Ripple Wavelength Research Articles

Bedform generation beneath shoaling nonlinear internal waves on a mild slope

Subaqueous sand waves have been observed where nonlinear internal waves (NLIWs) shoal on continental margins. To investigate their generation mechanisms, we propagated periodic NLIWs of depression to shoal upon a sloping bed in a laboratory flume. Following fission of the incident waves, ripple-type bedforms were observed between the point of incipient suspension and interaction point (where the quiescent pycnocline intersects the sediment bed). The largest ripples were centered on the bolus birth point, where the NLIWs of elevation, generated by fission, transform into boluses and maximum near-bed velocities occurred. The ripple height and wavelength were consistent with fluvial scaling. In two experiments, where bedload transport was not predicted, the observations showed resuspension to influence ripple generation. Net upslope sediment movement was observed beyond the turning point.

Field observations on the characteristics of sand ripples on tidal flats

Ripples on tidal flats significantly influence bedform roughness and near-bed turbulence, yet their dynamics in sandy and muddy environments remain incompletely understood. While laboratory studies have elucidated the effects of mud content and extracellular polymeric substances (EPSs) on ripple formation and stability, the interactions between ripple characteristics, EPS, and mud content in natural settings are more complex and not thoroughly explored. To address this gap, we conducted field studies on sand ripples at the central Jiangsu coast, China, using high-resolution drone photogrammetry to accurately measure ripple dimensions. We performed bedload sampling at both ripple crests and troughs to analyze median grain size, mud content, and EPS concentrations. Our results show that the investigated ripple wavelengths range from 34 to 46 mm, and heights vary between 2.7 and 5.3 mm. Ripples developed near tidal creeks show pronounced asymmetry. Significantly, EPS concentrations are markedly higher at the ripple crests than at the troughs, and it follows a power-law relationship with the median grain size. These results highlight the complex intricate relationship between the ripple morphology, environmental forcing conditions, and EPS content. Our findings enrich the understanding of ripple development and the factors influencing current-dominated ripples in natural environments. This research also adds to the better prediction of the bedform roughness and quantification of the near bed sediment transport.

Investigating ripple pattern formation and damage profiles in Si and Ge induced by 100 keV Ar+ ion beam: a comparative study.

Desired modifications of surfaces at the nanoscale may be achieved using energetic ion beams. In the present work, a complete study of self-assembled ripple pattern fabrication on Si and Ge by 100 keV Ar+ ion beam bombardment is discussed. The irradiation was performed in the ion fluence range of ≈3 × 1017 to 9 × 1017 ions/cm2 and at an incident angle of θ ≈ 60° with respect to the surface normal. The investigation focuses on topographical studies of pattern formation using atomic force microscopy, and induced damage profiles inside Si and Ge by Rutherford backscattering spectrometry and transmission electron microscopy. The ripple wavelength was found to scale with ion fluence, and energetic ions created more defects inside Si as compared to that of Ge. Although earlier reports suggested that Ge is resistant to structural changes upon Ar+ ion irradiation, in the present case, a ripple pattern is observed on both Si and Ge. The irradiated Si and Ge targets clearly show visible damage peaks between channel numbers (1000-1100) for Si and (1500-1600) for Ge. The clustering of defects leads to a subsequent increase of the damage peak in irradiated samples (for an ion fluence of ≈9 × 1017 ions/cm2) compared to that in unirradiated samples.

On icicle ripples

Natural icicles have an overall conical shape modulated by surface ripples. It has been noted from many observations of icicles formed in nature and in the laboratory that the wavelength of the ripples has a very narrow spectrum between about 8 and 12 mm and that, as time evolves, the phase of the ripples migrates upwards. In this pedagogical review, I explore some of the physical mechanisms that can cause and mediate the formation and migration of ripples on icicles using simple mathematical models. To keep the mathematics more straightforward and transparent, I confine attention to two dimensions. A key physical parameter is the surface tension between the film of water that coats an icicle and the air that surrounds it, which causes a phase shift between the film–air interface and the ice–film interface. I show that the wavelength of ripples is dominantly proportional to the cube root of the square of the gravity-capillary length times the thickness of the water film. At high film-flow rates, advection-dominated heat transfer coupled with the interfacial phase shift becomes the dominant driver of instability. Gibbs–Thomson undercooling provides an unexpectedly large stabilisation of small wavelengths at these large flow rates, sufficient to maintain wavelength selection at millimetre scales.

