The effects of random surface waves on the steady Ekman current solutions

The response of near-surface current profiles to wind and random surface waves are studied based on the approach of Jenkins [1989. The use of a wave prediction model for driving a near surface current model. Dtsch. Hydrogr. Z. 42,134-149] and Tang et al. [2007. Observation and modeling of surface currents on the Grand Banks: a study of the wave effects on surface currents. J. Geophys. Res. 112, C10025, doi:10.1029/2006JC004028]. Analytic steady solutions are presented for wave-modified Ekman equations resulting from Stokes drift, wind input and wave dissipation for a depth-independent constant eddy viscosity coefficient and one that varies linearly with depth. The parameters involved in the solutions can be determined by the two-dimensional wavenumber spectrum of ocean waves, wind speed, the Coriolis parameter and the densities of air and water, and the solutions reduce to those of Lewis and Belcher [2004. Time-dependent, coupled, Ekman boundary layer solutions incorporating Stokes drift. Dyn. Atmos. Oceans. 37, 313-351] when only the effects of Stokes drift are included. As illustrative examples, for a fully developed wind-generated sea with different wind speeds, wave-modified current profiles are calculated and compared with the classical Ekman theory and Lewis and Belcher's [2004. Time-dependent, coupled, Ekman boundary layer solutions incorporating Stokes drift. Dyn. Atmos. Oceans 37, 313-351] modification by using the Donelan and Pierson [1987. Radar scattering and equilibrium ranges in wind-generated waves with application to scatterometry. J. Geophys. Res. 92, 4971-5029] wavenumber spectrum, the WAM wave model formulation for wind input energy to waves, and wave energy dissipation converted to currents. Illustrative examples for a fully developed sea and the comparisons between observations and the theoretical predictions demonstrate that the effects of the random surface waves on the classical Ekman current are important, as they change qualitatively the nature of the Ekman layer. But the effects of the wind input and wave dissipation on surface current are small, relative to the impact of the Stokes drift. (C) 2008 Elsevier Ltd. All rights reserved.

Effect of surface roughness on diffusion-limited charge transfer

A theory is developed for diffusion-limited charge transfer on a non-fractally rough electrode. The perturbation expressions are obtained for concentration, current density and measured diffusion-limited current for arbitrary one- and two-dimensional surface profiles. The random surface model is employed for a rough electrode\electrolyte interface. In this model the gross geometrical property of an electrochemically active rough surface - the surface structure factor-is related to the average electrode current, current density and concentration. Under short and long time regimes, various morphological features of the rough electrodes, i.e. excess area (related to roughness slope), curvature, correlation length, etc. are related to the (average) current transients. A two-point Pade approximant is used to develop an all time average current expression in terms of partial morphological features of the rough surface. The inverse problem of predicting the surface structure factor from the observed transients is also described. Finally, the effect of surface roughness is studied for specific surface statistics, namely a Gaussian correlation function. It is shown how the surface roughness enhances the overall diffusion-limited charge transfer current.

Analysis of Strain Rates and Microstructural Evaluation during Metal Forming: Role of Surface Texture and Friction

The surface texture of a die plays an important role in friction during metal forming. In the present study, unidirectional and random surface finishes were produced on hardened steel plate surfaces. To understand the influence of surface texture on friction, experiments were conducted using Al-Mg alloy pins that slid against steel plates of different surface textures. In the sliding experiments, a high coefficient of friction was observed when the pins slid perpendicular to the unidirectional grinding marks and low friction occurred when the pins slid on the random surfaces. Finite element simulations were performed using the measured friction values to understand the stress and strain evolutions in the deforming material using dies with various friction. The numerical results showed that the states of stress and strain rates are strongly influenced by the friction at the interface and hence would influence the final material microstructure. To substantiate the numerical results, laboratory compression tests were conducted. Different surface textures were obtained in order to experience different friction values at different locations. A large variation in the microstructure at these locations was observed during experiments, verifying that surface texture and die friction significantly influence fundamental material formation behavior.

Absolute measurement of roughness and lateral-correlation length of random surfaces by use of the simplified model of image-speckle contrast

We present a method of image-speckle contrast for the nonprecalibration measurement of the root-mean-square roughness and the lateral-correlation length of random surfaces with Gaussian correlation. We use the simplified model of the speckle fields produced by the weak scattering object in the theoretical analysis. The explicit mathematical relation shows that the saturation value of the image-speckle contrast at a large aperture radius determines the roughness, while the variation of the contrast with the aperture radius determines the lateral-correlation length. In the experimental performance, we specially fabricate the random surface samples with Gaussian correlation. The square of the image-speckle contrast is measured versus the radius of the aperture in the 4f system, and the roughness and the lateral-correlation length are extracted by fitting the theoretical result to the experimental data. Comparison of the measurement with that by an atomic force microscope shows our method has a satisfying accuracy. (C) 2002 Optical Society of America.

