Equivalent Surface Roughness Research Articles

On the Parameterization of Surface Roughness at Regional Scales

Abstract A parameterization for surface roughness and blending height at regional scales, under neutral atmospheric stability, is studied and tested. The analysis is based on a suite of large-eddy simulations (LES) over surfaces with varying roughness height and multiple variability scales. The LES are based on the scale-dependent Lagrangian dynamic subgrid-scale model, and the surface roughnesses at the ground are imposed using the rough-wall logarithmic law. Several patterns of roughness distribution are considered, including random tiling of patches with a wide distribution of length scales. An integral length scale, based on the one-dimensional structure function of the spatially variable roughness height, is used to define the characteristic surface variability scale, which is a critical input in many regional parameterization schemes. Properties of the simulated flow are discussed with special emphasis on the turbulence properties over patches of unequal roughness. The simulations are then used to assess a generalized form of the parameterization for the blending height and the equivalent surface roughness at regional scales that has been developed earlier for regular patterns of surface roughness (regular stripes). The results are also compared with other parameterizations proposed in the literature. Good agreement is found between the simulations and the regional-scale parameterization for the surface roughness and the blending height when this parameterization is combined with the characteristic surface variability scale proposed in this paper.

Review of Thermal Joint Resistance Models for Nonconforming Rough Surfaces

The thermal contact resistance (TCR) in a vacuum is studied. The TCR problem is divided into three different parts: geometrical, mechanical, and thermal. Each problem includes a macro- and microscale subproblem; existing theories and models for each part are reviewed. Empirical correlations for microhardness, and the equivalent (sum) rough surface approximation, are discussed. Suggested correlations for estimating the mean absolute surface slope are summarized and compared with experimental data. The most common assumptions of existing thermal analyses are summarized. As basic elements of thermal analyses, spreading resistance of a circular heat source on a half-space and flux tube are reviewed; also existing flux tube correlations are compared. More than 400 TCR data points collected by different researchers during the last 40years are grouped into two limiting cases: conforming rough and elastoconstriction. Existing TCR models are reviewed and compared with the experimental data at these two limits. It is shown that the existing theoretical models do not cover both of the above-mentioned limiting cases. This review article cites 58 references.

Parameterizing the Sea Surface Roughness

Abstract The concept of an “equivalent surface roughness” over the ocean is useful in understanding the relation between wind speed (at some height) and the net momentum flux from air to sea. The relative performance of different physics-motivated scalings for this roughness can provide valuable guidance as to which mechanisms are important under various conditions. Recently, two quite different roughness length scalings have been proposed. Taylor and Yelland presented a simple formula based on wave steepness, defined as the ratio of significant wave height to peak wavelength, to predict the surface roughness. A consequence of this formula is that roughness changes due to fetch or duration limitations are small, an order of 10%. The wave steepness formula was proposed as an alternative to the classical wave-age scaling first suggested by Kitaigorodskii and Volkov. Wave-age scaling, in contrast to steepness scaling, predicts order-of-magnitude changes in roughness associated with fetch or duration. The existence of two scalings, with different roughness predictions in certain conditions, has led to considerable confusion among certain groups. At several recent meetings, including the 2001 World Climate Research Program/Scientific Committee on Oceanic Research (WCRP/SCOR) workshop on the intercomparison and validation of ocean–atmosphere flux fields, proponents of the two scalings met with the goal of understanding the merits and limitations of each scaling. Here the results of these efforts are presented. The two sea-state scalings are tested using a composite of eight datasets representing a wide range of conditions. In conditions with a dominant wind-sea component, both scalings were found to yield improved estimates when compared with a standard bulk formulation. In general mixed sea conditions, the steepness formulation was preferred over both bulk and wave-age scalings, while for underdeveloped “young” wind sea, the wave-age formulation yields the best results. Neither sea-state model was seen to perform well in swell-dominated conditions where the steepness was small, but the steepness model did better than the wave-age model for swell-dominated conditions where the steepness exceeded a certain threshold.