Mid‐Air Collisions Control the Wavelength of Aeolian Sand Ripples

AbstractThe wavelength of aeolian sand ripples increases with wind velocity, but the cause for this increase remained unclear until now. Using numerical simulations, we find that the relationship between the wind strength and the initial wavelength disappears without mid‐air collisions, which means that mid‐air collisions crucially contribute to the initial wavelength of ripples. As wind strength increases, the average hop length of non‐colliding particles decreases. Affected by the bed surface topography and the non‐uniform mid‐air colliding probability along the wavy surface, non‐colliding particles cause a surface modulated erosion/deposition flux. The first order contribution of the flux fluctuation destabilizes the original bed surface and has a wind‐dependent phase shift with respect to the surface profile. This phase shift leads to an initial wavelength that increases with wind velocity. Based on these findings we derive the scaling law for the initial wavelength of aeolian sand ripples, which agrees well with experimental results. A weak non‐linear relationship between ripple wavelength and wind velocity has been found, especially for large wind strengths.

Wavelength determination of ion-induced ripples

A novel approach for analysis of ion-induced ripples on a surface is presented. In a completely different model from what has been previously presented, thin stressed amorphous layer is considered to have elastic properties. Ion-induced compressive stress is anticipated to have both horizontal and vertical components. Ripples are supposed to form due to bending process of thin stressed layer under horizontal component of compressive stress. A relationship for ripple wavelengths is provided by minimizing bending and compression energy of thin stressed amorphous layer. The consistency of evaluated wavelength with experimental findings is explored.

Large-scale physical experimental study on the evolution of 3D bedform by irregular waves

A large-scale physical experiment was conducted to analyze the morphological seabed evolution in a large-wave flume at the Tianjin Research Institute for Water and Transport Engineering. The morphologies of the bedforms, ranging from two to three dimensions, were analyzed as wave mobility (represented by ѱw) increased. The sand-ripple morphology underwent four stages: straight, staggered, lunate and flat. Furthermore, the three-dimensional (3D) features and flat patterns were enhanced with increasing ѱw. The seabed ripple was processed using a wavelet transform and filter method to eliminate the effects of noise and dunes. The ripple wavelength followed the gamma and lognormal distributions for irregular waves, whereas the distribution of ripple height transitioned from normal to exponential with increasing ѱw. Furthermore, to predict the ripple-geometry statistics more accurately, a modified predictor was developed based on the acquired large-scale experimental data. The findings of this study can aid the development of innovative methods for evaluating bedform morphologies and statistical parameters.

Bragg Scattering of Surface Gravity Waves by a Submerged Composite Wavy Porous Plate

Abstract Surface gravity wave interaction of composite wavy porous plate is studied by developing a numerical model using the boundary element method in the context of two-dimensional linear potential theory. Bragg scattering phenomenon is studied by considering the linearized pressure drop condition known as Darcy’s law passing through the porous structure. Numerical results are obtained through the boundary element method for the special limiting case of the existing previous literature to authenticate the accuracy of the numerical solution. The influence of wave and structural design parameters such as the number of ripple wavelengths of the wavy plate, relative plate length, structural porosities, and relative submergence depth on hydrodynamics properties such as reflection, transmission, horizontal wave load, and vertical wave coefficients are discussed. The study results of composite wavy porous plate indicate improved hydrodynamic performance as compared to the horizontal porous plate and wavy porous plate. This study is significant for practical applications in coastal engineering environments.

Surface gravity wave interaction with a submerged tunnel in the presence of a submerged wavy porous plate

The present study deals with the surface gravity wave interaction of a submerged composite wavy porous plate in the presence of a tunnel placed at a finite distance under the assumption of small amplitude theory and a two-dimensional framework. To solve the boundary value problem, a numerical method using the multi-domain boundary element method (MDBEM) is implemented. Hydrodynamic characteristics of interest such as reflection coefficient and transmission coefficient are computed and studied for a wide range of dimensionless wavenumber and relative plate lengths. Various parametric studies are conducted to emphasize the effect of structural parameters like the number of relative ripple wavelengths, relative ripple amplitude, and relative submergence depth. Dimensionless wave force coefficients acting on the plate and the tunnel are calculated and investigated. The study reveals that the presence of composite wavy porous plate has a significant effect in the mitigation of wave-exerted force on the tunnel. Optimized results are shown for the efficient design of coupled breakwater and tunnel models, which can be used beneficially to protect against the severity of wave action in similar applications of ocean engineering in marine environments.