Slip flow and heat transfer in microbearings with fractal surface topographies

The effects of random surface roughness on slip flow and heat transfer in microbearings are investigated. A three-dimensional random surface roughness model characterized by fractal geometry is used to describe the multiscale self-affine roughness, which is represented by the modified two-variable Weierstrass- Mandelbrot (W-M) functions, at micro-scale. Based on this fractal characterization, the roles of rarefaction and roughness on the thermal and flow properties in microbearings are predicted and evaluated using numerical analyses and simulations. The results show that the boundary conditions of velocity slip and temperature jump depend not only on the Knudsen number but also on the surface roughness. It is found that the effects of the gas rarefaction and surface roughness on flow behavior and heat transfer in the microbearing are strongly coupled. The negative influence of roughness on heat transfer found to be the Nusselt number reduction. In addition, the effects of temperature difference and relative roughness on the heat transfer in the bearing are also analyzed and discussed. © 2012 Elsevier Ltd. All rights reserved.

Second-order solutions for random interfacial waves under steady uniform currents

In the present research, the study of Song (2004) for random interfacial waves in two-layer fluid is extended to the case of fluids moving at different steady uniform speeds. The equations describing the random displacements of the density interface and the associated velocity potentials in two-layer fluid are solved to the second order, and the wave-wave interactions of the wave components and the interactions between the waves and currents are described. As expected, the extended solutions include those obtained by Song (2004) as one special case where the steady uniform currents of the two fluids are taken as zero, and the solutions reduce to those derived by Sharma and Dean (1979) for random surface waves if the density of the upper fluid and the current of the lower fluid are both taken as zero.

Ensemble effects in the coupling of acetylene to benzene on a bimetallic surface: A study with Pd{111}/Au

Acetylene coupling to benzene on the Pd(lll) surface is greatly enhanced by the presence of catalytically inert Au atoms. LEED and Auger spectroscopy show that progressive annealing of Au overlayers on Pd(lll) leads to the formation of a series of random surface alloys with continuously varying composition. Cyclization activity is a strong function of surface composition-the most efficient catalyst corresponds to a surface of composition similar to 85% Pd. CO TPD and HREELS data show that acetylene cyclization activity is not correlated with the availability of singleton Pd atoms, nor just with the presence of 3-fold pure Pd sites-the preferred chemisorption site for C2H2 on Pd{111}. The data can be quantitatively rationalized in terms of a simple model in which catalytic activity is dominated by Pd6Au and Pd-7 surface ensembles, allowance being made for the known degree to which pure Pd{111} decomposes the reactant and product molecules.

Effect of tillage on fractal indices describing soil surface microrelief of a Brazilian Alfisol

Soil surface roughness is known to influence water infiltration, runoff and erosion. Soil surface roughness changes with management and weather and its mathematical description still remains an important issue. The main objective of this study was to investigate the effect of tillage on the two fractal indices, fractal dimension, D, and crossover length, 1, currently used in characterizing soil surface microrelief. The statistical index random roughness, RR, was also assessed. Field experiments were done on an Alfisol located at Rio Grande do Sul State (Brazil). Two tillage treatments (conventional versus direct drilling) were tested. The soil surface microrelief was assessed by point elevation measurements in 16 plots for each treatment. The sampling scheme was a square grid with 20 x 20 mm between point spacing and the plot size was 280 x 280 mm, so that each data set consisted of 225 individual elevation points. All indices were calculated after trend removal, both by slope correction, i.e., oriented microrelief, and by slope plus tillage marks correction, i.e., random microrelief. The implemented algorithm for estimating D and 1 consisted in evaluating the roughness around the local root mean square deviation (RMS) of the point elevation values. Irrespective of tillage treatment and detrending procedure, fractal behavior extended only over a bounded range of scales, from 40 to 100 mm, due to the experimental setup. In these conditions, assessing fractal indices was not always straightforward. The statistical index RR and the fractal index I were significantly different between tillage treatments for oriented and random surface conditions. D values of random soil surfaces were not affected by tillage treatment, whereas D values of oriented microrelief were significantly lower in the direct drilled plots. Removal of tillage marks trend resulted in a significant increase in D values. Within each tillage treatment, 1 and D were significantly correlated. (c) 2006 Elsevier B.V. All rights reserved.

强散射体产生的像面散斑对比度与随机表面及成像系统关系的研究

We study the statistical properties of the image speckles produced by strong-scattering objects in the 4f optical imaging system. Using the generic expression of the complex amplitude of speckles and the approximation of the double-exponential function, we first obtain the ensemble average of the speckle intensity. Then we derive the variance of the speckle intensity based on the rotational transformation of the real and imaginary parts of the complex amplitude of speckles. We finally obtain the expression for the contrast of the. speckles, which is explicitly related to the statistical parameters of random surface and to the parameters of the imaging system. Our results are an obvious improvement compared with those reported in the literature, where the relations including such implicit quantities as the average size of the scattering grains of the random surface and the number of scattering grains are usually used. The results of this paper would be helpful for the characterization of random surface by speckle contrast.

