).22.
P. D.
Weidman
and R.
Zakhem
, “Cylindrical solitary waves
,” J. Fluid Mech.
191
, 557
(1988
).23.
K.
Ko
and H. H.
Kuehl
, “Korteweg-de Vries soliton in a slowly varying medium
,” Phys. Rev. Lett.
40
, 233
(1978
).24.
T. B.
Benjamin
, “Internal waves of permanent form in fluids of great depth
,” J. Fluid Mech.
29
, 559
(1967
).25.
R. E.
Davis
and A.
Acrivos
, “Solitary internal waves in deep water
,” J. Fluid Mech.
29
, 593
(1967
).26.
H.
Ono
, “Algebraic solitary waves in stratified fluids
,” J. Phys. Soc. Jpn.
4
, 1082
(1975
).
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1992
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