Combined Wave-current Flow Research Articles

Phase lags in oscillatory sheet flow: experiments and bed load modelling

Sheet flow corresponds to the high velocity regime when small bed ripples are washed out and sand is transported in a thin layer close to the bed. Therefore, it is often assumed that sand transport in oscillatory sheet flow behaves quasi-steady: time-dependent transport rates are assumed to be instantaneously related to the near-bed orbital velocity. However, new experimental results show that even in sheet flow, phase lags between sediment concentration and near-bed velocity can become so large that they lead to a reduction of the net (wave-averaged) transport rate. A phase lag parameter is defined, which shows that phase lags become important for fine sand, high velocities and short wave periods. A semi-unsteady model is developed that includes the effects of phase lags on the net transport rate. New experiments were carried out in a large oscillating water tunnel with three different sands ( D 50=0.13, 0.21 and 0.32 mm) for a range of prototype, combined wave–current flow conditions. Measured net transport rates were compared with predictions of a quasi-steady model and the new semi-unsteady model. This comparison indicates that net transport rates are reduced if phase lags become important: the quasi-steady model overestimates the net transport rates and the semi-unsteady model gives better agreement with the data. Time-dependent measurements of velocities and concentrations show that the reduced net transport rates can indeed be explained by phase lag effects, because for tests with smaller net transport rates than predicted by the quasi-steady model, considerable phase lags between velocities and concentrations were observed, even inside the sheet flow layer. Verification of the semi-unsteady model against a larger data set confirms the occurrence of phase lag effects in oscillatory sheet flow. Also for the larger data set the semi-unsteady model yields better agreement with the data than the quasi-steady model.

Modelling intensive near-bed sand transport under wave–current flow versus laboratory and field data

The present study is focused on sand transport in combined wave–current flow (at any angle between them) in the intensive flow regime. The present model is based on the 1DV approximation. The mathematical method for the continuous description of processes from the immobile bed to the formation of sheet flow and suspended load is presented. The way of modelling of sediment–flow interaction is proposed, in which the near-bed flow is divided into three layers, as done previously by Kaczmarek and Ostrowski [Kaczmarek, L.M., Ostrowski, R., 1998. Modelling of a three-layer sediment transport system in oscillatory flow. Proc. 26th ICCE, ASCE, 2559–2572] for pure oscillatory flow. Measured by Katopodi et al. [Katopodi, I., Ribberink, J.S., Ruol, P., Lodahl, C., 1994. Sediment transport measurements in combined wave–current flows. Proc. Coastal Dynamics '94, ASCE, 837–851] and Dohmen-Janssen [Dohmen-Janssen, M., 1999. Grain size influence on sediment transport in oscillatory flow. FEBODRUK BV, ISBN 90-9012929-4, Enschede, The Netherlands], the time-averaged velocity profiles are compared with results provided by the present model for the respective conditions. The laboratory data of combined wave–current flow were further used to compare the model results for instantaneous and time-averaged concentration in the bedload (pick-up) layer and the contact load (upper sheet flow) layer, as well as for net sediment transport rate in the case of unidirectional ( γ=0) wave–current interaction. The model cases for non-zero wave–current angle were tested in the context of longshore sediment transport rate against field radio-isotopic tracer data of Lubiatowo (Poland) by Pruszak and Zeidler [Pruszak, Z., Zeidler, R.B., 1994. Sediment transport in various time scales. Proc. 24th ICCE, ASCE, 2513–2526] and field luminescent tracer data of Ancao Peninsula (Portugal), by Balouin and Howa [Balouin, Y., Howa, H., 2000. Correspondence contact with University of Bordeaux]. Generally, the agreement between the model results and the experimental data was found satisfactory in the context of the apparent roughness and time-averaged velocity profiles above the bed boundary layer. Further, the anti-phase behaviour of measured bedload concentration with respect to sediment concentration in the contact load layer and the asymmetric effects resulting from wave–current interaction are well represented by the model. Consequently, the present theoretical approach provides a useful tool for predictions of sand transport under wave–current flow within an accuracy factor of 1.5 either way.

Estimates of wave decay rates in the presence of turbulent currents

A full-depth numerical model solving the free surface flow induced by linear water waves propagating with collinear vertically sheared turbulent currents is presented. The model is used to estimate the wave amplitude decay rate in combined wave current flows. The decay rates are compared with data collected in wave flumes by Kemp and Simons [J Fluid Mech, 116 (1982) 227; 130 (1983) 73] and Mathisen and Madsen [J Geophys Res, 101 (C7) (1996) 16,533]. We confirm the main experimental finding of Kemp and Simons that waves propagating downstream are less damped, and waves propagating upstream significantly more damped than waves on fluid at rest. A satisfactory quantitative agreement is found for the decay rates of waves propagating upstream, whereas not more than a qualitative agreement has been observed for waves propagating downstream. Finally, some wave decay rates in the presence of favourable and adverse currents are provided in typical field conditions.