PROBABILISTIC PREDICTIONS OF EQUILIBRIUM RIPPLE GEOMETRY FOR TIME-DEPENDENT SEAFLOOR MODELING

We present a new equilibrium ripple predictor using a machine learning approach that outputs a probability distribution of wave-generated equilibrium wavelengths and statistics including an estimate of ripple height, the most probable ripple wavelength, and sediment and flow parameterizations. The Bayesian Optimal Model System (BOMS) is an ensemble machine learning system that combines two machine learning algorithms and two deterministic empirical ripple predictors with a Bayesian meta-learner to produce probabilistic wave-generated equilibrium ripple wavelength estimates in sandy locations.

Surface gravity wave interaction with a floating dock in the presence of a submerged composite wavy porous plate

A numerical model based on the multi-domain boundary element method is adopted to study surface gravity wave interaction with a finite floating dock in the presence of a submerged composite wavy porous plate in the two-dimensional Cartesian coordinate system. Physical parameters of interest such as reflection coefficient, transmission coefficient, dissipation coefficient, horizontal and vertical wave force coefficients of the wavy plate, vertical force and moment coefficients about the centre of the dock are calculated. The influence of structural parameters such as the number of ripple wavelengths, relative ripple amplitude, structural porosity and relative submergence depth of wavy plate, relative space between the plate and dock are computed and studied. An insight into the comparison of various types of plates such as flat plate, wavy plate and composite wavy plate is also presented. The study reveals that the mitigation of wave force on the dock is significant due to a wavy porous plate. Besides, the study exhibits that placing the wavy porous plate at a finite distance from the floating dock has a significant role in dissipating incident wave energy compared to that placing the submerged plate below the dock. Bragg reflection occurs due to the presence of the submerged wavy plate, which diminishes with an increase in structural porosity and depth of submergence of the wavy plate.

Study the behaviour of transient elastohydrodynamic lubrication contact at motion start-up in the presence of surface roughness

PurposeThis study aims to present a numerical solution for the analysis of the influence of surface roughness as presented by a sinusoidal ripple of different amplitude and wavelength on the performance of transient elastohydrodynamic lubrication at motion start-up under different operational parameters of entraining speed and load as well as different acceleration rates.Design/methodology/approachA statistical asperity micro-contact model represented by a sinusoidal ripple expressed by two parameters (wavelength and undeformed amplitude) is considered. The ball equation of motion is used to calculate the force on the ball as it starts to move. The time-dependent Reynolds equation is solved together with surface deformation and statistical asperity models using the Newton–Raphson technique with the Gauss–Seidel iteration method.FindingsThe behaviour of the film thickness was found to be strongly influenced by the acceleration rate for different ripple amplitude and wavelength parameters. The effect of increasing the final entraining speed will eventually lead to rapid film thickness build-up and increase the film thickness jump at the moment of motion start-up. The effect of increasing applied load is to reduce the deviation of the minimum film thickness jump at the start-up of motion, making its value approximately equal to the steady-state value over the entire run-time period.Originality/valueInfluence of surface roughness for various wavelength and undeformed amplitude on the performance of transient elastohydrodynamic lubrication at motion start-up is presented at different acceleration rates as well as for different operating parameters of entraining speed and load. Ball equation of motion is used to calculate the force on the ball as it starts to move.

Constraining the mechanisms of aeolian bedform formation on Mars through a global morphometric survey

Aeolian processes on Mars form a distinct class of meter-scale ripples, whose mechanisms of formation are debated. We present a global morphometric survey of Martian bedforms, adding relevant observational constraints to the ongoing debate. We compare our results with previous surveys, highlighting inconsistencies in data used in previous studies, namely for the bedforms located in the Tharsis highlands.We show that the bedforms located in the Tharsis region form a distinct group, not akin to the large dark-toned ripples which cover dune fields elsewhere on the planet. Tharsis bedforms form unique patterns, present distinct thermophysical characteristics and have higher albedos, suggesting they are formed and/or covered by finer materials.The relation between wavelength and atmospheric density derived from the new data is consistent with the predictions of a wind-drag mechanism, favoring the model that uses a saltation saturation length. Regardless of the mechanism that limits the size of bedforms, these results confirm the existence of a robust relationship between the wavelength of large ripples and atmospheric density (ripples' spacing increases with decreasing atmospheric density). This provides further support to the interpretation of paleoatmospheric conditions on Mars through the analysis of its aeolian sedimentary record.

