Scattering of electromagnetic waves by a randomly rough surface as a boundary problem of laser radiation interaction with light-scattering materials and media

The light scattering by a rough surface with random Gaussian fluctuations of roughness is studied in the case of coarse roughness, whose parameters—mean deviation and correlation length—are much greater than the radiation wavelength. Closed analytical solutions of the problem are presented in terms of radiophysics for the boundary conditions of an ideal conductor and the impedance boundary conditions. These solutions are formulated in terms of a photometric scattering indicatrix. The possibility of their application to the problems of photometry and theory of radiative transfer and scattering in turbid media, in particular, in simulation of the process of boundary scattering of laser radiation by rough surfaces of biological tissues and media, is discussed.     

粗糙界面板Lamb波的传播特征

弹性波在粗糙界面板中的传播问题对无损检测、地震波传播等问题有实际意义,但是多年来的研究限于相屏近似等方法。本文从严格的理论出发,把粗糙界面起伏看作空间位置变量的随机过程,在粗糙表面起伏很小的条件下,用多次散射相互独立假设得到了平均意义下的Rayleigh-Lamb频散方程。通过对方程进行求解,得到了Lamb波在粗糙界面板中传播时的衰减。结果表明Lamb波的衰减和界面的粗糙起伏方差近似成正比,和粗糙起伏相关长度关系不大。在理论分析的基础上,进行了实验验证。     

Large eddy simulations and parameterisation of roughness element orientation and flow direction effects in rough wall boundary layers

We conduct a series of large eddy simulations (LES) of turbulent boundary layers over arrays of cuboidal roughness elements at arbitrary orientation angles (non-frontal orientations with the incident flow). Flow response to changing roughness orientation is systematically studied at two ground coverage densities, λ_p = 0.06 and 0.11. As expected, the effective roughness heights z_o measured from LES are higher for λ_p = 0.11 than for λ_p = 0.06, although appreciable changes both in z_o and wall shear stress (friction velocity) are observed at both ground coverage densities as the roughness orientation angle changes. This suggests the necessity of accounting for detailed rough wall topology (including more information than just λ_p, λ_f) when relating rough wall morphology to its aerodynamic properties. To this end, a recently developed analytical rough wall parameterisation is used to predict the aerodynamic properties of the simulated rough surfaces. In this rough wall model, wake interactions among roughness elements are explicitly modelled using the concept of sheltering height and exponential attenuation coefficient. As a result, the parameterisation is responsive to detailed ground roughness arrangements and flow conditions, including roughness height variations, element orientation, incident flow direction, transverse displacements, etc. Model-predicted effective roughness heights, wall stress, mean velocity at the height of the roughness, and in some cases displacement height, are compared against the LES measurements from this study as well as numerical/experiment measurements from other authors. The predictions from the model are found to agree well with the measurements both in trends and in absolute values, thus extending the applicability of the analytical rough wall model to more general surfaces than those previously tested.     

Recent advances in utilizing acoustics to study surface roughness in agricultural surfaces

The evaluation of surface roughness in agricultural settings is investigated. Previous work has shown that sound propagating in a direction parallel to a smooth porous ground attenuates more rapidly than in a free space. This attenuation is due to absorption of the sound in the air filled pores in the ground. Previous work has also shown that a comparable attenuation phenomenon exists for propagation over a rough surface, albeit from different attenuation mechanisms. It is proposed that these additional attenuation mechanisms can be used to quantify the surface roughness, even on a porous surface. Attempts to model observed data with an effective impedance or reflection coefficient, in order to quantify the surface roughness, have had some success but have met with some problems for certain propagation geometries and surface configurations. Experimental data and modeling results will be presented and discussed for a variety of surfaces ranging in surface properties from impermeable to loosely packed soil and ranging in surface roughness scales from low sloped perturbations to steeply sloped wedges.     

