An experimental investigation of the velocity field under cnoidal waves over the asymmetric rippled bed

1 IntroductionIn coastal areas a ubiquitous phenomenon is theformation of ripples in the seabed. It is now widelyaccepted that the flow and sediment transport overseabed are vital in relation to erosion, surface wavedissipation and pollution dispersion et…     

Numerical simulation of oscillatory flows over a rippled bed by immersed boundary method

In this paper, a well-developed numerical model based on the immersed boundary (IB) method is used to study oscillatory flows over a bed with large-amplitude ripples in a systematic manner. The work shows that the complex flow over the rippled bed can be numerically dealt with in Cartesian coordinate by the IB method and that the IB method is able to provide main features of the flows near the ripples. An accurate simulation of vortices generation as a result of flow separation at the rippled bed is obtained. It is found that the oscillatory flows start to separate during the flow deceleration when the Keulegan–Carpenter (KC) number is small. The steady streaming for various ripple steepness is simulated and the criterion for separating the single and double structure streaming is also discussed. Moreover, a new type of steady streaming which consists of a pair of embedded recirculations in the vicinity of the ripple trough is obtained for relatively steep ripples in this work. The numerical results, including the steady streaming in particular, may be helpful to improve the understanding of the sediment transport and the seabed evolution with natural ripples under sea waves.     

Sand transport under combined current and wave conditions: A semi-unsteady,practical model

For the general purposes of morphodynamic computations in coastal zones, simple formula-based models are usually employed to evaluate sediment transport. Sediment transport rates are computed as a function of the bottom shear stress or the near bed flow velocity and it is generally assumed that the sediment particles react immediately to changes in flow conditions. It has been recognized, through recent laboratory experiments in both rippled and plane bed sheet flow conditions that sediment reacts to the flow in a complex manner, involving non-steady processes resulting from memory and settling/entrainment delay effects. These processes may be important in the cross-shore direction, where sediment transport is mainly caused by the oscillatory motions induced by surface short gravity waves.The aim of the present work is to develop a semi-unsteady, practical model, to predict the total (bed load and suspended load) sediment transport rates in wave or combined wave-current flow conditions that are characteristic of the coastal zone. The unsteady effects are reproduced indirectly by taking into account the delayed settling of sediment particles. The net sediment transport rates are computed from the total bottom shear stress and the model takes into account the velocity and acceleration asymmetries of the waves as they propagate towards the shore.A comparison has been carried out between the computed net sediment transport rates with a large data set of experimental results for different flow conditions (wave-current flows, purely oscillatory flow, skewed waves and steady currents) in different regimes (plane bed and rippled bed) with fine, medium and coarse uniform sand. The numerical results obtained are reasonably accurate within a factor of 2. Based on this analysis, the limits and validity of the present formulation are discussed.     

前进波作用下沙纹床面的净输沙方向与净输沙强度

在沙纹床面输沙过程中，假设水流从涡中取出并搬运的悬移质数量与推移质运动的沙星成比例，由12组细沙实验结果得到了沙纹床面净输沙的方向和输沙强度公式，并与他人的实验结果进行对比。     

Propagation of water waves over permeable rippled beds

Unsteady two-dimensional Navier-Stokes equations and Navier-Stokes type model equations for porous flow were solved numerically to simulate the propagation of water waves over a permeable rippled bed. A boundary-fitted coordinate system was adopted to make the computational meshes consistent with the rippled bed. The accuracy of the numerical scheme was confirmed by comparing the numerical results concerning the spatial distribution of wave amplitudes over impermeable and permeable rippled beds with the analytical solutions. For periodic incident waves, the flow field over the wavy wall is discussed in terms of the steady Eulerian streaming velocity. The trajectories of the fluid particles that are initially located close to the ripples were also determined. One of the main results herein is that under the action of periodic water waves, fluid particles on an impermeable rippled bed initially moved back and forth around the ripple crest, with increasing vertical distance from the rippled wall. After one or two wave periods, they are then lifted towards the next ripple crest. All of the marked particles on a permeable rippled bed were shifted onshore with a much larger displacement than those on an impermeable bed. Finally, the flow fields and the particle motions close to impermeable and permeable beds induced by a solitary wave are elucidated.     