Effect of Surface Waves on Air–Sea Momentum Exchange. Part I: Effect of Mature and Growing Seas

The effect of surface waves on air–sea momentum exchange over mature and growing seas is investigated by combining ocean wave models and a wave boundary layer model. The combined model estimates the wind stress by explicitly calculating the wave-induced stress. In the frequency range near the spectral peak, the NOAA/ NCEP surface wave model WAVEWATCH-III is used to estimate the spectra, while the spectra in the equilibrium range are determined by an analytical model. This approach allows for the estimation of the drag coefficient and the equivalent surface roughness for any surface wave fields. Numerical experiments are performed for constant winds from 10 to 45 m s−1 to investigate the effect of mature and growing seas on air–sea momentum exchange. For mature seas, the Charnock coefficient is estimated to be about 0.01 ∼ 0.02 and the drag coefficient increases as wind speed increases, both of which are within the range of previous observational data. With growing seas, results for winds less than 30 m s−1 show that the drag coefficient is larger for younger seas, which is consistent with earlier studies. For winds higher than 30 m s−1, however, results show a different trend; that is, very young waves yield less drag. This is because the wave-induced stress due to very young waves makes a small contribution to the total wind stress in very high wind conditions.

Combining and Contacting of Two Rough Surfaces with Asymmetric Distribution of Asperity Heights

The statistical approach of describing rough surfaces is extended to include the contact of two rough surfaces in which their distribution of asperity heights can either be symmetric or asymmetric, and the asymmetry is modeled using the normalized Weibull distribution. In considering the contact between two rough surfaces, as in most practical applications, the contact can be approximated by an equivalent rough surface in contact with a smooth plane. The roughness parameters of the equivalent surface are obtained using the spectral moment method, and its validity is verified using realistic surface roughness measurements. This paper presents a method to obtain the equivalent rough surface with a Weibull distribution of asperity heights, in which the standard deviation and skewness parameters of asperity heights of the actual contacting surfaces are preserved. The advantages of this method are demonstrated via direct comparisons with a previously proposed method as well as with exact numerical simulation of the contact parameters of several different actual surfaces from magnetic storage and MEMS applications. For practical engineering applications, where the roughness parameters of each individual surface are known, contour plots for the skewness value of the equivalent rough surface are provided for practical ranges of combinations of standard deviation ratios and skewness values. As expected when the roughness of one of the contacting surfaces dominates, the skewness is solely determined by the rougher surface.

Elastic-Plastic Finite Element Analysis for the Head-Disk Interface With Fractal Topography Description

An elastic-plastic contact analysis based on a finite element model and real surface topographies was performed to elucidate the evolution of deformation at the head-disk interface. The topographies of the head and disk surfaces were represented by an equivalent profile generated using a modified two-variable Weierstrass-Mandelbrot function, with fractal parameters determined from images of head and disk surfaces. A region of the equivalent rough surface profile was selected for analysis based on topography scale considerations and contact simulation results. The evolution of plasticity and the likelihood of cracking in the overcoat and the magnetic layer are interpreted in light of results for the subsurface von Mises equivalent stress, equivalent plastic strain, and maximum first principal stress. The finite element model provides insight into the elastic-plastic deformation behavior of the layered medium in terms of the thickness, mechanical properties, and residual stress in the carbon overcoat.

Contact of Rough Surfaces With Asymmetric Distribution of Asperity Heights

The Greenwood and Williamson (GW) statistical approach of characterizing rough surfaces is extended to include asymmetric distribution of asperity heights using the Weibull distribution. A key parameter that is used to characterize asymmetry is the skewness, and the corresponding Weibull parameters are investigated for a range of practical skewness values. The Weibull distribution is then adopted to model the asperity heights, and once normalized, is used to calculate the contact load, real area of contact and number of contacting asperities using the CEB elastic-plastic model of an equivalent rough surface in contact with a smooth plane. The effect of skewness on different levels of surface roughness, ranging from very smooth surfaces encountered in microtribological applications to rougher surfaces encountered in macrotribological applications is investigated, and also compared to the symmetric Gaussian case. Also, to allow for closed-form solution of the contact equations, simpler exponential distributions are curved-fitted to the contact side of the Weibull distribution, and the analytical results are favorably compared with the numerical results using the Weibull distribution.