Measurements of roughness noise

Experiments have been performed on the roughness noise produced by a two-dimensional turbulent wall jet boundary layer flowing over short fetches of sandpaper roughness. A range of rough surface sizes were studied from hydrodynamically smooth through fully rough. Velocity measurements were made to document the form of the wall jet boundary layer and the influence of the roughness upon it. Acoustic measurements showed background noise levels to be very low so that the sound produced by the rough surfaces could be clearly detected with signal to noise ratios as large as 20 dB. Even hydrodynamically smooth roughness was found to produce noise, conclusively indicating the presence of scattering as a source mechanism. Variations of the roughness noise spectra with flow speed and roughness size are found to be inconsistent with any simple parameter scaling. Boundary layer wall pressure fluctuation measurements made within the roughness fetches reveal a spectral form quite different than the roughness noise, and fluctuation levels some 50-70 dB higher. Despite these differences the wall pressure and roughness noise are found to be very simply related, at least at lower frequencies (<6 kHz). The roughness noise spectrum varies closely as the product of the wall pressure spectrum, the frequency squared, and the mean-square roughness height. This is the scaling predicted by scattering theory and implies a major simplification to the problem of roughness noise prediction for stochastic surfaces.     

Elastic contact mechanics: Percolation of the contact area and fluid squeeze-out

The dynamics of fluid flow at the interface between elastic solids with rough surfaces depends sensitively on the area of real contact, in particular close to the percolation threshold, where an irregular network of narrow flow channels prevails. In this paper, numerical simulation and experimental results for the contact between elastic solids with isotropic and anisotropic surface roughness are compared with the predictions of a theory based on the Persson contact mechanics theory and the Bruggeman effective medium theory. The theory predictions are in good agreement with the experimental and numerical simulation results and the (small) deviation can be understood as a finite-size effect. The fluid squeeze-out at the interface between elastic solids with randomly rough surfaces is studied. We present results for such high contact pressures that the area of real contact percolates, giving rise to sealed-off domains with pressurized fluid at the interface. The theoretical predictions are compared to experimental data for a simple model system (a rubber block squeezed against a flat glass plate), and for prefilled syringes, where the rubber plunger stopper is lubricated by a high-viscosity silicon oil to ensure functionality of the delivery device. For the latter system we compare the breakloose (or static) friction, as a function of the time of stationary contact, to the theory prediction.     

Dispersion and attenuation of surface shear acoustic waves with horizontal polarization on the free statistically rough surface of the hexagonal crystal

Expressions for dispersion of the phase velocity and inverse damping depth of surface acoustic waves with shear horizontal polarization are derived in an analytical form within perturbation theory using the modified mean-field method for the Z-cut hexagonal crystal with a free statically rough surface. Both two-and one-dimensionally rough surfaces are considered. The one-dimensionally rough surface is considered as a special case of the two-dimensionally rough surface. It is shown that shear surface waves with horizontal polarization cannot exist on the flat surface of the Z-cut hexagonal crystal. The derived expressions are studied analytically and numerically in the entire frequency range accessible in perturbation theory. The long-wavelength limit (most interesting from the experimental point of view) is considered, where the wavelength is much longer than the roughness correlation radius. The conditions for the existence of SH-polarized waves are determined for both roughness types. It is shown that dispersion and attenuation of SH polarized waves are qualitatively similar in character to those we considered previously for an isotropic medium.     

浅海海底界面混响平均强度特性仿真

海底粗糙界面是产生混响的主要因素之一。本文通过理论分析和数值仿真的方法,根据浅海全波动混响模型对不同海底粗糙界面所引起浅海混响平均强度特性进行研究,主要考虑Goff-Jordan谱、Gauss谱和指数谱三种不同粗糙界面条件下的海底反向散射强度和混响平均强度特性。计算结果表明:海底粗糙界面会引起海底反向散射强度的频率特性的差异,进而导致海底平均混响强度的频率特性的差异,但随入射角度的变化不大。即使界面起伏的方差和相关长度相同,不同的粗糙度谱也会引起平均混响强度的差异。     

Deduction of static surface roughness from complex excess attenuation

Data for complex excess attenuation have been used to determine the effective surface admittance and hence characteristic roughness size of a surface comprising a random distribution of semi-cylindrical rods on an acoustically hard plane. The inversion for roughness size is based on a simplified boss model. The technique is shown to be effective to within 4%, up to a threshold roughness packing density of 32%, above which the interaction between scattering elements appears to exceed that allowed by the model.     

Time-domain impedance formulation for transmission line matrix modelling of outdoor sound propagation

Outdoor sound propagation modelling has attracted considerable attention in the past and has lead to many analytical and numerical models. More recently, the increase of computational power has led to consider time-domain methods that enable to consider transient phenomena. Among these models, the transmission line matrix (TLM) method has been proposed, but the sound absorption at boundaries appears to be a somewhat underdeveloped aspect of this approach. In this paper, a specific implementation of impedance boundary condition is proposed. The method is based on the approximation of the impedance as a sum of linear systems, which allows the formulation of an equivalent impedance model in the time-domain. The proposed implementation is applied for two common impedance models of porous material. Numerical simulations have been carried out in the case of sound propagation over a flat ground with and without an impedance discontinuity, and for several values of specific airflow resistivity. TLM numerical predictions expressed in terms of excess attenuation relative to free field show a good agreement with analytical solutions.     

