A sufficient criterion for Rayleigh-Taylor instability of incompressible viscous three-layer flow

Using normal mode analysis Rayleigh-Taylor instability is investigated for three-layer viscous stratified incompressible steady flow, when the top 3rd and bottom 1st layers extend up to infinity, the middle layer has a small thickness δ. The wave Reynolds number in the middle layer is assumed to be sufficiently small. A dispersion relation (a seventh degree polynomial in wave frequency ω) valid up to the order of the maximal value of all possible Kj (j less-than-or-equals, slant 0, K is the wave number) in each coefficient of the polynomial is obtained. A sufficient condition for instability is found out for the first time, pursuing a medium wavelength analysis. It depends on ratios (α and β) of the coefficients of viscosity, the thickness of the middle layer δ, surface tension ratio T and wave number K. This is a new analytical criterion for Rayleigh-Taylor instability of three-layer fluids. It recovers the results of the corresponding problem for two-layer fluids. Among the results obtained, it is observed that taking the coefficients of viscosity of 2nd and 3rd layers same can inhibit the effect of surface tension completely. For large wave number K, the thickness of the middle layer should be correspondingly small to keep the domain of dependence of the threshold wave number Kc constant for fixed α, β and T.

ZnO films for surface acoustic wave microfluidic devices

SAW devices were fabricated on c-axis oriented ZnO films grown on Si substrates. Effects of film thickness on the film microstructure and acoustic frequencies were studied. Both Rayleigh and Sezawa mode waves were detected on the devices, and their resonant frequencies were found to decrease with increase in film thickness.

ZnO films for surface acoustic wave microfluidic devices

SAW devices were fabricated on c-axis oriented ZnO films grown on Si substrates. Effects of film thickness on the film microstructure and acoustic frequencies were studied. Both Rayleigh and Sezawa mode waves were detected on the devices, and their resonant frequencies were found to decrease with increase in film thickness.

Oscillatory Instability of Rayleigh-Marangoni-Benard Convection in Two-Layer System

The convective instabilities in two or more superposed layers heated from below were studied extensively by many scientists due to several interfacial phenomena in nature and crystal growth application. Most works of them were performed mainly on the instability behaviors induced only by buoyancy force, especially on the oscillatory behavior at onset of convection (see Gershuni et. Al.(1982), Renardy et. Al. (1985,2000), Rasenat et. Al. (1989), and Colinet et. Al.(1994)) . But the unstable situations of multi-layer liquid convection will become more complicated and interesting while considering at the same time the buoyancy effect combined with thermocapillary effect. This is the case in the gravity reduced field or thin liquid layer where the thermocapillary effect is as important as buoyancy effect. The objective of this study was to investigate theoretically the interaction between Rayleigh-Bénard instability and pure Marangoni instability in a two-layer system, and more attention focus on the oscillatory instability both at the onset of convection and with increasing supercriticality. Oscillatory behavious of Rayleigh-Marangoni-Bénard convective instability (R-M-B instability) and flow patterns are presented in the two-layer system of Silicon Oil (10cSt) over Fluorinert (FC70) for a larger various range of two-layer depth ratios (Hr=Hupper/Hdown) from 0.2 to 5.0. Both linear instability analysis and 2D numerical simulation (A=L/H=10) show that the instability of the system depends strongly on the depth ratio of two-layer liquids. The oscillatory instability regime at the onset of R-M-B convection are found theoretically in different regions of layer thickness ratio for different two-layer depth H=12,6,4,3mm. The neutral stability curve of the system displaces to right while we consider the Marangoni effect at the interface in comparison with the Rayleigh-Bénard instability of the system without the Marangoni effect (Ma=0). The numerical results show different regimes of the developing of convection in the two-layer system for different thickness ratios and some differences at the onset of pure Marangoni convection and the onset of Rayleigh-Bénard convections in two-layer liquids. Both traveling wave and standing wave were detected in the oscillatory instability regime due to the competition between Rayleigh-Bénard instability and Marangoni effect. The mechanism of the standing wave formation in the system is presented numerically in this paper. The oscillating standing wave results in the competition of the intermediate Marangoni cell and the Rayleigh convective rolls. In the two-layer system of 47v2 silicone oil over water, a transition form the steady instability to the oscillatory instability of the Rayleigh-Marangoni-Bénard Convection was found numerically above the onset of convection for ε=0.9 and Hr=0.5. We propose that this oscillatory mechanism is possible to explain the experimental observation of Degen et. Al.(1998). Experimental work in comparison with our theoretical findings on the two-layer Rayleigh-Marangoni-Bénard convection with thinner depth for H<6mm will be carried out in the near future, and more attention will be paid to new oscillatory instability regimes possible in the influence of thermocapillary effects on the competition of two-layer liquids

Diffraction integral formulas of the pulsed wave field in the temporal domain

To resolve the diffraction problems of the pulsed wave field directly in the temporal domain, we extend the Rayleigh diffraction integrals to the temporal domain and then discuss the approximation condition of this diffraction formula. (C) 1997 Optical Society of America.

