Secondary Instabilities of Surface Waves on Viscous Fluids in the Faraday Instability

Secondary instabilities of Faraday waves show three regimes: (1) As seen previously, low-viscosity (nu) fluids destabilize first into squares. At higher driving accelerations a, squares show low-frequency modulations corresponding to the motion of phase defects, while theory predicts a stationary transverse amplitude modulation (TAM). (2) High-nu fluids destabilize first to stripes. Stripes then show an oscillatory TAM whose frequency is incommensurate with the driving frequency. At higher a, the TAM undergoes a phase instability. At still higher a, edge dislocations form and fluid droplets are ejected. (3) Intermediate-nu fluids show a complex coexistence of squares and stripes, as well as stationary and oscillatory TAM instabilities of the stripes.Comment: REVTEX, with 3 separate uuencoded figures, to appear in Europhys. Let

Buoyant-thermocapillary instabilities of differentially heated liquid layers

URL: http://www-spht.cea.fr/articles/T95/103 Instabilités d'écoulements thermocapillaires en présence de gravitéInternational audienceThe stability of buoyant-thermocapillary-driven flows in a fluid layer subjected to a horizontal temperature gradient is analysed. Our purpose is the modelization of recent experimental results obtained for a fluid of Prandtl number Pr=7, by Daviaud and Vince [Phys. Rev. E, 4432 (1993)] who observed a transition between traveling waves and stationary rolls when the height of fluid is increased. Our model takes into account several effects which were examined separately in previous studies. The relative importance of buoyancy and thermocapillarity is controlled by the ratio W of Marangoni number to Rayleigh number. The fluid layer is bounded below by a rigid plane whose temperature varies linearly along the direction of the thermal gradient. A Biot number is introduced to describe heat transfer at the top free surface. Our stability analysis establishes the existence of a transition between stationary and oscillatory modes when W exceeds a value ${\rm W}_0$ which is function of the Biot number. Moreover, two types of oscillatory modes have been identified which differ by the range of variation of their critical parameters (wave number, frequency, angle of propagation) versus W

Localized and Cellular Patterns in a Vibrated Granular Layer

We propose a phenomenological model for pattern formation in a vertically vibrated layer of granular material. This model exhibits a variety of stable cellular patterns including standing rolls and squares as well as localized objects (oscillons and worms), similar to recent experimental observations(Umbanhowar et al., 1996). The model is an amplitude equation for the parametrical instability coupled to the mass conservation law. The structure and dynamics of the solutions resemble closely the properties of localized and cellular patterns observed in the experiments.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Let

Amplitude measurements of Faraday waves

A light reflection technique is used to measure quantitatively the surface elevation of Faraday waves. The performed measurements cover a wide parameter range of driving frequencies and sample viscosities. In the capillary wave regime the bifurcation diagrams exhibit a frequency independent scaling proportional to the wavelength. We also provide numerical simulations of the full Navier-Stokes equations, which are in quantitative agreement up to supercritical drive amplitudes of 20%. The validity of an existing perturbation analysis is found to be limited to 2.5% overcriticaly.Comment: 7 figure

2D characterization of near-surface V P/V S: surface-wave dispersion inversion versus refraction tomography

International audienceThe joint study of pressure (P-) and shear (S-) wave velocities (Vp and Vs ), as well as their ratio (Vp /Vs), has been used for many years at large scales but remains marginal in near-surface applications. For these applications, and are generally retrieved with seismic refraction tomography combining P and SH (shear-horizontal) waves, thus requiring two separate acquisitions. Surface-wave prospecting methods are proposed here as an alternative to SH-wave tomography in order to retrieve pseudo-2D Vs sections from typical P-wave shot gathers and assess the applicability of combined P-wave refraction tomography and surface-wave dispersion analysis to estimate Vp/Vs ratio. We carried out a simultaneous P- and surface-wave survey on a well-characterized granite-micaschists contact at Ploemeur hydrological observatory (France), supplemented with an SH-wave acquisition along the same line in order to compare Vs results obtained from SH-wave refraction tomography and surface-wave profiling. Travel-time tomography was performed with P- and SH- wave first arrivals observed along the line to retrieve Vtomo p and Vtomo s models. Windowing and stacking techniques were then used to extract evenly spaced dispersion data from P-wave shot gathers along the line. Successive 1D Monte Carlo inversions of these dispersion data were performed using fixed Vp values extracted from Vtomo p the model and no lateral constraints between two adjacent 1D inversions. The resulting 1D Vsw s models were then assembled to create a pseudo-2D Vsw s section, which appears to be correctly matching the general features observed on the section. If the pseudo-section is characterized by strong velocity incertainties in the deepest layers, it provides a more detailed description of the lateral variations in the shallow layers. Theoretical dispersion curves were also computed along the line with both and models. While the dispersion curves computed from models provide results consistent with the coherent maxima observed on dispersion images, dispersion curves computed from models are generally not fitting the observed propagation modes at low frequency. Surface-wave analysis could therefore improve models both in terms of reliability and ability to describe lateral variations. Finally, we were able to compute / sections from both and models. The two sections present similar features, but the section obtained from shows a higher lateral resolution and is consistent with the features observed on electrical resistivity tomography, thus validating our approach for retrieving Vp/Vs ratio from combined P-wave tomography and surface-wave profiling