40 research outputs found
Dynamics of counterpropagating waves in parametrically driven systems: dispersion vs. advection
The dynamics of parametrically driven counterpropagating waves in a one-dimensional extended nearly conservative annular system are described by two coupled, damped, parametrically driven nonlinear Schrödinger (NLS) equations with opposite transport terms due to the group velocity, and small dispersion. The system is characterized by two length scales defined by a balance between (a) forcing and dispersion (the dispersive scale), and (b) forcing and advection at the group velocity (the transport scale). Both are large compared to the basic wavelength of the pattern. The dispersive scale plays an important role in the structure of solutions arising from secondary instabilities of frequency-locked spatially uniform standing waves (SW), and manifests itself both in traveling pulses or fronts and in extended spatio-temporal chaos, depending on the signs of the dispersion coefficient and nonlinearity.
Author Keywords: Parametric resonance; Counterpropagating waves; Weak dispersion; Faraday wave
Delay of Disorder by Diluted Polymers
We study the effect of diluted flexible polymers on a disordered capillary
wave state. The waves are generated at an interface of a dyed water sugar
solution and a low viscous silicon oil. This allows for a quantitative
measurement of the spatio-temporal Fourier spectrum. The primary pattern after
the first bifurcation from the flat interface are squares. With increasing
driving strength we observe a melting of the square pattern. It is replaced by
a weak turbulent cascade. The addition of a small amount of polymers to the
water layer does not affect the critical acceleration but shifts the disorder
transition to higher driving strenghs and the short wave length - high
frequency fluctuations are suppressed
Parametric Generation of Second Sound by First Sound in Superfluid Helium
We report the first experimental observation of parametric generation of
second sound (SS) by first sound (FS) in superfluid helium in a narrow
temperature range in the vicinity of . The temperature dependence
of the threshold FS amplitude is found to be in a good quantitative agreement
with the theory suggested long time ago and corrected for a finite geometry.
Strong amplitude fluctuations and two types of the SS spectra are observed
above the bifurcation. The latter effect is quantitatively explained by the
discreteness of the wave vector space and the strong temperature dependence of
the SS dissipation length.Comment: 4 pages, 4 postscript figures, REVTE
Analysis of the phase images obtained during the collection of a holographic registration system based on the geometric phase effect and a polarization camera
The results of measuring the surface depth of the test object using digital holography are presented. The resulting image
was compared to a model based on the calibration slide documentation. In the presented holographic microscope,
instead of an eyepiece, a lens with a geometric phase effect is used, which converts a beam with linear polarization
into a pair of beams with circular polarizations (diverging and converging). The parallel phase shift method was used
to obtain phase distribution. Using a polarization camera, four interferograms corresponding to four different linear
projections of interfering waves with right and left circular polarizations were recorded in one exposure. Holograms
of a phase object-micrometer were obtained, according to which, by the method of parallel phase shift, the distribution
of phase lag introduced by the object was restored. To correct the aberration, subtraction of the recorded phase raid of
the illuminating wave — the experimentally obtained phase of the wavefront without an object is used. The developed
digital holographic phase microscope based on a geometric phase lens and a polarization camera makes it possible to
correctly visualize the surface relief profile. The microscope can be used as a tool for monitoring the state of biological
objects exposed to external effects
Square Patterns and Quasi-patterns in Weakly Damped Faraday Waves
Pattern formation in parametric surface waves is studied in the limit of weak
viscous dissipation. A set of quasi-potential equations (QPEs) is introduced
that admits a closed representation in terms of surface variables alone. A
multiscale expansion of the QPEs reveals the importance of triad resonant
interactions, and the saturating effect of the driving force leading to a
gradient amplitude equation. Minimization of the associated Lyapunov function
yields standing wave patterns of square symmetry for capillary waves, and
hexagonal patterns and a sequence of quasi-patterns for mixed capillary-gravity
waves. Numerical integration of the QPEs reveals a quasi-pattern of eight-fold
symmetry in the range of parameters predicted by the multiscale expansion.Comment: RevTeX, 11 pages, 8 figure
Coupled Mean Flow-Amplitude Equations for Nearly Inviscid Parametrically Driven Surface Waves
Nearly inviscid parametrically excited surface gravity-capillary waves in two-dimensional periodic domains of finite depth and both small and large aspect ratio are considered. Coupled equations describing the evolution of the amplitudes of resonant left- and right-traveling waves and their interaction with a mean flow in the bulk are derived, and the conditions for their validity established. In general the mean flow consists of an inviscid part together with a viscous streaming flow driven by a tangential stress due to an oscillating viscous boundary layer near the free surface and a tangential velocity due to a bottom boundary layer. These forcing mechanisms are important even in the limit of vanishing viscosity, and provide boundary conditions for the Navier-Stokes equation satisfied by the mean flow in the bulk. The streaming flow is responsible for several instabilities leading to pattern drift
Amplitude equations and pattern selection in Faraday waves
We present a systematic nonlinear theory of pattern selection for parametric
surface waves (Faraday waves), not restricted to fluids of low viscosity. A
standing wave amplitude equation is derived from the Navier-Stokes equations
that is of gradient form. The associated Lyapunov function is calculated for
different regular patterns to determine the selected pattern near threshold.
