Small-scale Roughness Research Articles

Modelling turbulent boundary layer flow over fractal-like multiscale terrain using large-eddy simulations and analytical tools

In recent years, there has been growing interest in large-eddy simulation (LES) modelling of atmospheric boundary layers interacting with arrays of wind turbines on complex terrain. However, such terrain typically contains geometric features and roughness elements reaching down to small scales that typically cannot be resolved numerically. Thus subgrid-scale models for the unresolved features of the bottom roughness are needed for LES. Such knowledge is also required to model the effects of the ground surface 'underneath' a wind farm. Here we adapt a dynamic approach to determine subgrid-scale roughness parametrizations and apply it for the case of rough surfaces composed of cuboidal elements with broad size distributions, containing many scales. We first investigate the flow response to ground roughness of a few scales. LES with the dynamic roughness model which accounts for the drag of unresolved roughness is shown to provide resolution-independent results for the mean velocity distribution. Moreover, we develop an analytical roughness model that accounts for the sheltering effects of large-scale on small-scale roughness elements. Taking into account the shading effect, constraints from fundamental conservation laws, and assumptions of geometric self-similarity, the analytical roughness model is shown to provide analytical predictions that agree well with roughness parameters determined from LES.This article is part of the themed issue 'Wind energy in complex terrains'.

Contact angle variation on single floating spheres and its impact on the stability analysis of floating particles

The contact angle (CA) as a measure of surface hydrophobicity is of scientific and technological importance for many wetting and dewetting processes. CA hysteresis (i.e., the difference between the advancing and receding CAs) due to roughness on a flat surface has been recognized but is not considered in the stability analysis of floating particles. In this study, the CA of single floating spheres at the air-water interface was determined directly from the deformed meniscus by applying a new method recently developed by our team (Feng, D.-x. and Nguyen, A. V., 2016. A novel quantitative analysis of the local deformation of the air-water surface by a floating sphere. Colloids and Surfaces A: Physicochemical and Engineering Aspects, Vol. 504, pp. 407–413). The experiments for each of the single spheres were repeated to estimate the variation in the CA. The experimental results show a normal distribution of the CA. The CA hysteresis occurs randomly because of the dispersion of small-scale surface roughness. This random hysteresis substantially affects the stability analysis of floating spheres. The analysis also shows that the CA determined by the force balance method (valid for ideally smooth surfaces) yields higher values than those determined on the basis of the deformed meniscus around the particle. This difference is attributed to the effect of surface roughness on the CA hysteresis, which should be considered in analyses of the stability and detachment of floating particles.

小尺度表面粗糙度与介质吸收对介质折射率测量的影响

小尺度表面粗糙度与介质吸收对介质折射率测量的影响

Impingement jet array heat transfer with small-scale cylinder target surface roughness arrays

The present investigation considers special small-scale roughness patterns on impingement target surfaces to increase surface heat transfer augmentation levels of impingement jet array cooling. Utilized are three different heights of cylinder small roughness elements, which are mounted on three different test surfaces. The cylinder-shaped roughness is small-scale because diameter is 7.5 percent and maximum height is 25 percent of impingement hole diameter. Associated results are compared with spatially-averaged Nusselt number ratio distributions measured on target surfaces with triangle small roughness, or rectangle small roughness. Data are obtained for impingement jet Reynolds numbers of 900, 1500, 5000, and 11,000. Nusselt number variations for the small cylinder roughness show different trends with streamwise development and changing roughness height, compared to target plates with small rectangle roughness and small triangle roughness. In general, this is because roughness elements which contain surface shapes with sharp edges generate increased magnitudes of vorticity with length scales of the order of the roughness element diameter. Such generation is not always present in an abundant fashion with the small cylinder roughness because of the smooth contours around each roughness element periphery. Such effects are illustrated by several data sets, including Nusselt numbers associated with the small cylinder roughness with a height of 0.250D at a turbulent Reynolds number of 11,000.