Effective Impedance of a Slightly Rough Surface of an Arbitrarily Anisotropic Medium

We consider a boundary-value problem for the electromagnetic field in an arbitrarily anisotropic half-space with a rough surface. In the case of a small roughness height, we derive the impedance boundary condition with a nonlocal impedance in the fourth order of the perturbation theory. In addition to the general case, we analyze the case of a perfectly conductive surface with a Gaussian roughness.     

Wave diffraction by a concave statistically rough surface

We consider a statistically rough impedance surface that is concave on average in contrast to a plane. Backscattering from such a surface is considered based on the small perturbation theory method. The diffraction problem is divided into two parts which are considered separately: the problem of scattering by small roughness (assumed to be local) and the propagation of incident and scattered fields over a smooth large-scale concave surface. In contrast to the 'two-scale' scattering model, the zero-order unperturbed wavefield is not assumed to be specularly reflected from the local tangent plane to the smooth surface, but it is a solution of a corresponding diffraction problem. Two particular cases of smooth surfaces are considered: first, the inner surface of a concave cylinder with a constant radius and finite angular pattern, and second, a compound surface that consists of a coupled half-plane and the cylindrical surface mentioned above. In a geometrical optics limit and with propagation at low grazing angles, the analytical results for a zero-order (unperturbed) field are obtained for these two cases in the form of a series over multiple specular reflected fields. It is shown that these non-local processes lead to the essential increase in the backscattering cross section in comparison with the two-scale model and tangent-plane approach.     

Acoustic insertion loss due to two dimensional periodic arrays of circular cylinders parallel to a nearby surface

The acoustical performances of regular arrays of cylindrical elements, with their axes aligned and parallel to a ground plane, have been investigated through predictions and laboratory experiments. Semi-analytical predictions based on multiple scattering theory and numerical simulations based on a boundary element formulation have been made. Measurements have been made in an anechoic chamber using arrays of (a) cylindrical acoustically-rigid scatterers (PVC pipes) and (b) thin elastic shells. Insertion loss (IL) spectra due to the arrays have been measured without and with ground planes for several receiver heights. Data and predictions have been compared. The minima in the excess attenuation spectrum i.e., attenuation maxima due to the ground alone resulting from destructive interference between direct and ground-reflected sound waves, tend to have an adverse influence on the band gaps (BG) related to a periodic array in the free field when these two effects coincide. On the other hand, the presence of rigid ground may result in an IL for an array near the ground similar to or, in the case of the first BG, greater than that resulting from a double array, equivalent to the original array plus its ground plane mirror image, in the free field.     

Law-of-the-wall in a boundary-layer over regularly distributed roughness elements

As opposed to the log-region, the roughness sublayer present above rough surfaces is still poorly understood due to the complex interaction between wakes developing behind roughness elements. To investigate the spatially averaged flow velocity in this region, a data-set has been collected from several direct numerical simulations and wind-tunnel experiments available in the literature. A generalised law-of-the-wall has been derived, applicable to a roughness sublayer present over regularly distributed roughness elements. The key roughness parameter of this new law is the effective height ?, which characterises the interaction between the roughness and the outer flow in a temporally and spatially averaged sense. A morphometric study reveals that ? is closely related to a new roughness density parameter, λ₂, that accounts for the roughness element shape and the inter-element spacing. This allows ? to be a universal parameter on roughness characterisation. The derived values of the classical roughness length z₀ of the log-law compare well with previous experimental data and geometrical model predictions. Finally, the main properties of the roughness sublayer such as its height are discussed using the geometrical and the roughness parameters proposed in the study.     

A multiscale molecular dynamics approach to contact mechanics

The friction and adhesion between elastic bodies are strongly influenced by the roughness of the surfaces in contact. Here we develop a multiscale molecular dynamics approach to contact mechanics, which can be used also when the surfaces have roughness on many different length-scales, e.g., for self affine fractal surfaces. As an illustration we consider the contact between randomly rough surfaces, and show that the contact area varies linearly with the load for small load. We also analyze the contact morphology and the pressure distribution at different magnification, both with and without adhesion. The calculations are compared with analytical contact mechanics models based on continuum mechanics.     

