Ripple Predictors Research Articles

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.

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.

Eulerian Two‐Phase Model Reveals the Importance of Wave Period in Ripple Evolution and Equilibrium Geometry

AbstractThe evolution of ripple geometries and their equilibrium states due to different wave forcing parameters are investigated by a Reynolds‐averaged two‐phase model, SedFoam, in a two‐dimensional domain. Modeled ripple geometries, for a given uniform grain diameter, show a good agreement with ripple predictors that include the wave period effect explicitly, in addition to the wave orbital excursion length (or wave orbital velocity amplitude). Furthermore, using a series of numerical experiments, the ripple's response to a step‐change in the wave forcing is studied. The model is capable of simulating “splitting,” “sliding,” “merging,” and “protruding” as the ripples evolve to a new equilibrium state. The model can also simulate the transition to sheet flow in energetic wave conditions and ripple reformation from a nearly flat bed condition. Simulation results reveal that the equilibrium state is such that the “primary” vortices reach half of the ripple length. Furthermore, an analysis of the suspended load and near‐bed load ratio in the equilibrium state indicates that in the orbital ripple regime, the near‐bed load is dominant while the suspended load is conducive to the ripple decaying regime (suborbital ripples) and sheet flow condition.

THE FLOW OVER ASYMMETRICAL RIPPLES: EXPERIMENTAL INVESTIGATION ON THE MORPHODYNAMIC BEHAVIOR

This paper reports on an experimental campaign focused on the generation and evolution of small scale bedforms over a sloping sandy beach. The wave propagation over a sloping bed triggers a flow asymmetry that reflects on the bedform characteristics. Morphodynamic analyses on ripple evolution and migration led to observe that at the equilibrium the ripples have larger offshore flanks and are leant toward the beach. However migration velocity may be onshore or offshore directed. The equilibrium ripple characteristics seem to be well described by Nielsen (1981) ripple predictor.

Characterizing and hindcasting ripple bedform dynamics: Field test of non-equilibrium models utilizing a fingerprint algorithm

Ripple bedform response to near bed forcing has been found to be asynchronous with rapidly changing hydrodynamic conditions. Recent models have attempted to account for this time variance through the introduction of a time offset between hydrodynamic forcing and seabed response with varying success. While focusing on temporal ripple evolution, spatial ripple variation has been partly neglected. With the fingerprint algorithm ripple bedform parameterization technique, spatial variation can be quickly and precisely characterized, and as such, this method is particularly useful for evaluation of ripple model spatio-temporal validity. Using time-series hydrodynamic data and synoptic acoustic imagery collected at an inner continental shelf site, this study compares an adapted time-varying ripple geometric model to observed field observations in light of the fingerprint algorithm results. Multiple equilibrium ripple predictors are tested within the time-varying model, with the algorithm results serving as the baseline geometric values. Results indicate that ripple bedforms, in the presence of rapidly changing high-energy conditions, reorganize at a slower rate than predicted by the models. Relict ripples were found to be near peak-forcing wavelengths after rapidly decaying storm events, and still present after months of sub-critical flow conditions.

Predicting wave‐induced ripple equilibrium geometry

A comprehensive database of existing (since 1954) field and laboratory measurements of ripple geometry is compiled and combined with newly collected field data to examine the performance of ripple equilibrium predictors. Reanalysis of this enlarged ripple geometry data set reveals that ripples formed from monochromatic waves scale differently than ripples formed from random waves for many existing ripple predictors. Our analysis indicates that ripple wavelengths from the two data sets collapse into a single scaling when the semiorbital excursion and sediment grain diameter are used as normalizing factors. Ripple steepness remains relatively constant for both regular and irregular wave conditions, and it only slightly increases for shorter ripple wavelengths. These findings allowed for the development of a new equilibrium ripple predictor suitable for application in a wide range of wave and sediment conditions.

