Introduction of a new friction routine into the SWAN model that evaluates roughness due to bedform and sediment size changes

The significant loss of wave energy due to seabed interaction in finite depths is a known effect and bottom friction terms are used in the wave models to account for this dissipation. In this paper, a new bottom-interaction function is tested by means of the SWAN model, based on measurements at two field sites, Lake George and Lakes Entrance, both in Australia. The function accounts for dependence of the friction on the formation process of bottom ripples and on the grain size of the sediment. The overall improvement of the model prediction both for the wave height and wave period is demonstrated.     

An extended time-dependent numerical model of the mild-slope equation with weakly nonlinear amplitude dispersion

In the present paper, by introducing the effective wave elevation, we transform the extended ellip- tic mild-slope equation with bottom friction, wave breaking and steep or rapidly varying bottom topography to the simplest time-dependent hyperbolic equation. Based on this equation and the empirical nonlinear amplitude dispersion relation proposed by Li et al. (2003), the numerical scheme is established. Error analysis by Taylor expansion method shows that the numerical stability of the present model succeeds the merits in Song et al. (2007)’s model because of the introduced dissipation terms. For the purpose of verifying its performance on wave nonlinearity, rapidly vary- ing topography and wave breaking, the present model is applied to study: (1) wave refraction and diffraction over a submerged elliptic shoal on a slope (Berkhoff et al., 1982); (2) Bragg reflection of monochromatic waves from the sinusoidal ripples (Davies and Heathershaw, 1985); (3) wave transformation near a shore attached breakwater (Watanabe and Maruyama, 1986). Comparisons of the numerical solutions with the experimental or theoretical ones or with those of other models (REF/DIF model and FUNWAVE model) show good results, which indicate that the present model is capable of giving favorably predictions of wave refraction, diffraction, reflection, shoaling, bottom friction, breaking energy dissipation and weak nonlinearity in the near shore zone.     

Morphodynamics and cobbles behavior in and near the surf zone

The evolution of an initially flat sandy slope and the dynamics of large objects (cobbles/mines) emplaced on it are studied in a laboratory wave tank under simulated surf conditions. Upon initiation of wave forcing, the initially flat beach undergoes bedform changes before reaching a quasi-steady morphology characterized by a system of sand ripples along the slope and a large bar near the break point. Although the incoming wave characteristics are held fixed, the bottom morphology never reaches a strict steady state, but rather slowly changes due to the migration of ripples and bar transformation. When the wave characteristics are changed, the bedform adjusts to a new quasi-steady state after a suitable adjustment time. Studies conducted by placing model cobbles/mines on the evolving sandy bottom subjected to wave forcing show four distinct scenarios: (i) periodic cobble oscillations with zero mean displacement and small scour around the cobbles, (ii) mean onshore motion of relatively light cobbles, (iii) periodic burial of relatively heavy cobbles when their sizes are comparable to those of sand ripples, and (iv) the burial of relatively large cobbles under the bar, when the bar migrates due to changes of incoming waves. Quantitative data on the characteristics and dynamics of the bedform, including ripple-formation front propagating down the slope, ripple growth and drift, and flow around ripples, are presented. Physical explanations are provided for the observations.     

Estimation of the wave-related ripple characteristics and induced bed shear stress

A large data set on ripples was collected and examined. A set of new formulas for the prediction of the ripple characteristics is proposed with an emphasis on the disappearance of the ripples. The ripple wavelength was observed to be proportional to the bottom wave excursion but also to be a function of the grain-related Shields parameter and wave period parameter introduced by Mogridge et al. (1994). The ripple steepness was found to be nearly constant for orbital ripples, and with a sharp decrease for suborbital ripples. Two empirical functions are added including the effects of the critical Shields parameters (inception of transport and inception of sheet flow), i.e. giving the boundaries for the ripple existence's domain. The proposed formulas yield better prediction capabilities compared to the previously published formulas, especially when ripples are washed out. The effect of the ripple characteristics on the roughness height and the calculation of the bed shear stress is also discussed. It appeared that the bed shear stress calculation is more sensitive to the empirical coefficient a_r introduced in the estimation of the ripple-induced roughness height or to the limits of existence of the ripples than the ripple characteristics themselves.     