Acoustic attenuation of hybrid silencers

The acoustic attenuation of a single-pass, perforated concentric silencer filled with continuous strand fibers is investigated first theoretically and experimentally. The study is then extended to a specific type of hybrid silencer that consists of two single-pass perforated filling chambers combined with a Helmholtz resonator. One-dimensional analytical and three-dimensional boundary element methods (BEM) are employed for the predictions of the acoustic attenuation in the absence of mean flow. To account for the wave propagation in absorbing fiber, the complex-valued characteristic impedance and wave number are measured. The perforation impedance facing the fiber is also presented in terms of complex-valued characteristic impedance and wave number. The effects of outer chamber diameter and the fiber density are examined. Comparisons of predictions with the experiments illustrate the need for multi-dimensional analysis at higher frequencies, while the one-dimensional treatment provides a reasonable accuracy at lower frequencies, as expected. The study also shows a significant improvement in the acoustic attenuation of the silencer due to fiber absorption. Multi-dimensional BEM predictions of a hybrid silencer demonstrate that a reactive component such as a Helmholtz resonator can improve transmission loss at low frequencies and a higher duct porosity may be effective at higher frequencies.     

Reconstruction of the surface power spectrum from reflectivity data

An analytical approach is used to determine the power spectrum of the surface roughness from experimental data for the reflectivity of randomly rough surfaces. A one-dimensional, randomly rough, perfectly conducting surface that is illuminated by s-polarized light whose plane of incidence is perpendicular to the generators of the surface is considered, and the power spectrum is obtained within the framework of phase perturbation theory. Good agreement with numerically generated experimental data is obtained.     

Wave diffraction by a concave statistically rough surface

Abstract

We consider a statistically rough impedance surface that is concave on average in contrast to a plane. Backscattering from such a surface is considered based on the small perturbation theory method. The diffraction problem is divided into two parts which are considered separately: the problem of scattering by small roughness (assumed to be local) and the propagation of incident and scattered fields over a smooth large-scale concave surface. In contrast to the ‘two-scale’ scattering model, the zero-order unperturbed wavefield is not assumed to be specularly reflected from the local tangent plane to the smooth surface, but it is a solution of a corresponding diffraction problem. Two particular cases of smooth surfaces are considered: first, the inner surface of a concave cylinder with a constant radius and finite angular pattern, and second, a compound surface that consists of a coupled half-plane and the cylindrical surface mentioned above. In a geometrical optics limit and with propagation at low grazing angles, the analytical results for a zero-order (unperturbed) field are obtained for these two cases in the form of a series over multiple specular reflected fields. It is shown that these non-local processes lead to the essential increase in the backscattering cross section in comparison with the two-scale model and tangent-plane approach.     

Thermal and kinetic surface roughening studied by scanning tunneling microscopy and atomic force microscopy

Recent studies of thermal roughening on Si surfaces and kinetic roughening of some growing films, copper and tungsten, by using scanning tunneling microscopy and atomic force microscopy are reviewed. A logarithmic divergence of the surface height fluctuations of Si(111) vicinal surfaces is confirmed, in agreement with the theoretical prediction of rough surface in thermal equilibrium. For the kinetically formed rough surfaces, power law dependences of the interface width on the system size are clearly observed. Furthermore, the tungsten films show a short-range scaling regime and a long-range “smooth” regime. The roughness exponents α are compared with theoretical predictions: for the typical Cu electrode position condition (α=1/2), the exponent appears to be close to that found for local growth models, and for tungsten films (0.7～0.8), it is consistent with recent predictions for growth where surface diffusion is predominant.     

Roughness effects on the double-layer charge capacitance: the case of Helmholtz layer induced roughness attenuation

For electrical double layers, the presence of a Helmholtz layer could lead to electrode roughness attenuation. The latter is assumed of self-affine type which is characterized by the roughness amplitude w, the correlation length ξ, and the roughness exponent H. For sufficiently rough metal electrode surfaces (H1 and/or ratios w/ξ0.1) the diffuse/Helmholtz layer interface would not have the same roughness parameters with the metal electrode surface. If the latter is smoothened at lateral length scales smaller than a healing length Λ (ξ), the diffuse charge capacitance decreases and approaches values close to that of the Gouy–Chapman theory for flat electrodes.