The Missing Link between Terrain-Induced Potential Vorticity Banners and Banded Convection

AbstractOn 1 February 2014, the southern side of the Alps was affected by a severe snowstorm that forced authorities to issue the highest level of avalanche danger in southern parts of Austria. The northern side of the Alps was mostly dry. Nevertheless, radar imagery captured the evolution of quasi-steady convective cloud bands over the northern Alpine foreland with a remarkable length of up to 300 km. This study illuminates the processes that generated these cloud bands based on numerical simulations. The storm was associated with a deep large-scale trough that caused strong southwesterly cross-Alpine flow, orographic precipitation on the southern side, and foehnlike subsidence on the northern side of the Alps. Orographic potential vorticity (PV) banners developed at small-scale topographic features embedded in the Alps and extended downstream over the northern Alpine foreland. Convective cloud bands were aligned parallel to these PV banners. They formed in an environment of inertial instability (negative absolute vorticity) and conditional instability. Sensitivity experiments reveal that the structure and size of these cloud bands are strongly sensitive to the small-scale terrain roughness. Removing small-scale topographic features suppresses the formation of orographic vorticity banners, which in turn suppresses the development of cloud bands. These results suggest that the release of inertial instability at negative orographic vorticity banners was crucial for establishing circulations and associated uplift that triggered conditional instability. To summarize, inertial instability was most likely responsible for the banded structure and conditional instability for the convective nature of these cloud bands.

Estimating seabed structure from perturbed layer resonance fringes

Waves reflecting from layered media give rise to constructive and destructive interference fringes. These well-known fringes occur at integer multiples of half- and quarter-wavelength conditions respectively. When any of the layer boundaries are rough, the fringe pattern is perturbed. One class of observed perturbations is when the when the fringe exhibits a stair-step pattern in frequency and angle, instead of the smooth behavior predicted by theory. These perturbations can lead to difficulties for statistical inference when using the flat layer assumption. First, the physics behind the stair-step perturbations are described. Then, from the physics we show how to estimate or bound small-scale roughness parameters from the stair-step perturbations. Both simulations and measured data are employed to probe the information content of reflection data for small-scale roughness in layered media. [Research supported by the ONR Ocean Acoustics Program.]

On the Contact Area of Nominally Flat Hertzian Contacts

In a recent paper, Pastewka and Robbins (Appl Phys Lett 108:221–601, 2016) state an analytical expression for the real contact area of a Hertzian tip with small-scale roughness. We confirm that their formula predicts real contact areas quite well—with less than 10 % error. Nonetheless, the complementary contact area does not show the proper scaling to the continuum results at large loads. This shortcoming is fixed in the present work by abandoning a mean-field approximation made in the original work. Analytical results can even be made essentially perfect with a relation giving the accurate dependence of contract area on pressure for contacts between solids with nominally flat surfaces.

Effect of the Local Backscattering Pattern of the Sea Surface to the Reflected Signal of a Precision Airborne Radar Altimeter at Low Altitude

When designing a high-precision airborne radar altimeter, the approach of an analysis of the characteristics of radio signals reflected from a statistically rough sea surface based on its steady-state model becomes invalid. In the measurement of the sea surface profile, a characteristic of the reflection properties is the local backscattering pattern of the radar cross section, which depends on the time and the relative position of the low-altitude carrying vehicle from the surface. The effective width of the local backscattering pattern is determined by the statistical characteristics both of the small-scale roughness and the large-scale roughness of the surface. The location of the maximum value of the local backscattering pattern depends on the derivative of the large-scale roughness of the sea surface, i.e., the shifts in proportion to the slopes of the large-scale surface roughness. These effects must be considered when analyzing the measurement errors of a low-altitude radar altimeter.

INVESTIGATION OF SURFACE ROUGHNESS IMPACT ON MEAN WIND FLOW USING RNG k-ε MODEL

Wind flow in the urban boundary layer is influenced by both large- and small-scale surface roughness. In this study, Reynolds-averaged Navier-Stokes simulations using the renormalisation group (RNG) k-ε model were performed to study the wind flow in square arrays with small-scale roughness elements at the front and back of cubical obstacles at packing densities of 25.0% and 30.9%. The presence of small-scale roughness reduces streamwise velocity but increases turbulent kinetic energy. Moreover, small vortices are formed within the canopy because of small-scale roughness. The generated streamwise velocity profiles are similar at packing densities of 25.0% and 30.9%, but the drag coefficient is higher in the latter case. In brief, the impact of small-scale roughness on urban wind flow is considerable. The results of this study can contribute to future research on wind flow, particularly in the urban environment.