Dynamic states in rotating Rayleigh-Bénard convection systems

A new geometry-independent state - a traveling-wave wall state - is proposed as the mechanism whereby which the experimentally observed wall-localized states in rotating Rayleigh-Bénard convection systems preempt the bulk state at large rotation rates. Its properties are calculated for the illustrative case of free-slip top and bottom boundary conditions. At small rotation rates, this new wall state is found to disappear. A detailed study of the dynamics of the wall state and the bulk state in the transition region where this disappearance occurs is conducted using a Swift-Hohenberg model system. The Swift-Hohenberg model, with appropriate reflection-symmetry- breaking boundary conditions, is also shown to exhibit traveling-wave wall states, further demonstrating that traveling-wave wall states are a generic feature of nonequilibrium pattern-forming systems. A numerical code for the Swift-Hohenberg model in an annular geometry was written and used to investigate the dynamics of rotating Rayleigh-Bénard convection systems.

Microfluidics based on ZnO/nanocrystalline diamond surface acoustic wave devices.

Surface acoustic wave (SAW) devices with 64 μm wavelength were fabricated on a zinc oxide (ZnO) film deposited on top of an ultra-smooth nanocrystalline diamond (UNCD) layer. The smooth surface of the UNCD film allowed the growth of the ZnO film with excellent c-axis orientation and low surface roughness, suitable for SAW fabrication, and could restrain the wave from significantly dissipating into the substrate. The frequency response of the fabricated devices was characterized and a Rayleigh mode was observed at ∼65.4 MHz. This mode was utilised to demonstrate that the ZnO/UNCD SAW device can be successfully used for microfluidic applications. Streaming, pumping, and jetting using microdroplets of 0.5 and 20 μl were achieved and characterized under different powers applied to the SAW device, focusing more on the jetting behaviors induced by the ZnO SAW.

Characterization of the surface acoustic wave devices based on ZnO/nanocrystalline diamond structures

Nanocrystalline ZnO films with strong (0002) texture and fine grains were deposited onto ultra-nanocrystalline diamond (UNCD) layers on silicon using high target utilization sputtering technology. The unique characteristic of this sputtering technique allows room temperature growth of smooth ZnO films with a low roughness and low stress at high growth rates. Surface acoustic wave (SAW) devices were fabricated on ZnO/UNCD structure and exhibited good transmission signals with a low insertion loss and a strong side-lobe suppression for the Rayleigh mode SAW. Based on the optimization of the layered structure of the SAW device, a good performance with a coupling coefficient of 5.2% has been realized, promising for improving the microfluidic efficiency in droplet transportation comparing with that of the ZnO/Si SAW device. An optimized temperature coefficient of frequency of -23.4 ppm°C-1 was obtained for the SAW devices with the 2.72 μm-thick ZnO and 1.1 μm-thick UNCD film. Significant thermal effect due to the acoustic heating has been redcued which is related to the temperature stability of the ZnO/UNCD SAW device. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Distributed Temperature Sensing System Based on Rayleigh Scattering BOTDA

A distributed temperature sensor based on Rayleigh scattering Brillouin optical time domain analysis (Rayleigh-BOTDA) is proposed in this paper. The sensor uses Rayleigh backscattering effect of microwave modulated pulse base sidebands as probe wave and a high sensitive photon counting detector for Brillouin signal intensity detection. Compared with a conventional BOTDA system, the Rayleigh-BOTDA effectively suppresses polarization-induced signal fluctuation resulting in improved signal intensity. The experimental scheme presented is simplified by using a single laser with one-end access. The temperature accuracy of the new sensing system was demonstrated as 1 degrees C on spatial resolution of 3 m.

Statistical distribution of nonlinear random wave height

A statistical model of random wave is developed using Stokes wave theory of water wave dynamics. A new nonlinear probability distribution function of wave height is presented. The results indicate that wave steepness not only could be a parameter of the distribution function of wave height but also could reflect the degree of wave height distribution deviation from the Rayleigh distribution. The new wave height distribution overcomes the problem of Rayleigh distribution that the prediction of big wave is overestimated and the general wave is underestimated. The prediction of small probability wave height value of new distribution is also smaller than that of Rayleigh distribution. Wave height data taken from East China Normal University are used to verify the new distribution. The results indicate that the new distribution fits the measurements much better than the Rayleigh distribution.

Wave height analysis from 10 years of observations in the Norwegian Sea

Large waves pose risks to ships, offshore structures, coastal infrastructure and ecosystems. This paper analyses 10 years of in-situ measurements of significant wave height (Hs) and maximum wave height (Hmax) from the ocean weather ship Polarfront in the Norwegian Sea. During the period 2000 to 2009, surface elevation was recorded every 0.59 s during sampling periods of 30 min. The Hmax observations scale linearly with Hs on average. A widely-used empirical Weibull distribution is found to estimate average values of Hmax/H s and Hmax better than a Rayleigh distribution, but tends to underestimate both for all but the smallest waves. In this paper we propose a modified Rayleigh distribution which compensates for the heterogeneity of the observed dataset: the distribution is fitted to the whole dataset and improves the estimate of the largest waves. Over the 10-year period, the Weibull distribution approximates the observed Hs and Hmax well, and an exponential function can be used to predict the probability distribution function of the ratio Hmax/Hs. However, the Weibull distribution tends to underestimate the occurrence of extremely large values of Hs and Hmax. The persistence of Hs and Hmax in winter is also examined. Wave fields with Hs > 12 m and Hmax > 16 m do not last longer than 3 h. Low-to-moderate wave heights that persist for more than 12 h dominate the relationship of the wave field with the winter NAO index over 2000–2009. In contrast, the inter-annual variability of wave fields with Hs > 5.5 m or Hmax > 8.5 m and wave fields persisting over ~2.5 days is not associated with the winter NAO index.