Properties of dental resins submitted to pH catalysed hydrolysis

Objectives: This study evaluated the surface microhardness (SM) and roughness (SR) alterations of dental resins submitted to pH catalysed degradation regimens. Methods: Thirty discs of each TPH Spectrum (Dentsply), Z100 (3M-ESPE), or an unfilled experimental bis-GMA/TEGDMA resin were fabricated, totaling 90 specimens. Each specimen was polymerized for 40 s, finished, polished, and individually stored in deionized water at 37 degrees C for 7 days. Specimens were randomly assigned to the following pH solutions: 1.0, 6.9 or 13, and for SM or SR evaluations (n = 5). Baseline Knoop-hardness of each specimen was obtained by the arithmetic mean of five random micro-indentations. For SR, mean baseline values were obtained by five random surface tracings (R-a). Specimens were then soaked in one of the following storage media at 37 degrees C: (1) 0.1 M, pH 1.0 HCl, (2) 0.1 N, pH 13.0 NaOCl, and (3) deionized water (pH 6.9). Solutions were replaced daily. Repeated SM and SR measurements were performed at the 3-, 7- and 14-day storage time intervals. For each test and resin, data were analysed by two-way ANOVA followed by Tukey's test (alpha = 0.05). Results: There was significant decrease in SM and increase in SR values of composites after storage in alkaline medium. TPH and Z100 presented similar behaviour for SM and SR after immersion in the different media, whereas unfilled resin values showed no significant change. Conclusion: Hydrolytic degradation of resin composites seems to begin with the silanized inorganic particles and therefore depend on their composition. Significance: To accelerate composite hydrolysis and produce quick in vitro microstructural damage, alkaline medium appears to be more suitable than acidic medium. Contemporary resin composite properties seem to withstand neutral and acidic oral environments tolerably well. (C) 2012 Elsevier Ltd. All rights reserved.

Normal mode sound propagation in an ocean with random narrow-band surface waves

Normal mode sound propagation in an isovelocity ocean with random narrow-band surface waves is considered, assuming the root-mean-square wave height to be small compared to the acoustic wavelength. Nonresonant interaction among the normal modes is studied straightforward perturbation technique. The more interesting case of resonant interaction is investigated using the method of multiple scales to obtain a pair of stochastic coupled amplitude equations which are solved using the Peano-Baker expansion technique. Equations for the spatial evolution of the first and second moments of the mode amplitudes are also derived and solved. It is shown that, irrespective of the initial conditions, the mean values of the mode amplitudes tend to zero asymptotically with increasing range, the mean-square amplitudes tend towards a state of equipartition of energy, and the total energy of the modes is conserved.

Downscaling of surface moisture flux and precipitation in the Ebro Valley (Spain) using analogues and analogues followed by random forests and multiple linear regression

In this paper, reanalysis fields from the ECMWF have been statistically downscaled to predict from large-scale atmospheric fields, surface moisture flux and daily precipitation at two observatories (Zaragoza and Tortosa, Ebro Valley, Spain) during the 1961-2001 period. Three types of downscaling models have been built: (i) analogues, (ii) analogues followed by random forests and (iii) analogues followed by multiple linear regression. The inputs consist of data (predictor fields) taken from the ERA-40 reanalysis. The predicted fields are precipitation and surface moisture flux as measured at the two observatories. With the aim to reduce the dimensionality of the problem, the ERA-40 fields have been decomposed using empirical orthogonal functions. Available daily data has been divided into two parts: a training period used to find a group of about 300 analogues to build the downscaling model (1961-1996) and a test period (19972001), where models' performance has been assessed using independent data. In the case of surface moisture flux, the models based on analogues followed by random forests do not clearly outperform those built on analogues plus multiple linear regression, while simple averages calculated from the nearest analogues found in the training period, yielded only slightly worse results. In the case of precipitation, the three types of model performed equally. These results suggest that most of the models' downscaling capabilities can be attributed to the analogues-calculation stage.

Statistical distribution of wave-surface elevation for second-order random directional ocean waves in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, a statistical distribution of the wave-surface elevation is derived by using the characteristic function expansion method. It is found that the distribution, after normalization of the wave-surface elevation, depends only on two parameters. One parameter describes the small mean bias of the surface produced by the second-order wave-wave interactions. Another one is approximately proportional to the skewness of the distribution. Both of these two parameters can be determined by the water depth and the wave-number spectrum of ocean waves. As an illustrative example, we consider a fully developed wind-generated sea and the parameters are calculated for various wind speeds and water depths by using Donelan and Pierson spectrum. It is also found that, for deep water, the dimensionless distribution reduces to the third-order Gram-Charlier series obtained by Longuet-Higgins [J. Fluid Mech. 17 (1963) 459]. The newly proposed distribution is compared with the data of Bitner [Appl. Ocean Res. 2 (1980) 63], Gaussian distribution and the fourth-order Gram-Charlier series, and found our distribution gives a more reasonable fit to the data. (C) 2002 Elsevier Science B.V. All rights reserved.