On the drag of freely falling non-spherical particles

We present a new general model for the prediction of the drag coefficient of non-spherical solid particles of regular and irregular shapes falling in gas or liquid valid for sub-critical particle Reynolds numbers (i.e. Re<3×105). Results are obtained from experimental measurements on 300 regular and irregular particles in the air and analytical solutions for ellipsoids. Depending on their size, irregular particles are accurately characterized with a 3D laser scanner or SEM micro-CT method. The experiments are carried out in settling columns with height of 0.45 to 3.60m and in a 4m-high vertical wind tunnel. In addition, 881 additional experimental data points are also considered that are compiled from the literature for particles of regular shapes falling in liquids. New correlation is based on the particle Reynolds number and two new shape descriptors defined as a function of particle flatness, elongation and diameter. New shape descriptors are easy-to-measure and can be more easily characterized than sphericity. The new correlation has an average error of ~10%, which is significantly lower than errors associated with existing correlations. Additional aspects of particle sedimentation are also investigated. First, it is found that particles falling in dense liquids, in particular at Re>1000, tend to fall with their maximum projection area perpendicular to their falling direction, whereas in gases their orientation is random. Second, effects of small-scale surface vesicularity and roughness on the drag coefficient of non-spherical particles found to be <10%. Finally, the effect of particle orientation on the drag coefficient is discussed and additional correlations are presented to predict the end members of drag coefficient due to change in the particle orientation.

Reconstruction of Concealed Objects in a Corrugated Wall With a Smoothly Varying Roughness Using the Linear Sampling Method

Two-dimensional reconstruction of concealed objects in a wall with two-scale surface roughness is presented. The linear sampling method (LSM) as a single-frequency qualitative imaging technique is exploited. The method uses the background Green's function along with the multistatic response matrix of the overall structure. The Green's function of the wall with deterministic corrugated interfaces is derived analytically here; hence, the computations are extremely efficient. The transmission and reflection matrices of the boundaries are employed along with the generalized scattering matrix theory to find the Green's function of the geometry with the source in the wall. Since the scattering matrix of each surface is only evaluated once for the whole process, the inversion algorithm becomes very suitable for real-time applications. The method is general and could be extended to any multilayered media as well. The LSM is robust against noise and clutter; therefore, the small-scale random roughness on the interfaces does not prevent the method from detection of the objects, verified by the results.

Structure of turbulent wedges created by isolated surface roughness

Isolated surface roughness in a laminar boundary layer can create a wedge of turbulence that spreads laterally into the surrounding laminar flow. Some recent studies have identified high- and low-speed streaks along the exterior of turbulent wedges. In this experiment, developing turbulent wedges are measured to observe the creation of these streaks. Naphthalene shear stress surface visualization and hotwire measurements are utilized to investigate the details of turbulent wedges created by cylinders in a laminar flat-plate boundary layer. Both the surface visualization and the hotwire measurements show high- and low-speed streaks in the wake of the cylinder that devolve into a turbulent wedge. The turbulent wedge spreading is associated with the emergence of these high- and low-speed streaks along the outside of the wedge. As the wedge evolves in the streamwise direction, these streaks persist inside of the core of the wedge, while new, lower amplitude streaks form along the outside of the wedge. Adding asymmetry to the cylinder moved the virtual origin closer to the roughness and increased the vortex shedding frequency, while adding small-scale roughness features did not strongly affect turbulent wedge development. Intermittency calculations additionally show the origin of the turbulent core inside of the wedge. The structure and spacing of the high-speed streaks along the extremities of the turbulent wedge give insight into the spreading angle of the turbulent wedge.

The sensitivity of past and near-future lunar radio experiments to ultra-high-energy cosmic rays and neutrinos

Various experiments have been conducted to search for the radio emission from ultra-high-energy (UHE) particles interacting in the lunar regolith. Although they have not yielded any detections, they have been successful in establishing upper limits on the flux of these particles. I present a review of these experiments in which I re-evaluate their sensitivity to radio pulses, accounting for effects which were neglected in the original reports, and compare them with prospective near-future experiments. In several cases, I find that past experiments were substantially less sensitive than previously believed. I apply existing analytic models to determine the resulting limits on the fluxes of UHE neutrinos and cosmic rays (CRs). In the latter case, I amend the model to accurately reflect the fraction of the primary particle energy which manifests in the resulting particle cascade, resulting in a substantial improvement in the estimated sensitivity to CRs. Although these models are in need of further refinement, in particular to incorporate the effects of small-scale lunar surface roughness, their application here indicates that a proposed experiment with the LOFAR telescope would test predictions of the neutrino flux from exotic-physics models, and an experiment with a phased-array feed on a large single-dish telescope such as the Parkes radio telescope would allow the first detection of CRs with this technique, with an expected rate of one detection per 140 h.