VORTEX SHEDDING FROM A CIRCULAR CYLINDER IN OSCILLATORY FAR FLOW

By using a process of successive approximations, the Boundary-Layer equations are solved to determine the separation points of a circular cylinder in oscillatory flow under the conditions of vortex existing. Combining with the discrete vortex model, the separation points and the fluid force coefficients are calculated at different KC numbers and Re numbers, A modified Morison equation is used in calculating the inline forces, and good agreements are obtained between the calculated results and those from other's experiments.     

A two-phase numerical model for sediment transport prediction under oscillatory sheet flows

To predict sediment transport under oscillatory sheet flow condition, especially for fine sand, is still a challenging research subject in coastal engineering. This paper describes a newly-developed numerical model based on two-phase theory with the use of a one-equation turbulence closure, and its applications in predicting fine sediment suspension in near-prototype oscillatory sheet flow conditions. Model results were compared with comprehensive laboratory measurements of flow velocity and sediment concentration under both symmetrical and asymmetrical oscillatory sheet flows from a large-scale water tunnel. Good agreements between the model results and measurements were achieved and the results demonstrated that the model is capable of reproducing detailed characteristics of sediment entrainment process in the sheet flow regime. The comparisons also revealed the fact that the concentration peaks at flow reversal is associated with the strong vertical sediment transport flux in the pickup layer, which has been widely observed in many laboratory experiments. The effects of flow reversal events on total sediment transport were also discussed.     

A linear model for the structure of turbulence beneath surface water waves

The structure of turbulence in the ocean surface layer is investigated using a simplified semi-analytical model based on rapid-distortion theory. In this model, which is linear with respect to the turbulence, the flow comprises a mean Eulerian shear current, the Stokes drift of an irrotational surface wave, which accounts for the irreversible effect of the waves on the turbulence, and the turbulence itself, whose time evolution is calculated. By analysing the equations of motion used in the model, which are linearised versions of the Craik–Leibovich equations containing a ‘vortex force’, it is found that a flow including mean shear and a Stokes drift is formally equivalent to a flow including mean shear and rotation. In particular, Craik and Leibovich’s condition for the linear instability of the first kind of flow is equivalent to Bradshaw’s condition for the linear instability of the second. However, the present study goes beyond linear stability analyses by considering flow disturbances of finite amplitude, which allows calculating turbulence statistics and addressing cases where the linear stability is neutral. Results from the model show that the turbulence displays a structure with a continuous variation of the anisotropy and elongation, ranging from streaky structures, for distortion by shear only, to streamwise vortices resembling Langmuir circulations, for distortion by Stokes drift only. The TKE grows faster for distortion by a shear and a Stokes drift gradient with the same sign (a situation relevant to wind waves), but the turbulence is more isotropic in that case (which is linearly unstable to Langmuir circulations).     

Numerical study on the characteristics of flow field and wave propagation near submerged breakwater on slope

In this study,characteristics of flow field and wave propagation near submerged breakwater on a sloping bed are investigated with numerical model. The governing equations of the vertical twodimensional model are Reynolds Averaged Navier Stokes equations. The Reynolds stress terms are closed by a nonlinear k ε turbulence transportation model. The free surface is traced through the PILC-VOF method. The proposed numerical model is verified with experimental results. The numerical result shows that the wave profile may become more asymmetrical when wave propa-gates over breakwater. When wave crest propagates over breakwater,the anticlockwise vortex may generate. On the contrary,when wave hollow propagates over breakwater,the clockwise vortex may generate. Meanwhile,the influenced zone of vortex created by wave crest is larger than that created by wave hollow. All the maximum values of the turbulent kinetic energy,turbulent dissi-pation and eddy viscosity occur on the top of breakwater. Both the turbulent dissipation and eddy viscosity increase as the turbulent kinetic energy increases. Wave energy may rapidly decrease near the breakwater because turbulent dissipation increases and energy in lower harmonics is transferred into higher harmonics.     