For fluids of large viscosity, the selected wave pattern consists of parallel
stripes. At lower viscosity, patterns of square symmetry are obtained in the
capillary regime (large frequencies). At lower frequencies (the mixed
gravity-capillary regime), a sequence of six-fold (hexagonal), eight-fold, ...
patterns are predicted. The regions of stability of the various patterns are in
quantitative agreement with recent experiments conducted in large aspect ratio
systems.Comment: 12 pages, 1 figure, Revte
Nearly inviscid Faraday waves in annular containers of moderately large aspect ratio
Nearly inviscid parametrically excited surface gravity–capillary waves in two-dimensional domains of finite depth and large aspect ratio are considered. Coupled equations describing the evolution of the amplitudes of resonant left- and right-traveling waves and their interaction with a mean flow in the bulk are derived, and the conditions for their validity established. Under suitable conditions the mean flow consists of an inviscid part together with a viscous mean flow driven by a tangential stress due to an oscillatory viscous boundary layer near the free surface and a tangential velocity due to a bottom boundary layer. These forcing mechanisms are important even in the limit of vanishing viscosity, and provide boundary conditions for the Navier–Stokes equation satisfied by the mean flow in the bulk. For moderately large aspect ratio domains the amplitude equations are nonlocal but decouple from the equations describing the interaction of the slow spatial phase and the viscous mean flow. Two cases are considered in detail, gravity–capillary waves and capillary waves in a microgravity environment
Parametric generation of second sound in superfluid helium: linear stability and nonlinear dynamics
We report the experimental studies of a parametric excitation of a second
sound (SS) by a first sound (FS) in a superfluid helium in a resonance cavity.
The results on several topics in this system are presented: (i) The linear
properties of the instability, namely, the threshold, its temperature and
geometrical dependencies, and the spectra of SS just above the onset were
measured. They were found to be in a good quantitative agreement with the
theory. (ii) It was shown that the mechanism of SS amplitude saturation is due
to the nonlinear attenuation of SS via three wave interactions between the SS
waves. Strong low frequency amplitude fluctuations of SS above the threshold
were observed. The spectra of these fluctuations had a universal shape with
exponentially decaying tails. Furthermore, the spectral width grew continuously
with the FS amplitude. The role of three and four wave interactions are
discussed with respect to the nonlinear SS behavior. The first evidence of
Gaussian statistics of the wave amplitudes for the parametrically generated
wave ensemble was obtained. (iii) The experiments on simultaneous pumping of
the FS and independent SS waves revealed new effects. Below the instability
threshold, the SS phase conjugation as a result of three-wave interactions
between the FS and SS waves was observed. Above the threshold two new effects
were found: a giant amplification of the SS wave intensity and strong resonance
oscillations of the SS wave amplitude as a function of the FS amplitude.
Qualitative explanations of these effects are suggested.Comment: 73 pages, 23 figures. to appear in Phys. Rev. B, July 1 st (2001
Pattern formation in 2-frequency forced parametric waves
We present an experimental investigation of superlattice patterns generated
on the surface of a fluid via parametric forcing with 2 commensurate
frequencies. The spatio-temporal behavior of 4 qualitatively different types of
superlattice patterns is described in detail. These states are generated via a
number of different 3--wave resonant interactions. They occur either as
symmetry--breaking bifurcations of hexagonal patterns composed of a single
unstable mode or via nonlinear interactions between the two primary unstable
modes generated by the two forcing frequencies. A coherent picture of these
states together with the phase space in which they appear is presented. In
addition, we describe a number of new superlattice states generated by 4--wave
interactions that arise when symmetry constraints rule out 3--wave resonances.Comment: The paper contains 34 pages and 53 figures and provides an extensive
review of both the theoretical and experimental work peformed in this syste