Separation of thermal inertia and roughness effects from Dawn/VIR measurements of Vesta surface temperatures in the vicinity of Marcia Crater

A physical model of small scale roughness has been applied to the analyses of VIR (Visible InfraRed mapping spectrometer) – measured surface temperatures in the Marcia Crater region of asteroid Vesta. Model-generated surface temperatures which include the effects of minicrater-induced flux enhancements and viewing geometry are compared with the measured surface temperature dependence on solar incidence and emission angles. Results indicate that an extremely low thermal inertia (I=<5JK−1m−2s−1/2) and high roughness (rms slopes ∼35°) characterizes almost all of the areas in and around Marcia Crater. The one clear exception is the relatively cool pitted terrain region within Marcia Crater which requires either a higher thermal inertia value (I∼10) or significantly less roughness to match the VIR data. The I∼5 finding is the lowest value found for the regolith of any airless body in the inner Solar System and is difficult to reproduce in either laboratory measurements or theoretical models of the thermal conductivity of dry granular materials in vacuum.

EVALUATION OF WAVELET DENOISING METHODS FOR SMALL-SCALE JOINT ROUGHNESS ESTIMATION USING TERRESTRIAL LASER SCANNING

Abstract. The precision of Terrestrial Laser Scanning (TLS) data depends mainly on the inherent random range error, which hinders extraction of small details from TLS measurements. New post processing algorithms have been developed that reduce or eliminate the noise and therefore enable modelling details at a smaller scale than one would traditionally expect. The aim of this research is to find the optimum denoising method such that the corrected TLS data provides a reliable estimation of small-scale rock joint roughness. Two wavelet-based denoising methods are considered, namely Discrete Wavelet Transform (DWT) and Stationary Wavelet Transform (SWT), in combination with different thresholding procedures. The question is, which technique provides a more accurate roughness estimates considering (i) wavelet transform (SWT or DWT), (ii) thresholding method (fixed-form or penalised low) and (iii) thresholding mode (soft or hard). The performance of denoising methods is tested by two analyses, namely method noise and method sensitivity to noise. The reference data are precise Advanced TOpometric Sensor (ATOS) measurements obtained on 20 × 30 cm rock joint sample, which are for the second analysis corrupted by different levels of noise. With such a controlled noise level experiments it is possible to evaluate the methods’ performance for different amounts of noise, which might be present in TLS data. Qualitative visual checks of denoised surfaces and quantitative parameters such as grid height and roughness are considered in a comparative analysis of denoising methods. Results indicate that the preferred method for realistic roughness estimation is DWT with penalised low hard thresholding.

Accounting for the effects of sastrugi in the CERES clear-sky Antarctic shortwave angular distribution models

Abstract. The Cloud and the Earth's Radiant Energy System (CERES) instruments on NASA's Terra, Aqua and Soumi NPP satellites are used to provide a long-term measurement of Earth's energy budget. To accomplish this, the radiances measured by the instruments must be inverted to fluxes by the use of a scene-type-dependent angular distribution model (ADM). For permanent snow scenes over Antarctica, shortwave (SW) ADMs are created by compositing radiance measurements over the full viewing zenith and azimuth range. However, the presence of small-scale wind blown roughness features called sastrugi cause the BRDF (bidirectional reflectance distribution function) of the snow to vary significantly based upon the solar azimuth angle and location. This can result in monthly regional biases between −12 and 7.5 Wm−2 in the inverted TOA (top-of-atmosphere) SW flux. The bias is assessed by comparing the CERES shortwave fluxes derived from nadir observations with those from all viewing zenith angles, as the sastrugi affect fluxes inverted from the oblique viewing angles more than for the nadir viewing angles. In this paper we further describe the clear-sky Antarctic ADMs from Su et al. (2015). These ADMs account for the sastrugi effect by using measurements from the Multi-Angle Imaging Spectro-Radiometer (MISR) instrument to derive statistical relationships between radiance from different viewing angles. We show here that these ADMs reduce the bias and artifacts in the CERES SW flux caused by sastrugi, both locally and Antarctic-wide. The regional monthly biases from sastrugi are reduced to between −5 and 7 Wm−2, and the monthly-mean biases over Antarctica are reduced by up to 0.64 Wm−2, a decrease of 74 %. These improved ADMs are used as part of the Edition 4 CERES SSF (Single Scanner Footprint) data.