The estimation of shear stresses from near-bed turbulent velocities for combined wave–current flows

High frequency near-bottom velocities measured by a combined pressure gauge and flow-meter are analysed with a view to understanding and modelling waves and sediment transport in shallow waters. Data from five stations in different water depth, wave and current conditions are compared. Wave, tide/surge and turbulence components have been separated from the bottom velocity data and are used to derive a friction velocity and examine the bottom stress parameterisation. The horizontal component of turbulent velocity fluctuations near the bed is found to be well-correlated with the bed shear stress from a combined wave and current model. The model of Christoffersen and Jonsson [Christoffersen, J.B., Jonsson, I.G., 1985. Bed friction and dissipation in a combined current and wave motion. Ocean Engineering, 12, 5, 387–423] is in reasonable agreement with the observed data. The observed turbulence can shed light on the wave bed shear stress as well as the shear stress due to the current. A fitting procedure gives a derived Nikuradse length scale for each station which is similar to that obtained independently from bed grain size estimates.

Velocity and turbulence distributions in combined wavecurrent flows over a rippled bed

This paper describes an experimental programme carried out in a laboratory channel, to investigate the velocity distributions over a rippled bed in combined wave-current flows. In this study, waves propagate against a turbulent current. Velocity measurements were made with a laser-Doppler anemometer. The Nikuradse roughness length k s , of the bed has been estimated from the traditional logarithmic velocity profile for current alone. The most significant effect of the superposition of waves on a current is the increase of the apparent roughness of the bed with increasing wave height. This effect is well described by Sleath's [49] model. As for rough flat beds, the turbulence intensity over ripples varies inversely with height at sufficiently large distance from the bed for wave-dominated flows.

A simple system for laser-illuminated video imaging of sediment suspension and bed topography

A simple underwater video system has been developed for simultaneously imaging sediment suspension and monitoring bed profiles under waves and combined wave-current flows. This consists of a diode-laser-generated light plane and a black-and-white underwater video camera. The laser light illuminates suspended material in section and also provides a bed profile at the bottom. Orthogonal laser/camera pairs are used to obtain both cross-shore and alongshore views. During deployments, the system has been augmented by acoustic backscatter devices for measurement of sediment concentration. As with all video techniques, visibility is a limiting factor, but where turbidity is low to moderate, the results are encouraging. Results on cross-shore and alongshore bed elevation variations and suspension event stales obtained with the video/laser system are presented for two experiments: one at the National Research Council Wave Research Flume in Ottawa, Canada, and the other in the field at Queensland Beach, N.S., Canada,.

Comparisons between sediment transport models and observations made in wave and current flows above plane beds

As a part of the MAST2 G8-M Coastal Morphodynamics project, the predictions of four sediment transport models have been compared with detailed laboratory data sets obtained in the bottom boundary layer beneath regular waves, asymmetrical waves, and regular waves superimposed co-linearly on a current. Each data set was obtained in plane bed, sheet flow, conditions and each of the four untuned numerical models has provided a one-dimensional vertical (1DV), time-varying, representation of the various experimental situations. Comparisons have been made between the model predictions and measurements of both time-dependent sediment concentration, and also wave-averaged horizontal velocity and concentration. For the asymmetrical waves and for the combined wave-current flows, comparisons have been made with vertical profiles of the cycle-averaged sediment flux, and also with the vertically-integrated net sediment transport rate. Each of the turbulence diffusion models gives an accurate estimate of the net transport rate (invariably well within a factor of 2 of the measured value). In contrast, none of the models provides a good detailed description of the time-dependent suspended sediment concentration, due mainly to the inability of conventional turbulence diffusion schemes to represent the entrainment of sediment into suspension by convective events at flow reversal. However, in the cases considered here, this has not seriously affected the model predictions of the net sediment flux, due to the dominance of the near-bed transport. The comparisons in this paper are aimed not only at testing the predictive capability of existing sediment transport modelling schemes, but also at highlighting some of their deficiencies.

Towards Predicting Sediment Transport in Combined Wave-Current Flow

A one-dimensional, vertical (1DV) grid model has been developed for the prediction of sediment transport in combined wave-current flow under sheet flow conditions. The model uses a one-equation turbulence closure scheme to simulate vertical mixing processes, and a time-varying reference concentration as the bottom boundary condition for the suspended sediment layer. Comparison with recent experimental data shows that the model gives good predictions (within 30%) of the measured net sediment transport rates under different conditions. The results also demonstrate the importance of the “wave-related” contribution to the suspended transport, due to the unsteadiness in the velocity and sediment concentration fields. At certain elevations above the bed, the suspended flux may be in the direction opposite to that of the mean current as a result of the phase relationship between the horizontal velocity and sediment concentration.