Large Eddy Simulation for Plunge Breaker and Sediment Suspension

Breaking waves are a powerful agent for generating turbulence that plays an important role in many fluid dynamical processes, particularly in the mixing of materials. Breaking waves can dislodge sediment and throw it into suspension, which will then be carried by wave-induced steady current and tidal flow. In order to investigate sediment suspension by breaking waves, a numerical model based on large-eddy-simulation (LES) is developed. This numerical model can be used to simulate wave breaking and sediment suspension. The model consists of a free-surface model using the surface marker method combined with a two-dimensional model that solves the flow equations. The turbulence and the turbulent diffusion are described by a large-eddy-simulation (LES) method where the large turbulence features are simulated by solving the flow equations, and a subgrid model represents the small-scale turbulence that is not resolved by the flow model. A dynamic eddy viscosity subgrid scale stress model has been used for the     

Practical sand transport formula for non-breaking waves and currents

Many existing practical sand transport formulae for the coastal marine environment are restricted to a limited range of hydrodynamic and sand conditions. This paper presents a new practical formula for net sand transport induced by non-breaking waves and currents. The formula is especially developed for cross-shore sand transport under wave-dominated conditions and is based on the semi-unsteady, half wave-cycle concept, with bed shear stress as the main forcing parameter. Unsteady phase-lag effects between velocities and concentrations, which are especially important for rippled bed and fine sand sheet-flow conditions, are accounted for through parameterisations. Recently-recognised effects on the net transport rate related to flow acceleration skewness and progressive surface waves are also included. To account for the latter, the formula includes the effects of boundary layer streaming and advection effects which occur under real waves, but not in oscillatory tunnel flows. The formula is developed using a database of 226 net transport rate measurements from large-scale oscillatory flow tunnels and a large wave flume, covering a wide range of full-scale flow conditions and uniform and graded sands with median diameter ranging from 0.13 mm to 0.54 mm. Good overall agreement is obtained between observed and predicted net transport rates with 78% of the predictions falling within a factor 2 of the measurements. For several distinctly different conditions, the behaviour of the net transport with increasing flow strength agrees well with observations, indicating that the most important transport processes in both the rippled bed and sheet flow regime are well captured by the formula. However, for some flow conditions good quantitative agreement could only be obtained by introducing separate calibration parameters. The new formula has been validated against independent net transport rate data for oscillatory flow conditions and steady flow conditions.     

Wave–current interaction with a vertical square cylinder

A three-dimensional numerical model is developed in this study to investigate the problem of wave–current–body interaction. The model solves the spatially averaged Navier–Stokes equations. Turbulence effects are modeled by a subgrid-scale (SGS) model using the concept of large eddy simulation (LES). The model is employed to study the wave–current interaction with a square cylinder that is mounted on the bottom and vertically pierces the free surface. The force analysis demonstrates that the presence of waves can reduce both the strength and frequency of vortex shedding induced by a uniform current due to the nonlinear wave–current interaction. The free surface elevation, strain rates of the mean flow, and eddy viscosity are found to closely correlate with the mechanism of vortex shedding. It is also shown that when the vortex shedding is neglected in the calculation such as by the potential flow approach, one may significantly underestimate the magnitude of in-line force. The energy spectral analysis reveals that there exist initiating, growing, and decaying regions for shedding vortices around the cylinder. In the vortex initiating region, both coherent and turbulent structures are nearly two-dimensional that become three-dimensional in the vortex growing region. The kinetic energy of both coherent and turbulent motions is dissipated in the vortex decaying region, within which the mean flow gradually returns back to two-dimensional.     