Tidal-cycle changes in oscillation ripples on the inner part of an estuarine sand flat

Oscillation ripples form on subaqueous sand beds when wave-generated, near-bottom water motions are strong enough to move sand grains. The threshold of grain motion is the lower bound of the regime of oscillation ripples and the onset of sheet flow is the upper bound. Based on the relation between ripple spacing and orbital diameter, three types of symmetrical ripples occur within the ripple regime. In the lower part of the ripple regime (orbital ripples), spacing is proportional to orbital diameter; in the upper part (anorbital ripples) spacing is independent of orbital diameter. Between these regions occurs a transitional region (suborbital ripples).

Oscillation ripples develop on a sandy tidal flat in Willapa Bay, Washington, as a result of waves traversing the area when it is submerged. Because wave energy is usually low within the bay, the ripples are primarily orbital in type. This means that their spacing should respond in a systematic way to changes in wave conditions. During the high-water parts of some tidal cycles, ripples near the beach decrease in spacing during the latter stage of the ebb tide while ripples farther offshore do not change. Observations made over several tidal cycles show that the zone of active ripples shifts on- or offshore in response to different wave conditions.

Detailed bed profiles and current measurements taken during the high-water part of spring tides show the manner in which the oscillation ripples change with changes in orbital diameter. Changes in ripple spacing at the study site could be correlated with changes in orbital diameter in the manner suggested by the criterion for orbital ripples. However, there appeared to be a lag time between a decrease in orbital diameter and the corresponding decrease in ripple spacing. Absence of change during a tidal cycle could be attributed to orbital velocities below the threshold for grain motion that negated the effects of changes in orbital diameter.

Because changes in sand-flat ripples depend both upon changes in orbital diameter and upon the magnitude of the orbital velocity, exposed ripples were not necessarily produced during the preceding high tide. In fact, some ripples may have been just produced, while others, farther offshore, may have been produced an unknown number of tides earlier. Therefore, when interpreting past wave conditions over tidal flats from low-tide ripples, one must remember that wave periods have to be short enough to produce velocities greater than the threshold velocity for the orbital diameters calculated from the observed ripple spacings.     

波浪-海流-微地形耦合的沉积动力模式建立及应用

沙纹微地形普遍存在于海底,沙纹的消长能改变底部应力进而影响泥沙的运移。以往研究较多侧重于波致沙纹,并已应用于波浪模式的底摩擦计算,而较少考虑波流联合效应产生的沙纹,也未将其应用于综合的水动力模式和沉积物输运模式。本文在POM水动力模式中嵌入新南威尔士大学泥沙模式,通过耦合波流共同作用的微地形模型与波流相互作用底边界层模型,发展了波浪-海流-微地形（沙纹）耦合的沉积动力模式。本文将该模式应用于澳大利亚Jervis湾,针对波主导和波流联合主导沙纹两种类型,分别进行了沙纹发展状态、几何形态的分布及悬浮泥沙的模拟。结果表明:波致沙纹比波流联合作用的沙波具有更大的波高和波长,因此当波主导时沙纹对悬浮泥沙起着关键作用。通过考虑随沙纹变化的粗糙度,相比于以往模式设置均一的粗糙度,该模型能对悬浮物浓度的骤升过程进行更精细的预测。     

On the Downshift of Wave Frequency for Bragg Resonance

For surface gravity waves propagating over a horizontal bottom that consists of a patch of sinusoidal ripples, strong wave reflection occurs under the Bragg resonance condition. The critical wave frequency, at which the peak reflection coefficient is obtained, has been observed in both physical experiments and direct numerical simulations to be downshifted from the well-known theoretical prediction. It has long been speculated that the downshift may be attributed to higher-order rippled bottom a...     