Comparative wettability study of bulk and thin film of polytetrafluoroethylene after low energy ion irradiation

A comparative wettability study was carried out on bulk polytetrafluoroethylene (PTFE) and physical vapor deposited PTFE-like thin films using low-energy Argon ion beam irradiation. Both bulk PTFE and PTFE-like thin film surfaces were irradiated with the beam energy of 300 and 800 eV for 5 min. The angle of incidence of the ion beam was varied from 0° to 70° with respect to the surface normal. Ion beam irradiation produced the tilted sharp-edged microstructures on PTFE sheets elongated in the direction of the beam. After irradiation with 800 eV at 20°, the bulk PTFE sheet became superhydrophobic, the water contact angle increased from 105° to 157°, and again decreased to 132° after irradiation at 70° Whereas nanoripple-like patterns formed on PTFE-like thin films after ion beam irradiation. The maximum wavelength of such ripples was found to be 212 nm for an 800 eV irradiated surface at an angle of 50° Beyond this angle, a clear transition from ripple to facet-like patterns was observed. The contact angles of the irradiated thin film were found to be varying from 105° to 112° up to 30° irradiation and again decreased to 83° after irradiation at 70° PTFE thin film showed strong anisotropic wettability behavior with a variation of 12° of contact angle values perpendicular to the ion beam direction, and water droplets did not roll off from the surface like in the case of bulk PTFE. X-ray photoelectron spectroscopy revealed that the bulk PTFE had C−C, and CF2 bonding on the surface, whereas PTFE thin films formed additional CF, CF‒CFn, and CF3 bonding, which was not observed in the bulk PTFE. After irradiation, additional CF-CFn and CF3 bonding in bulk PTFE were observed. However, in the case of thin films, ion irradiation causes severe chain scission, crosslinking, and defluorination of the surface.

Selection of vortex ripple dimensions in sinusoidal oscillatory flows. Part 1. Ripple dimensions and fluid kinematics

Subaqueous vortex ripples in equilibrium are characterized by their unique geometry and dimensions. Motivated by the recent direct numerical simulation study of oscillatory turbulent flow over a wavy bottom by Önder & Yuan (J. Fluid Mech., vol. 858, 2019, pp. 264–314), the objective of this study is to further investigate the fluid dynamical controls that determine the distinctive equilibrium dimensions of vortex ripples. We use direct numerical simulations to investigate the differences in flow kinetics between sinusoidal oscillatory flow over equilibrium and out-of-equilibrium vortex ripples. In comparison with the equilibrium case, the spanwise coherent vortices, the averaged bottom shear stress on overlying flow and the shear stress distribution on the ripple surface are identified as the key fluid dynamical controls on equilibrium dimensions. Based on these controls, we propose mechanisms in the selection of vortex ripple dimensions. We observe that the flow adjusts in such a way that the interaction between overlying flow and vortex ripples tends to generate the strongest coherent vortices while the ripple surface (or overlying flow) experiences the smallest shear stress averaged over ripple wavelength during the selection process. Through a triple decomposition of the flow, the component of the ripple-induced fluctuation is found to dictate these fluid dynamical controls, which implies that this component plays an important role in the evolution of vortex ripples.

Towards ordered Si surface nanostructuring: role of an intermittent ion beam irradiation approach

The dynamical characteristics of surface nanopatterning using low-energy ion beams remains a central theme within ion beam sputtering. Most previous studies have focused on nanostructure evolution by bombarding surfaces using a continuous ion beam. Here, we study the effect of sputtering from an intermittent ion beam on nanopatterning of a Si surface, using a 900 eV or (mostly) 500 eV Ar+ ion beam at an incident angle of 67°, up to a total fluence of 10 × 1019 ions cm−2. Nanoripples are predominantly found on the irradiated surfaces, alongside a hierarchical triangular morphology at the lower energy condition. Ripple ordering is superior for intermediate values of the sputtering interval used in the intermittent sputtering approach. The area of the triangular structures also depends on the intermittent sputtering time intervals. At larger length scales than the ripple wavelength or the triangular structures, all surfaces display strong height fluctuations with a well-defined roughness exponent. Our results can be rationalized via known properties of the nonlinear regime of evolution for surfaces that become amorphous under irradiation and relax stress via ion-induced viscous flow, as borne out from numerical simulations of a continuum model previously proven to provide a significant description of the present class of experiments.