Modelling and measurement of sand transport processes over full-scale ripples in oscillatory flow

A new series of laboratory experiments was performed in the Aberdeen Oscillatory Flow Tunnel (AOFT) and the Large Oscillating Water Tunnel (LOWT) to investigate time-averaged suspended sand concentrations and transport rates over rippled beds in regular and irregular oscillatory flow. The wave-induced oscillatory near-bed flows were simulated at full-scale. Five series of experiments were carried out. During the two AOFT experimental series, ripple dimensions, ripple migration rates and net sand transport rates were measured under regular and irregular asymmetric flow for two different sand types. The three LOWT experimental series focussed on measurements of the ripple dimensions, ripple migration rates, time-averaged suspended sand concentrations and net sand transport rates under regular asymmetric and irregular weakly asymmetric flow for two different sand types. From analysis of new and other full-scale data, it is concluded that the lower part of the time- and bed-averaged concentration profile (up to two times the ripple height above the ripple crest level) has an exponential profile. A new reference concentration formula is proposed based on the formula of Bosman and Steetzel [Bosman, J.J., Steetzel, H.J., 1986. Time- and bed-averaged concentration under waves. Proc. 20th ICCE Taipei, ASCE, pp. 986–1000], which includes the grain-size influence. Furthermore, it is shown that the concentration decay length is strongly related to the ripple height and that the simple formula R_c = 1.27η gives good agreement with the data. A new transport model is proposed for the wave-related net transport over full-scale ripples based on a modified half wave cycle concept of Dibajnia and Watanabe [Dibajnia, M., Watanabe, A., 1992. Sheet flow under nonlinear waves and currents. Proc. 23rd ICCE Venice, ASCE, pp. 2015–2028; Dibajnia, M., Watanabe, A., 1996. A transport rate formula for mixed sands. Proc. 25th ICCE Orlando, ASCE, pp. 3791–3804]. The magnitudes of the half wave cycle transport contributions are related to the grain-related Shields parameter, the degree of wave asymmetry and a newly defined vortex suspension parameter P, which is the ratio between the ripple height and the median grain-size. The new model has been calibrated using transport data from the new regular flow experiments and has subsequently been validated using other data, including measurements from irregular flow experiments. The new model is seen to perform better overall than existing practical models for ripple regime net sand transport.     

潮流波浪联合输沙及海床冲淤演变的理论体系与其数学模拟

根据近岸带及河口区潮流、波浪、湍流各自物理尺度的不同,从Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程和质量传输方程出发,利用Ｒｅｙｎｏｌｄｓ分解的方法,建立了模拟波浪 流联合输沙及海床冲淤演变的理论体系,给出了潮流作用下近岸波浪传播方程、波浪作用下潮流运动方程并通过利用波流合成底部切应力、底层湍流脉动随机特性,得出了波流联合作用下不平衡沙计算中泥沙起悬与沉降量的确定方法。本文模型应用于“广西合浦围垦工程潮流波浪     

Reynolds number variation in oscillatory boundary layers: Part I. Purely oscillatory motion

A numerical model based upon a low Reynolds number turbulence closure is proposed to study Reynolds number variation in reciprocating oscillatory boundary layers. The model is used to compute the boundary layer for flow regimes ranging from smooth laminar to rough turbulent. Criteria for fully developed turbulence are derived for walls of the smooth and rough types. In particular, a new criterion to identify the rough turbulent regime is determined based on the time-averaged turbulence intensity. The reliability of the present model is assessed through comparisons with detailed experimental data collected by other investigators. The model globally improves upon standard high Reynolds number closures. Variation through the wave cycle of the main flow variables (ensemble-averaged velocity, shear stress, turbulent kinetic energy) is remarkably well-predicted for smooth walls. Predictions are satisfactory for rough walls as well. Yet, the turbulence level in the rough turbulent regime is overpredicted in the vicinity of the bed.     