Characterization of bedform morphology generated under combined flows and currents using wavelet analysis

The wavelet transform (WT) has been successfully implemented in many fields such as signal and image processing, communication theory, optics, numerical analysis, and fluid mechanics. However, the application of WT to describe bedform morphology in coastal areas, oceans, and rivers is rare. The present study demonstrates the capability of WT analysis to fully represent the space–frequency characteristics of signals describing bed topography generated in marine and river environments. In this study WT is used to examine the morphological characteristics of bedforms generated in two separate laboratory facilities: a wave tank and a meandering channel. In the wave tank a set of ripples superimposed upon large wave ripples were generated; while in the meandering channel, 2D and 3D migrating ripples and dunes were observed. The WT proved to be a useful tool in detecting the complex variability of the generated bedform structures. The size distribution of the bottom features such as ripples, large wave ripples and sandbars were first examined along a 2D bed profile. Later analysis studied the variability of features in the transverse direction by using the power Hovmöller. Experiments in the wave tank were conducted for a mobility number of ψ=(10, 28), and a Reynolds wave number of R_ew=(17,500, 83,500) which correspond to waves alone (WA) and to combined flow (CF) scenarios, respectively. Experiments in the meandering channel were conducted under a morphological regime that produced mainly migrating sandbars.     

基于近底原位观测的小尺度海底沙波地形小波分解

浅海海床发育着不同尺度的活动性砂体,在大型活动性砂体上常叠加发育着大量小尺度沙波(纹),分析这些小尺度沙波(纹)有助于揭示活动性砂体的成因机制。但它们的尺度较小,常规分析方法往往将其作为高频噪声滤除,难以对该尺度海底沙波(纹)进行分离量化研究。为了解决这个问题,本文设计并实现了一种基于小波分析的小尺度海底沙波地形分解方法,并以台湾浅滩典型区域的高精度近底原位观测数据为例,实现了小尺度海底沙波地形的分解和定量分析,分解出背景地形、小型沙波和沙波纹(波长小于0.6 m)3种地貌类型。本文提出的小尺度海底沙波地形分解量化方法,可广泛应用于浅海高活动性地貌发育演化和海底边界层沉积动力过程研究,对评估海洋工程的稳定性也具有一定的实用价值。     

海岸破波带内水底悬沙浓度形成机理实验研究

通过大尺度水槽波浪引起泥沙悬移的动床模型实验,研究了沙坝海岸破波带内水底悬沙浓度形成机理,通过比较时间平均水底悬沙浓度与时间平均水底波浪水质点动能或时间平均水底湍动能之间的相关性,论证了利用时间平均湍动能比利用时间平均波浪水质点动能计算时间平均水底悬沙浓度更为适用,并提出了以上时间平均水底悬沙浓度与水底湍动能之间的关系也可以用来近似表达时间变化的水底悬沙浓度与时间变化的水底湍动能之间的关系。研究针对规则波、波群和不规则波3种波浪形态进行,并分别对破波带内的爬坡区、内破波区和沙坝区3个区域实验结果进行讨论。     

On the stability of the moments of the maximum entropy wind wave spectrum

The stability of some current wind wave parameters as a function of high-frequency cut-off and degrees of freedom of the spectrum has been numerically investigated when computed in terms of the moments of the wave energy spectrum.From the Pierson-Moskovitz wave spectrum type, a sea surface profile is simulated and its wave energy spectrum is estimated by the Maximum Entropy Method (MEM). As the degrees of freedom of the MEM spectral estimation are varied, the results show a much better stability of the wave parameters as compared to the classical periodogram and correlogram spectral approaches. The stability of wave parameters as a function of high-frequency cut-off result the same as obtained by the classical techniques.     

近岸浅水波的计算

采用理论推导与实验资料验证相结合的方法对近岸浅水波衰减计算进行研究。研究表明，波浪与浅水区运动传播衰减是各种能耗共同作用的结果，为此总结了分子粘性能耗、湍流能耗、底部渗透能耗、底部摩擦能耗、软泥海底弹性能耗等，由建立波能流平衡方程出发进行理论推导，得出各种能耗影响下波浪衰减的计算公式，并将该理论公式与作者１９８０年波浪水槽试验资料比较，两者基本吻合，可适用于线性及非线性各种波能耗情况的计算。     

Depth- and current-induced effects on wave propagation into the Altamaha River Estuary, Georgia