Discussion on Formation Mechanism of Surface Roughness of Cold Rolled Steel Sheets.

In order to clarify the formation mechanism of surface roughness of steel sheets in cold rolling, the cold rolling experiments are made using carbon steel (SPCC) and stainless steel (SUS430) sheets with various surface roughness at the entry of rolling, and in neat lubrication of two mineral oils with different viscosities. Also, the shifting coefficient of weighted average roughness, which is called m-value, in a surface roughness equation is calculated by applying the rolling experiment data to the surface roughness equation proposed in this paper. Then, the formation mechanism of surface roughness of cold rolled steel sheets is discussed. As a result, it has been found that the m-value is larger than 1 and increases with increase of the initial equivalent surface roughness.

Studies in the nonlinear evolution of the Rayleigh–Taylor and Richtmyer–Meshkov instabilities and their role in inertial confinement fusion

Hydrodynamic instabilities, such as the Rayleigh–Taylor and Richtmyer–Meshkov instabilities, play a central role when trying to achieve net thermonuclear fusion energy via the method of inertial confinement fusion (ICF). The development of hydrodynamic instabilities on both sides of the compressed shell may cause shell breakup and ignition failure. A newly developed statistical mechanics model describing the evolution of the turbulent mixing zone from an initial random perturbation is presented. The model will be shown to compare very well both with full numerical simulations and with experiments, performed using high power laser systems, and using shock tubes. Applying the model to typical ICF implosion conditions, an estimation of the maximum allowed target, in-flight aspect ratio as a function of equivalent surface roughness, will be derived.

Static Friction and Initiation of Slip at Magnetic Head-Disk Interfaces

The apparent friction force and electric contact resistance at the magnetic head-disk interface were measured simultaneously for textured and untextured disks lubricated with perfluoropolyether films of different thicknesses. The initial stick time, representing the time between the application of a driving torque and the initiation of interfacial slip, was determined based on the initial rise of the apparent friction force and the abrupt increase of the electric contact resistance. Relatively thin lubricant films yielded very short initial stick times and low static friction coefficients. However, for a film thickness comparable to the equivalent surface roughness, relatively long initial stick times and high static friction coefficients were observed. The peak value of the apparent friction coefficient was low for thin lubricant films and increased gradually with the film thickness. The variations of the initial stick time, static friction coefficient, and peak friction coefficient with the lubricant film thickness and surface roughness are interpreted in the context of a new physical model of the lubricated interface. The model accounts for the lubricant coverage, effective shear area, saturation of interfacial cavities, limited meniscus effects, and the increase of the critical shear stress of thin liquid films due to the solid-like behavior exhibited at a state of increased molecular ordering. [S0742-4787(00)03101-5]

Non-Traditional Applications of near Infrared Spectroscopy Based on the Optical Characteristic Models for a Biological Material Having Cellular Structure

Non-destructive measurements, based on near infrared (NIR) spectroscopy, on biological material with a cellular structure like wood require a non-traditional approach. We have developed new concepts to model the optical properties of a sample having cellular structure, for the illumination conditions of the spectrometer available to us. A set of optical models, which consisted of the directional characteristics models, the light-path models and the equivalent surface roughness model was proposed to clarify the behaviour of light propagation in a wood sample. Furthermore, the mean optical path length, which was derived by incorporating the nth power cosine model of radiant intensity into the diffusion process model in consideration of the parallel beam component of incident light, was calculated. By introducing the concept of equivalent sample thickness, compatible with the mean optical path length, into the Kubelka–Munk theory, generalised input/output equations for radiation were constructed. In this non-traditional application of NIR spectroscopy, these optical concepts make it possible to analyse both the physical condition and chemical composition of a biological material with a cellular structure.

Underwater Acoustic Scattering from Arctic Ice

Comparison of the roughness-wavenumber spectrum of an underice sonar profile with that of an equivalent rough surface deduced from reverberation measurements shows levels of the latter to be excessively high. This, together with the apparent disparity between experiment and theory in the dependence of reverberation strength on grazing angle, indicates a need for improvement in the scattering model.