Using RANS to simulate vortex generation and dissipation around impermeable submerged double breakwaters

In this paper, a Reynolds Averaged Navier–Stokes (RANS) model was developed to simulate the vortex generation and dissipation caused by progressive waves passing over impermeable submerged double breakwaters. The dynamics of the turbulence are described by introducing a k–ɛ model with Boussinesq closure. The Height Function (HF) is implemented to define the free-surface configuration. The governing equations are discretized by means of a finite volume method based on a staggered grid system with variable width and height. The feasibility of the numerical model was verified through a series of comparisons of numerical results with the existing analytical solutions and the experimental data. The good agreements demonstrate the satisfactory performance of the developed numerical model. The flow separation mechanism both near the upstream and the downstream edges of the obstacles demonstrates the physical and expected nature of development of the flow. The present model provides an accurate and efficient tool for the simulation of flow field and wave transformation near coastal structures without breaking.     

Large-scale turbulence under a solitary wave

The structure of large-scale turbulence under a broken solitary wave on a 1 in 50 plane slope was studied. Three-component velocity measurements were taken at different heights above a smooth bed in the middle surf zone using an acoustic Doppler velocimeter. The measured data showed that turbulent velocity components were well correlated in the middle part of the water column. The velocity correlations could be produced by an oblique vortex similar to the obliquely descending eddy observed previously by other investigators. The vertical distributions of the relative values of the components of the Reynolds stress tensor showed that the structure of turbulence evolved continuously between the free surface and the bottom. The evolution was related to transition from two-dimensional to three-dimensional flow structures and the effect of the solid bottom on flow structures. Time histories of measured turbulent kinetic energy and turbulence stresses showed episodic turbulent events near the free surface but more sporadic turbulence in the lower layer. Large or intense turbulent events were found to have short duration and time lag relative to the wave crest point. These events also maintained good correlations between the turbulence velocity components close to the bottom.Instantaneous turbulent velocity fields were measured near the bottom at the same cross-shore location by using a stereoscopic particle image velocimetry system. These measurements showed that the near-bed flow field was characterized by large-scale, coherent flow structures that were the sources of most of the turbulent kinetic energy and turbulence stresses. The types of organized flow structures observed included vortices and downbursts of turbulence descending directly from above, lateral spreading of turbulent fluid along the bed, and formation of vortices in shear layers between fluid streams. A common feature of the organized flow structures near the bed was the large turbulence velocities in the longitudinal and transverse directions, which reflected the influence of a solid bottom on the breaking-wave-generated turbulence arriving at the bed.     

Comparative Experimental and Numerical Study of Wave Loads on A Monopile Structure Using Different Turbulence Models

This study numerically and experimentally investigates the effects of wave loads on a monopile-type offshore wind turbine placed on a 1: 25 slope at different water depths as well as the effect of choosing different turbulence models on the efficiency of the numerical model. The numerical model adopts a two-phase flow by solving Unsteady Reynolds-Averaged Navier-Stokes(URANS) equations using the Volume Of Fluid(VOF) method and three different turbulence models. Typical environmental conditions from the East China Sea are studied. The wave run-up and the wave loads applied on the monopile are investigated and compared with relevant experimental data as well as with mathematical predictions based on relevant theories. The numerical model is well validated against the experimental data at model scale. The use of different turbulence models results in different predictions on the wave height but less differences on the wave period. The baseline turbulence model and Shear-Stress Transport(SST) turbulence model exhibit better performance on the prediction of hydrodynamic load, at a model-scale water depth of 0.42 m, while the laminar model provides better results for large water depths. The SST turbulence model performs better in predicting wave run-up for water depth 0.42 m, while the laminar model and standard model perform better at water depth 0.52 m and 0.62 m, respectively.