A study of sea surface wave propagation and its energy deformation was carried out using field observations and numerical experiments over a region spanning the midshelf of the South Atlantic Bight (SAB) to the Altamaha River Estuary, GA. Wave heights on the shelf region correlate with the wind observations and directional observations show that most of the wave energy is incident from the easterly direction. Comparing midshelf and inner shelf wave heights during a time when there was no wind and hence no wave development led to an estimation of wave energy dissipation due to bottom friction with corresponding wave dissipation factor of 0.07 for the gently sloping continental shelf of the SAB. After interacting with the shoaling region of the Altamaha River, the wave energy within the estuary becomes periodic in time showing wave energy during flood to high water phase of the tide and very little wave energy during ebb to low water. This periodic modulation inside the estuary is a direct result of enhanced depth and current-induced wave breaking that occurs at the ebb shoaling region surrounding the Altamaha River mouth at longitude 81.23°W. Modelling results with STWAVE showed that depth-induced wave breaking is more important during the low water phase of the tide than current-induced wave breaking during the ebb phase of the tide. During the flood to high water phase of the tide, wave energy propagates into the estuary. Measurements of the significant wave height within the estuary showed a maximum wave height difference of 0.4 m between the slack high water (SHW) and slack low water (SLW). In this shallow environment these wave–current interactions lead to an apparent bottom roughness that is increased from typical hydraulic roughness values, leading to an enhanced bottom friction coefficient.     

Impact of parameterized lee wave drag on the energy budget of an eddying global ocean model

The impact of parameterized topographic internal lee wave drag on the input and output terms in the total mechanical energy budget of a hybrid coordinate high-resolution global ocean general circulation model forced by winds and air-sea buoyancy fluxes is examined here. Wave drag, which parameterizes the generation of internal lee waves arising from geostrophic flow impinging upon rough topography, is included in the prognostic model, ensuring that abyssal currents and stratification in the model are affected by the wave drag.An inline mechanical (kinetic plus gravitational potential) energy budget including four dissipative terms (parameterized topographic internal lee wave drag, quadratic bottom boundary layer drag, vertical eddy viscosity, and horizontal eddy viscosity) demonstrates that wave drag dissipates less energy in the model than a diagnostic (offline) estimate would suggest, due to reductions in both the abyssal currents and stratification. The equator experiences the largest reduction in energy dissipation associated with wave drag in inline versus offline estimates. Quadratic bottom drag is the energy sink most affected globally by the presence of wave drag in the model; other energy sinks are substantially affected locally, but not in their global integrals. It is suggested that wave drag cannot be mimicked by artificially increasing the quadratic bottom drag because the energy dissipation rates associated with bottom drag are not spatially correlated with those associated with wave drag where the latter are small. Additionally, in contrast to bottom drag, wave drag is a non-local energy sink.All four aforementioned dissipative terms contribute substantially to the total energy dissipation rate of about one terawatt. The partial time derivative of potential energy (non-zero since the isopycnal depths have a long adjustment time), the surface advective fluxes of potential energy, the rate of change of potential energy due to diffusive mass fluxes, and the conversion between internal energy and potential energy also play a non-negligible role in the total mechanical energy budget. Reasons for the <10% total mechanical energy budget imbalance are discussed.     

240-kHz bistatic bottom scattering measurements in shallow water

High-frequency bistatic sediment scattering experiment was conducted in the shallow waters off the east coasts of Korea. Acoustic data were taken as a function of grazing angle (30°, 45°, and 60°), scattered angle (30°, 45°, and 60°), and bistatic (azimuthal) angle (0°, 60°, and 120°). Besides a flat bottom it was artificially raked so as to produce directional ripples. The measured scattering strengths for a flat bottom were compared to model predictions of D.R. Jackson et al. (1986). The surface reverberation component is seen to dominate over the volume scattering part at the frequency of 240 kHz. Compared to the flat bottom case, the scattering strengths for directional ripples showed lower and higher variation depending on the ripple's orientation     