Ripple pattern formation on silicon carbide surfaces by low-energy ion-beam erosion

A versatile experimental facility air insulated high current medium energy 200 kV Ion Accelerator, with the terminal voltage in the range of 30-200 kV has been running successfully at Ion Beam Centre, KUK for carry out multifarious experiments in material science and surface physics. This system offers single charge state, switching magnet with five exit ports and large area irradiation/implantation using hollow cathode ion source. Ion beam induced structures on the surfaces of semiconductors have potential applications in photonics, magnetic devices, photovoltaics, and surface-wetting tailoring etc. In this regard, silicon carbide (SiC) is a fascinating wide-band gap semiconductor for high-temperature, high-power and high-frequency applications. In this work, fabrication of ripple patterns is carried out on the SiC surfaces using 80 keV Ar+ ion beam for different fluences at oblique incidence of 500. AFM study demonstrates that ripple wavelength and amplitude, ordering and homogeneity of these patterns vary linearly with argon ion fluence. The formation of such surface structures is attributed to the preferential sputtering of silicon in comparison to carbon. The evolution of high degrees of order is explained with the help of existing formalisms of coupling between surface topography and preferential sputtering.

A distinct ripple-formation regime on Mars revealed by the morphometrics of barchan dunes

Sand mobilized by wind forms decimeter-scale impact ripples and decameter-scale or larger dunes on Earth and Mars. In addition to those two bedform scales, orbital and in situ images revealed a third distinct class of larger meter-scale ripples on Mars. Since their discovery, two main hypotheses have been proposed to explain the formation of large martian ripples—that they originate from the growth in wavelength and height of decimeter-scale ripples or that they arise from the same hydrodynamic instability as windblown dunes or subaqueous bedforms instead. Here we provide evidence that large martian ripples form from the same hydrodynamic instability as windblown dunes and subaqueous ripples. Using an artificial neural network, we characterize the morphometrics of over a million isolated barchan dunes on Mars and analyze how their size and shape vary across Mars’ surface. We find that the size of Mars’ smallest dunes decreases with increasing atmospheric density with a power-law exponent predicted by hydrodynamic theory, similarly to meter-size ripples, tightly bounding a forbidden range in bedform sizes. Our results provide key evidence for a unifying model for the formation of subaqueous and windblown bedforms on planetary surfaces, offering a new quantitative tool to decipher Mars’ atmospheric evolution.

Numerical Simulations of Large Martian Impact Ripples

Ripples made from unimodal fine sands can grow much larger on Mars than on Earth, reaching wavelengths of 1–3 m and heights exceeding 1 dm. Smaller decimeter-wavelength ripples can be superimposed on them. Classification and origins of these bedforms have been debated. They have been interpreted as analogous to subaqueous ripples on Earth, or as aeolian impact ripples with a range of grain sizes that reach large maximum sizes on Mars. This study uses a mathematical model to evaluate the formation of large Martian ripples as aeolian impact ripples to further investigate this hypothesis. The model parameters were computed using COMSALT for 100 µm grains under shear velocity of 0.65 m/s, which is a reasonable shear velocity for sand transport on Mars according to recent estimations of threshold Martian winds. The numerical experiments utilize a large grid 8 m long. Experiments also evaluate the development of secondary small ripples between the large ripples from random perturbations. The numerical simulations show the evolution of ripple wavelength and height. According to the results, the time scale for the formation of the large ripples is about 2–3 years, which is a much longer time scale compared to terrestrial impact ripples. Small secondary ripples develop only if the space between the large ripples is sufficiently large.

A machine learning approach to predicting equilibrium ripple wavelength

Sand ripples are geomorphic features on the seafloor that affect bottom boundary layer dynamics including wave attenuation and sediment transport. We present a new equilibrium ripple predictor using a machine learning approach that outputs a probability distribution of wave-generated equilibrium wavelengths and statistics including an estimate of ripple height, the most probable ripple wavelength, and sediment and flow parameterizations. The Bayesian Optimal Model System (BOMS) is an ensemble machine learning system that combines two machine learning algorithms and two deterministic empirical ripple predictors with a Bayesian meta-learner to produce probabilistic wave-generated equilibrium ripple wavelength estimates in sandy locations. A ten-fold cross validation of BOMS resulted in an adjusted R-squared value of 0.93 and an average root mean square error (RMSE) of 8.0 cm. During both cross validation and testing on three unique field datasets, BOMS provided more accurate wavelength predictions than each individual base model and other common ripple predictors.