Comparison of measurements and models of bed stress, bedforms and suspended sediments under combined currents and waves

This study presents an analysis of data collected in an embayment off a sandy beach protected by shore parallel breakwaters. Observations were carried out over a forty day period including spring and neap tidal cycles and low and high wave activity. Measurements were collected on the waves, currents, bedforms and suspended sediments and these were used to derive estimates of the bed shear-stresses, ripple dimensions, reference concentrations and suspended sediment profiles. The aim of the present study was to use the measurements to assess commonly employed empirical formulations applied to sediment modelling in the coastal marine environment. Assessments are made of four ripple predictors, two formulations of reference concentration and power law and exponential suspended sediment shape functions. In some cases predicted parameters are well represented during low wave conditions, whilst other parameters are better predicted under high wave events. The outcome from the work is an evaluation of the predictive capability of the selected empirical formulae at the sandy location and discussions on the comparison between the observations and predictions.

Ripple morphology under oscillatory flow: 1. Prediction

Recent laboratory and field experiments have shown the inability of existing oscillatory flow ripple predictors to accurately predict both ripple size and ripple planform geometry. However, at this time, only partial adaptations of these predictors have been proposed to account for the observed discrepancies with new experimental data. The present work starts by presenting a comprehensive data set compiled from 27 literature studies and our own experimental data, which are presented in a companion paper. Dimensional analysis is used both to clarify the importance of the different variables involved in the development of ripples and to generate the basic dimensionless framework for the study of ripple morphology under oscillatory flow. Several ripple size and planform geometry predictors are contrasted against the compiled data set. Afterward, a new ripple wavelength and height predictor and a new planform geometry predictor are proposed, which overcome several of the limitations found in the earlier formulations. The new predictors emphasize the existence of local and global sediment transport mechanisms over a ripple bed, each of them acting at different scales. In particular, sediment size is found to have an important effect on the size and geometry of bed forms that can be generated by oscillatory flows.

Relaxation time effects of wave ripples on tidal beaches

Seabed roughness due to wave ripples is a key factor in controlling sediment transport processes in the nearshore zone. Roughness is commonly considered a function of the ripple geometry, which in turn, can be predicted from sediment and hydrodynamic parameters. Existing ripple predictors consider the bed morphology to be in equilibrium with the hydrodynamics, whereas recent laboratory measurements show that the time scale for ripple development is of the order of tens of minutes to hours. Here we show that wave ripples on tidal beaches are significantly affected by relaxation time effects, with ripple height and length progressively increasing during the rising tide and remaining constant during the falling tide. Moreover, we examine the ripples in the context of existing empirical models and suggest how the temporal evolution over a tidal cycle may be predicted.

SEDTRANS96: the upgraded and better calibrated sediment-transport model for continental shelves

The sediment transport model SEDTRANS has been significantly upgraded based on new advances in both cohesive and non-cohesive sediment transport studies. For given input data of wave, current, and seabed conditions, the model applies the combined wave–current bottom boundary layer theories to derive the near-bed velocity profile and bed shear stresses, and then calculates sediment transport for currents only or combined waves and currents over either cohesive or non-cohesive sediments. Critical shear stresses for various sediment transport modes tested for combined waves and currents are adopted in SEDTRANS96. An explicit combined-flow ripple predictor is included in the model to provide time-dependent bed roughness prediction. SEDTRANS96 also predicts the vertical profiles of velocity and suspended sediment concentration and their product is integrated through depth to derive the suspended-load transport rate. More rigorous calibration of the model using measured sediment transport rates over fine and medium sands shows that the difference between the predicted and measured transport rates has been reduced from more than one order of magnitude to less than a factor of five. The proposed new cohesive sediment algorithm separates cohesive sediment transport into depositional, stable and erosional states. The applied shear stress, erosion/deposition time duration and the down-core profile of the critical shear stress for erosion are numerically integrated to predict the final erosion or deposition rate, suspension concentration and transport rate for cohesive sediment.