Movable bed roughness and current profiles in the presence of irregular waves with an arbitrary angle to currents

The bed roughness k s and current velocity profiles in the presence of waves with an arbitrary angle θ to currents are studied. It is found that the movable bed roughness is affected by both the wave and the current and only slightly by the angle θ between the wave propagation and the current, and that existing formulae derived in purely oscillatory flows generally fail to predict k s . In the present study, a new formula which takes account the effect of the wave and the current on the bed roughness is suggested to calculate k s in combined wave-current flows. With the present formula, the current profiles calculated by the model of You agree satisfactorily with the laboratory data of van Kampen and Nap and Havinga, and the field measurements of Grant and Williams and Drake et al.

A simple model for current velocity profiles in combined wave-current flows, by Z.-J. You: comments

A simple model for current velocity profiles in combined wave-current flows, by Z.-J. You: comments

A simple model for current velocity profiles in combined wave-current flows: reply to the comments by P. Nielsen

A simple model for current velocity profiles in combined wave-current flows: reply to the comments by P. Nielsen

A simple model for current velocity profiles in combined wave-current flows

Current velocity profiles in combined wave-current flows are investigated on the basis of available laboratory and field data. From the laboratory measurements of Van Doorn's (1982) S10RAL, S20RAL, M10RAL and M20RAL, it is found that there exists a boundary interaction layer (which includes the wave boundary layer) where the current eddy viscosity ϵ c is dominated by the wave motion inside the boundary interaction layer and then by the current upwards. Based on this finding, a new and simple model is developed to predict current velocity profiles in the presence of waves. The input parameters used in the model are wave height H, wave period T, water depth h, bed roughness K s, and a reference current velocity u ̄ r . In comparison with the former models of Christoffersen and Jonsson (1985), Coffey and Nielsen (1986) and Sleath (1991), the present model provides a simple method to explicitly calculate the wave friction factor, current friction velocity and current velocities without laborious iterations involved. Another new aspect of the model is that calculation of current friction velocities and current velocity profiles is quite simple and can be carried out with a simple scientific calculator. Results from the model are sufficiently accurate for engineering purposes.

Eddy viscosities and velocities in combined wave-current flows

The eddy viscosities for the steady and the periodic components of combined wave-current flows have been studied quantitatively from the presently available experimental data. It has been found that inside the boundary interaction layer [ z < δ] the eddy viscosity ε c for the steady flow is increased in the presence of waves while outside the boundary interaction layer [ z > δ] it is affected little by the wave motion, and that the eddy viscosity ε w for the wave motion in the boundary layer is independent of the current strength U ∗ . On the other hand, a new eddy viscosity model is presented to give a good prediction of the velocity distributions of the waves and currents in comparison with experimental data.

Transient effects in wave-current boundary layer flow

Abstract Previous studies of combined wave and current bottom boundary layer flow have concentrated on the final converged state of the flow following the addition of waves to a current. While this final state is of primary interest to modellers and engineers, it pre-supposes that such a state is actually attained in reality, and this may not always be the case. In addition, it overlooks the interesting and complicated transient effects which occur as a wave-current flow evolves from one state to another. The present study concentrates attention on the transient effects predicted by a “one-equation” turbulence closure model. Results of case studies are presented in which waves are superimposed co-linearly on a current (“forward problem”), and are then removed from the converged wave-current flow (“backward problem”). Two formulations of the “forward” and “backward” problems are discussed. In the first the steady component of the pressure gradient driving the mean flow is held constant throughout, and in the second the steady component of the mass flux is held constant. In each case the detailed evolution of the profiles of mean velocity, turbulent energy, mixing length, eddy viscosity and shear stress are discussed. More generally, the question of the convergence timescale of a combined wave-current flow is considered, and a convergence criterion is proposed.

EXPERIMENTAL INVESTIGATION ON UNIFORM AND NON-UNIFORM BOUNDARY LAYER UNDER WAVE AND WAVE-CURRENT COMBINATIONS

Flume experiments were carried out in order to study the velocity field in the boundary layer under wave and wave-current combinations. These included both smooth and rough of flat and sloping beds. The particle velocity was measured by an LDV. The particle velocity on the sloping bed was found to follow the logarithmic law of wall as for the flat bed. However, significant differences in the time mean velocity and the mass transport velocity for the combined wavecurrent flows are found. The comparisons in terms of the friction factor and roughness parameter were made with several theoretical models.

Explicit modelling of bottom friction in combined wave-current flow

A direct, explicit solution technique is developed to estimate the time-mean bed shear stress and its frictional dissipation rate in combined wave-current flow. The present paper is the final part of the series papers concerned with the refinements of Bijker's modelling approach. In the early paper it was shown that Bijker's approach is widely applicable if consideration is given for the current velocity reduction as well as the near-bed velocity profile of wave motion. In the last paper the velocity reduction factor was shown to be represented by explicit expression so that numerical efficiency can be significantly improved. In the present paper the explicit expressions of various time-integrals and reduction factor are further modified by considering various flow conditions in order to improve the numerical accuracy in any flow conditions. The refined model is again tested against several sets of laboratory data including those published in recent years, and discussion is made on the computational results produced by various mathematical models.