Study of a Wind Front over the Northern South China Sea Generated by the Freshening of the North-East Monsoon

Wind fronts associated with cold-air outbreaks from the Chinese continent in the winter are often observed over the northern South China Sea and are well studied. However, wind fronts caused by another type of synoptic setting, the sudden increase or freshening of the north-east monsoon, which is caused by the merging of two anticyclonic regions over the Chinese continent, are also frequently encountered over the northern South China Sea. For the first time, such an event is investigated using multi-sensor satellite data, weather radar images, and a high-resolution atmospheric numerical model. It is shown that the wind front generated by the freshening of the north-east monsoon is quite similar to wind fronts generated by cold-air outbreaks. Furthermore, we investigate fine-scale features of the wind front that are visible on synthetic aperture radar (SAR) images through variations of the small-scale sea-surface roughness. The SAR image was acquired by the Advanced SAR of the European Envisat satellite over the South China Sea off the coast of Hong Kong and has a resolution of 150 m. It shows notches (dents) in the frontal line and also radar signatures of embedded rain cells. This (rare) SAR image, together with a quasi-simultaneously acquired weather radar image, provide excellent data with which to test the performance of the pre-operational version of the Atmospheric Integrated Rapid-cycle (AIR) forecast model system of the Hong Kong Observatory with respect to modelling rain cells at frontal boundaries. The calculations using a horizontal resolution with 3-km resolution show that the model reproduces quite well the position of the notches where rain cells are generated. The model shows further that at the position of the notches the vorticity of the airflow is increased leading to the uplift of warmer, moister air from the sea-surface to higher levels. With respect to the 10-km resolution model, the comparison of model data with the near-surface wind field derived from the SAR image shows that the AIR model overestimates the wind speed in the lee of the coastal mountains east of Hong Kong, probably due to the incorrect inclusion of the coastal topography.

Reflectance and transmittance model for multilayer optical coatings with roughness at oblique incidence

Surface roughness is really important to the ultra-low loss of multilayer optical coatings. Reflectance and transmittance model for multilayer optical coatings with surface roughness has been established at normal incidence by A. V. Tikhonravov et al. in 2003. However, under the condition of oblique incidence, no further model which is based on the model of Tikhonravov has ever been reported. In this paper, an approximate reflectance and transmittance model is established for the thin film system with roughness at oblique incidence by analogy and usage of the concept of equivalent refractive index. The small-scale roughness model's effectiveness has been theoretically demonstrated according to the effective medium theory. However, the large-scale roughness model's effectiveness needs other methods to be proved, as the scattering effect of different scale roughness is different. This model might play a significant role to research the scattering loss of oblique incident thin film systems, such as mirrors in ring lasers, deep ultraviolet lasers and interferometers with ultra long cavity length.

Comparison of measured acoustic reflection fluctuations and estimates based on roughness

The extent to which the roughness of the seabed can account for the acoustic reflection fluctuations is investigated. The roughness of selected areas of the seabed off Panama City, FL, was measured with a laser profiler, as part of Target and Reverberation EXperiment of 2013 (TREX13). The site may be characterized as having small-scale roughness due to bioturbation overlying larger sand ripples due to current activity. It was largely composed of sand with shell hash crossed by ribbons of softer sediment at regular intervals. Simultaneous with the roughness measurement, the seabed reflection was measured with a wide beam echo sounder centered about 10 kHz. Both instruments were deployed on a remotely operated vehicle (ROV) at a height of approximately 2 m above the seabed. Significant fluctuations in the acoustic reflection were observed. By modeling the acoustic scattering due to the roughness, the extent to which the roughness can account for the acoustic fluctuations will be investigated. [Work supported by the Office of Naval Research, Ocean Acoustics Program.]

A joint shear model incorporating small-scale and large-scale irregularities

The strength and dilation of rock joints in the field cannot be evaluated solely on the basis of parameters scaled from laboratory data, but also requires assessment of large-scale irregularities not present in the laboratory sample. A constitutive model for rock joints has been developed that considers the dilation and strength along both small-scale joint roughness scaled from laboratory data, and large-scale waviness determined from geologic observations. The model’s performance is illustrated by providing its correlation with experimental results taken from literature. The degradation in dilation and post-peak strength along small-scale irregularities is modeled using the plastic work done in shear, and the degradation along large-scale irregularities is modeled using a sinusoidal function. A dimensionless product of plastic work, rock strength, and wavelength of irregularities has been developed which fits the direct shear test results. An approach to scaling shear strength and shear displacement from laboratory to field-scale is also suggested.