Investigating the dynamics of laser induced sparks in atmospheric helium using Rayleigh and Thomson scattering

We have used optical Rayleigh and Thomson scattering to investigate the expansion dynamics of laser induced plasma in atmospheric helium and to map its electron parameters both in time and space. The plasma is created using 9 ns duration, 140 mJ pulses from a Nd:YAG laser operating at 1064 nm, focused with a 10 cm focal length lens, and probed with 7 ns, 80 mJ, and 532 nm Nd:YAG laser pulses. Between 0.4 μs and 22.5 μs after breakdown, the electron density decreases from 3.3 × 1017 cm−3 to 9 × 1013 cm−3, while the temperature drops from 3.2 eV to 0.1 eV. Spatially resolved Thomson scattering data recorded up to 17.5 μs reveal that during this time the laser induced plasma expands at a rate given by R ∼ t0.4 consistent with a non-radiative spherical blast wave. This data also indicate the development of a toroidal structure in the lateral profile of both electron temperature and density. Rayleigh scattering data show that the gas density decreases in the center of the expanding plasma with a central scattering peak reemerging after about 12 μs. We have utilized a zero dimensional kinetic global model to identify the dominant particle species versus delay time and this indicates that metastable helium and the He2 + molecular ion play an important role.

Threshold Optimization for Energy Detection-Based Spectrum Sensing Over Hyper-Rayleigh Fading Channels

Spectrum sensing is a key function of cognitive radio systems. Sensing performance is determined by three main factors including the wireless channel between the primary system and the cognitive radio nodes, the detection threshold, and the sensing time. In this letter a closed-form expression for the average probability of detection for energy detection based spectrum sensing over two-wave with diffuse power fading channels is derived. This expression is then used to optimize the detection threshold for cognitive radio nodes, which operate in confined structures that exhibit worse than Rayleigh fading conditions. Such fading conditions can represent a behavioral model of cognitive machine-to-machine systems deployed in enclosed structures such as in-vehicular environments.

Energy Detection based Spectrum Sensing over Two-wave with Diffuse Power Fading Channels

One of the most important factors that affects the performance of energy detection (ED) is the fading channel between the wireless nodes. This article investigates the performance of ED-based spectrum sensing, for cognitive radio (CR), over two-wave with diffuse power (TWDP) fading channels. The TWDP fading model characterizes a variety of fading channels, including well-known canonical fading distributions, such as Rayleigh and Rician, as well as worse than Rayleigh fading conditions modeled by the two-ray fading model. Novel analytic expressions for the average probability of detection over TWDP fading that account for single-user and cooperative spectrum sensing as well as square law selection diversity reception are derived. These expressions are used to analyze the behavior of ED-based spectrum sensing over moderate, severe and extreme fading conditions, and to investigate the use of cooperation and diversity as a means of mitigating the fading effects. Our results indicate that TWDP fading conditions can significantly degrade the sensing performance; however, it is shown that detection performance can be improved when cooperation and diversity are employed. The presented outcomes enable us to identify the limits of ED-based spectrum sensing and quantify the trade-offs between detection performance and energy efficiency for cognitive radio systems deployed within confined environments such as in-vehicular wireless networks.

The importance of friction in mountain wave drag amplification by Scorer parameter resonance

A mechanism for amplification of mountain waves, and their associated drag, by parametric resonance is investigated using linear theory and numerical simulations. This mechanism, which is active when the Scorer parameter oscillates with height, was recently classified by previous authors as intrinsically nonlinear. Here it is shown that, if friction is included in the simplest possible form as a Rayleigh damping, and the solution to the Taylor-Goldstein equation is expanded in a power series of the amplitude of the Scorer parameter oscillation, linear theory can replicate the resonant amplification produced by numerical simulations with some accuracy. The drag is significantly altered by resonance in the vicinity of n/l_0 = 2, where l_0 is the unperturbed value of the Scorer parameter and n is the wave number of its oscillation. Depending on the phase of this oscillation, the drag may be substantially amplified or attenuated relative to its non-resonant value, displaying either single maxima or minima, or double extrema near n/l_0 = 2. Both non-hydrostatic effects and friction tend to reduce the magnitude of the drag extrema. However, in exactly inviscid conditions, the single drag maximum and minimum are suppressed. As in the atmosphere friction is often small but non-zero outside the boundary layer, modelling of the drag amplification mechanism addressed here should be quite sensitive to the type of turbulence closure employed in numerical models, or to computational dissipation in nominally inviscid simulations.