Modeling the erosion of cohesive clay coasts

A model was developed to study the erosion of cohesive clay coasts in macro- to non-tidal environments. The model shares some of the characteristics of previous models, including the erosion of bare clay surfaces by wave generated bottom shear stresses, and of mobile, sediment-covered surfaces by abrasion. It differs from previous models, however, in several important ways. The morphodynamics of beaches with clay foundations, under different wave conditions, are based on a previously developed model for beaches on rocky shore platforms. Sediment thickness along a beach profile is calculated at regular intervals and compared with the maximum thickness that could be moved at that location under prevailing wave conditions. Wave friction factors are determined, where necessary, according to the occurrence and morphology of ripples on the bottom. In addition to abrasion and the effect of wave induced shear stresses on the clay bottom, erosion by stresses generated by wave impact at the bluff foot and on the intertidal platform is calculated using an expression derived from hard rock coastal models. Tides are represented by their computed tidal duration values, the amount of time each year that the water level falls within each 0.1 m vertical interval. Water depths are modified by wave setup and set-down conditions. Several preliminary model runs were made. The profiles were concave in the submarine zone and roughly linear in the intertidal zone. Equilibrium profiles developed which were maintained as they migrated landwards.     

A Model for Nonlinear Irregular Waves in Coastal Area

Based on the refraction-diffraction theory of irregular waves in the waters of slowly-varying cur-rents and depths,and the generation dissipation theory of wind wave,a model for nonlinear irregular wavesin coastal area is developed.In light of the specific conditions of coastal wave character and engineering ap-plication,a practical mathematical model for the nonlinear irregular waves is presented.with directional spec-trum in coastal area.Coast effect,refraction,whitecapping.bottom friction.current,wind and nonlinearaction are considered in this model.The numerical methods and schemes for wave refraction ray,energy con-servation of propagation,energy balance of the generation and dissipation of wind waves have been studied.Finally,the model is used for the directional wave spectrum computation in the Daya Bay.Compared withthe measured data with 956 wave bouys in the Daya Bay,the model results are in good agreement with themeasured results.     

An energy approach to non-breaking wave-induced motion of bottom sediment particles

A general equation, which applies to incipient motion, general surface motion and disappearance of ripples under non-breaking water waves, is derived using an energy approach. Lower and upper limits of ripple development are derived, showing that existing criteria are not entirely sufficient. An explicit formula for the dissipation factor as a function of D/A (grain diameter near-bed wave amplitude) is also obtained. The formula has been used to evaluate the variation of f_e with increasing flow characteristics for constant grain diameter. Finally, values of the sand grain roughness height, k_s, in relation to grain diameter are given for different types of bottom motion.     

多方向不规则波传播变形数值模拟

在推广的缓坡方程数学模型基础上建立了多方向不规则波数学模型,综合考虑了波浪折射、绕射、反射、底摩擦和风能输入等因素。基于线性波浪理论,将波浪方向谱在频率和方向上按等能量分割法离散后,分别计算各组成波的传播变形,再计算合成波要素。缓坡方程数学模型采用改进的ADI法求解,计算效率高,稳定性好。采用椭圆形浅滩不规则波模型试验结果和单突堤不规则波绕射理论解对数学模型进行了验证,数值模拟结果和试验值及理论解符合良好。利用该模型进行了某港港内波浪折射、绕射和反射的联合数值模拟,给出了合理的港内波高分布。     

Simulation of Random Waves and Associated Laminar Bottom Shear Stresses

This work presents a new approach for simulating the random waves in viscous fluids and the associated bottom shear stresses. By generating the incident random waves in a numerical wave flume and solving the unsteady two-dimensional Navier-Stokes equations and the fully nonlinear free surface boundaiy conditions for the fluid flows in the flume, the viscous flows and laminar bottom shear stresses induced by random waves axe determined. The deterministic spectral amplitude method implemented by use of the fast Fourier transform algorithm was adopted to generate the incident random waves. The accuracy of the numerical scheme is confirmed by comparing the predicted wave spectrum with the target spectrum and by comparing the nanlerical transfer function between the shear stress and the surface elevation with the theoretical transfer function. The maximum bottom shear stress caused by random waves, computed by this wave model, is compared with that obtained by Myrhaug＇ s model （1995）. The transfer function method is also employed to determine the maximum shear stress, and is proved accurate.