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

Study of the factors affecting the karst volume assessment in the Dead Sea sinkhole problem using microgravity field analysis and 3-D modeling

Thousands of sinkholes have appeared in the Dead Sea (DS) coastal area in Israel and Jordan during two last decades. The sinkhole development is recently associated with the buried evaporation karst at the depth of 25–50 m from earth's surface caused by the drop of the DS level at the rate of 0.8–1.0 m/yr. Drop in the Dead Sea level has changed hydrogeological conditions in the subsurface and caused surface to collapse. The pre-existing cavern was detected using microgravity mapping in the Nahal Hever South site where seven sinkholes of 1–2 m diameter had been opened. About 5000 gravity stations were observed in the area of 200×200 m<sup>2</sup> by the use of Scintrex CG-3M AutoGrav gravimeter. Besides the conventional set of corrections applied in microgravity investigations, a correction for a strong gravity horizontal gradient (DS Transform Zone negative gravity anomaly influence) was inserted. As a result, residual gravity anomaly of –(0.08÷0.14) mGal was revealed. The gravity field analysis was supported by resistivity measurements. We applied the Emigma 7.8 gravity software to create the 3-D physical-geological models of the sinkholes development area. The modeling was confirmed by application of the <i>GSFC</i> program developed especially for 3-D combined gravity-magnetic modeling in complicated environments. Computed numerous gravity models verified an effective applicability of the microgravity technology for detection of karst cavities and estimation of their physical-geological parameters. A volume of the karst was approximately estimated as 35 000 m<sup>3</sup>. The visual analysis of large sinkhole clusters have been forming at the microgravity anomaly site, confirmed the results of microgravity mapping and 3-D modeling

Three-dimensional magnetic resonance imaging for groundwater

International audienceThe surface nuclear magnetic resonance method (SNMR) is an established geophysical tool routinely used for investigating one-dimensional (1D) and sometimes 2D subsurface water-saturated formations. We have expanded the tool by developing a 3D application. 3D-SNMR is a large-scale method that allows magnetic resonance imaging of groundwater down to about 80 m. Similar to most surface geophysical methods, 3D-SNMR has limited resolution, but it is effective for investigating water-saturated geological formations larger than several tens of meters. Because the performance of the method depends on variable survey conditions, we cannot estimate it in general. For demonstration purposes, we present an example of numerical modeling under fixed conditions. Results show that under certain conditions it is possible to detect a water volume as small as 500 m(3) and the detection threshold depends on the ambient electromagnetic noise magnitude and on the location of the target volume relative to the SNMR loops. The 3D-SNMR method was used to investigate accumulated water within the Tete Rousse glacier (French Alps). Inversion of the field measurements made it possible to locate the principal reservoir in the central part of the glacier and estimate the volume of accumulated water. These results were verified by 20 boreholes installed after the 3D-SNMR results were obtained and by pumping water out of the glacier. Very good correspondence between the 3D-SNMR and borehole results was observed

Removing Regional Trends in Microgravity in Complex Environments: Testing on 3D Model and Field Investigations in the Eastern Dead Sea Coast (Jordan)

Microgravity investigations are now recognized as a powerful tool for subsurface imaging and especially for the localization of underground karsts. However numerous natural (geological), technical, and environmental factors interfere with microgravity survey processing and interpretation. One of natural factors that causes the most disturbance in complex geological environments is the influence of regional trends. In the Dead Sea coastal areas the influence of regional trends can exceed residual gravity effects by some tenfold. Many widely applied methods are unable to remove regional trends with sufficient accuracy. We tested number of transformation methods (including computing gravity field derivatives, self-adjusting and adaptive filtering, Fourier series, wavelet, and other procedures) on a 3D model (complicated by randomly distributed noise), and field investigations were carried out in Ghor Al-Haditha (the eastern side of the Dead Sea in Jordan). We show that the most effective methods for regional trend removal (at least for the theoretical and field cases here) are the bilinear saddle and local polynomial regressions. Application of these methods made it possible to detect the anomalous gravity effect from buried targets in the theoretical model and to extract the local gravity anomaly at the Ghor Al-Haditha site. The local anomaly was utilized for 3D gravity modeling to construct a physical-geological model (PGM)

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

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