Predicting ripple geometry and bed roughness under combined waves and currents in a continental shelf environment

Waves, current and seabed response data collected by an instrumented tripod deployed on the Scotian Shelf during the winter of 1993/94 are analyzed to derive a ripple predictor for combined flows and to evaluate the applicability of existing ripple- and bedload-roughness algorithms under combined waves and current. Wave-dominant ripples developed during storms were generally higher and steeper than current-dominant ones. The ratio of the skin-friction wave shear velocity to that of the steady current, u ∗ ws /u ∗ cs , can be used to define the various types of ripples under combined flows. By comparing the measured ripple geometry and the predictions by existing ripple predictors, the wave-ripple predictors of Nielsen (1981), and Grant and Madsen (1982) are found to over-predict ripple height and ripple roughness for combined flows under the conditions of the present study. These methods also neglect the enhancement of shear stress at the ripple crest. A new empirical ripple predictor is proposed and it uses the combined shear velocity and the ratio u ∗ ws /u ∗ cs to predict the heights and wavelengths of ripples and their dynamic transition under combined flows. The effect of enhanced shear velocity at the ripple crest is also incorporated for the prediction of ripples in the weaktransport range. A simplified logarithmic profile method and the values of the bedload shear velocity due to the combined grain size and bedload roughnesses are used to evaluate the applicability of various ripple- and bedload-roughness height algorithms under combined flows. While the ripple roughness height algorithm of Grant and Madsen (1982) is found to give good predictions of the total current shear velocity u ∗ c and apparent bottom roughness z 0c, the algorithm of Nielsen (1992), tends to underpredict both parameters. The bedload roughness algorithms of Nielsen (1992) and Li et al. (1997) are both found to give reasonable predictions under combined flows. The total bed roughness height under combined flows can be expressed as k b=2.5 D+27.7 η 2/ λ+170 D( θ cws− θ cr) 0.5.

Predicting ripple roughness and sand resuspension under combined flows in a shoreface environment

Ripple measurements and flow and sediment dynamical data obtained from the shoreface of the Middle Atlantic Bight using instrumented tripods were analyzed to evaluate various predictors of ripple geometry and roughness. Ripple roughness controls on sand resuspension and suspended sediment concentration profiles under combined waves and currents were also evaluated. The limited observation of sand ripples in the field indicates that the Grant and Madsen (1982) method overestimates ripple roughness, while the Nielsen (1981) method tends to under-predict ripple roughness. A modified ripple predictor is thus proposed based on the Grant and Madsen method, and it is shown to give reasonable predictions under the present experiment conditions. This modified ripple prediction along with wave, current and suspended sediment concentration data recorded by the tripods were then brought into the combined-flow bottom boundary layer model of Grant and Madsen (1986) and the modified Rouse equation of Glenn and Grant (1987) to calculate sand resuspension coefficient γ 0 and to predict suspended sediment concentration profiles. It was found that under low-energy fair-weather conditions, sand ripples are in the equilibrium range and ripple roughness increases with the bed shear stress. This causes strong vortex activity close to seabed and thus higher resuspension coefficient. Reference concentrations are moderate due to this high resuspension coefficient, even though bed shear stresses are low. Under moderate storm conditions, ripple break off occurs and ripple roughness will decrease with bed shear stress. This reduces the vortex activity and hence sand resuspension coefficient γ 0. The combination of this moderately high bed shear stress and reduced but still moderate ripple roughness favours sand suspension and produces the highest reference concentration for the encountered experimental conditions. As bed shear stress is further increased, ripples are nearly washed out and sand resuspension coefficient is further decreased approaching the previously-suggested constant value of 1.3 × 10 −4. This corresponds with the lowest reference concentration despite the high bed shear stress. Suspended sediment concentrations predicted by the modified Rouse equation using this time variable resuspension coefficient and properly calculated bottom boundary layer parameters are reasonable compared to the field measured concentration profiles.