Bars formed by horizontal diffusion of suspended sediment

The mechanism responsible for the ubiquitous presence of convex beach profiles and shoreward migration of linear bars is examined using numerical circulation and sediment transport models. The models are validated against laboratory measurements and observed natural beach cross-sections. While not discounting the importance of infragravity and advective horizontal circulation or bed-return flow mechanisms, a robust diffusive process explains the convex profile shape and bar formation. In the presence of concentration gradients across the surf zone, a diffusive sediment flux from high to low concentration results in the transfer of sediment outwards from the breakpoint, both onshore and offshore, and the subsequent formation of a “diffusion bar” and “diffusion profile”. The profiles are characterised by single- and double-convex dome-like shapes, developing during shoreward migration of the bars by the diffusion mechanism. The mechanism explains several phenomena observed on natural beaches, including (i) convex beach profiles; (ii) shoreward migration of the bar with concomitant beach accretion under narrow-band swell; (iii) reduced propensity for bar formation on low-gradient, fine-sand beaches or under wide-band wave spectra (even though multiple bars are common on some low-gradient beaches) and (iv) offshore migration of the bar during periods of increasing wave height. The diffusion mechanism can be dependent on orbital motion alone and, as such, requires no frequency selection or strong correlation between multiple processes for bar formation.     

Second-order theory for coupling 2D numerical and physical wave tanks: Derivation,evaluation and experimental validation

A full second-order theory for coupling numerical and physical wave tanks is presented. The ad hoc unified wave generation approach developed by Zhang et al. [Zhang, H., Schäffer, H.A., Jakobsen, K.P., 2007. Deterministic combination of numerical and physical coastal wave models. Coast. Eng. 54, 171–186] is extended to include the second-order dispersive correction. The new formulation is presented in a unified form that includes both progressive and evanescent modes and covers wavemaker configurations of the piston- and flap-type. The second order paddle stroke correction allows for improved nonlinear wave generation in the physical wave tank based on target numerical solutions. The performance and efficiency of the new model is first evaluated theoretically based on second order Stokes waves. Due to the complexity of the problem, the proposed method has been truncated at 2D and the treatment of regular waves, and the re-reflection control on the wave paddle is also not included. In order to validate the solution methodology further, a series of nonlinear, periodic waves based on stream function theory are generated in a physical wave tank using a piston-type wavemaker. These experiments show that the new second-order coupling theory provides an improvement in the quality of nonlinear wave generation when compared to existing techniques.     

Rapid wave-driven advective pore water exchange in a permeable coastal sediment

In this study we present in-situ measurements of pore water flow velocities in a coastal sandy sediment (permeability=3.65×10⁻¹⁰ m²). The advective pore water flows were driven by the interaction of oscillating boundary flows with sediment wave ripples, (amplitude=7 cm, wavelength=30 to 50 cm). The measurements were carried out in the Mediterranean Sea at 50 to 70 cm water depth during a phase of very low wave energy (max. wave amplitude=10 cm). An optode technique is introduced that permits direct pore water flow measurements using a fluorescent tracer. Near the sediment surface (0.5 cm depth) pore water reached velocities exceeding 40 cm h⁻¹. Thus, advective transport exceeded transport by molecular diffusion by at least 3 orders of magnitude. Based on the pore water velocity measurements and ripple spacing, we calculate that 140 L m⁻² d⁻¹ are filtered through the sediment. Pore water visualisation experiments revealed a flow field with intrusion of water in the ripple troughs and pore water release at the ripple crests. The wave-driven water flow through the sediment, thus, was directly linked to the wave-generated sediment topography, and its spatial dimensions. These results show that surface waves cause water filtration through permeable sediments at water depths smaller than half the wavelength. We conclude that surface gravity waves constitute an important hydromechanical process that may convert large areas of the continental shelves into expansive filter systems. Surface gravity waves thereby could affect suspended particle concentration and cycling of matter in the shelf.     

A method of accounting for tidal changes in regional climates of a water basin under conditions of an ice-free Barents Sea

To account for tidal variations in the regional climate of a water basin, we propose adding up the vertical eddy diffusivity, determined by wind and thermohaline forcings, and the diapycnal diffusivity, determined from the solution to the problem of the internal tidal wave (ITW) dynamics. This approach agrees with the approximation of “weak interaction” between turbulence of various origins. Then, the hydrothermodynamics equations are integrated with and without regard for ITW-induced diapycnal diffusion until a quasistationary solution is reached. Next we compare these solutions, found by using the 3D finite-element hydrostatic model QUODDY-4. This comparison shows that the contribution of tides to the formation of the Barents Sea climate in summer is not negligible with respect to certain hydrological characteristics. We present the fields of the dynamic topography of a free surface, surface current velocities, and seawater temperature and salinity at the depth of the pycnocline in the sea to illustrate the occurrence of tidal effects.     

Dynamics of surf-zone turbulence in a strong plunging breaker

The characteristics of turbulence created by a plunging breaker on a 1 on 35 plane slope have been studied experimentally in a two-dimensional wave tank. The experiments involved detailed measurements of fluid velocities below trough level and water surface elevations in the surf zone using a fibre-optic laser-Doppler anemometer and a capacitance wave gage. The dynamical role of turbulence is examined making use of the transport equation for turbulent kinetic energy (the k-equation). The results show that turbulence under a plunging breaker is dominated by large-scale motions and has certain unique features that are associated with its wave condition. It was found that the nature of turbulence transport in the inner surf zone depends on a particular wave condition and it is not similar for different types of breakers. Turbulent kinetic energy is transported landward under a plunging breaker and dissipated within one wave cycle. This is different from spilling breakers where turbulent kinetic energy is transported seaward and the dissipation rate is much slower. The analysis of the k-equation shows that advective and diffusive transport of turbulence play a major role in the distribution of turbulence under a plunging breaker, while production and dissipation are not in local equilibrium but are of the same order of magnitude. Based on certain approximate analytical approaches and experimental measurements it is shown that turbulence production and viscous dissipation below trough level amount to only a small portion of the wave energy loss caused by wave breaking. It is suggested that the onshore sediment transport produced by swell waves may be tied in a direct way to the unique characteristics of turbulent flows in these waves.     

非绝热加热对热带气旋径向非均匀结构的影响

利用平面极坐标系下无摩擦有外源(非绝热加热)的正压无辐散方程,将热带气旋的物理量分解成环境场和扰动,进而求出了热带气旋扰动的行波解,并分析了风场(切向、径向)和重力位势扰动场的径向非均匀松紧结构.表明:这种松紧结构与热带气旋所在纬度的科氏参数(f)、热带气旋的强度(Ω)、热带气旋扰动的圆频率(ω)、热带气旋扰动在θ方向的角波数(m)有关,且不同要素的松紧结构不尽相同;同时还受非绝热加热(Q₁)的影响,这种影响主要表现在使风场(切向、径向)呈内紧外松的非均匀分布.     

Transformation of a wave energy spectrum from encounter to absolute domain when observing from an advancing ship

The article presents a practical approach to transform a wave energy spectrum from encounter domain to absolute domain. This problem has its specific relevance, when shipboard sea state estimation is conducted by the wave buoy analogy; notably for some particular implementation solving for the sea state directly in the encounter domain. In this context, the encounter domain is that observed from a ship when it advances in a seaway, whereas the absolute domain is that corresponding to making observations from a fixed point in the inertial frame. Spectrum transformation can be uniquely carried out if the ship sails “against” the waves (beam to head sea) but in following sea conditions there exists no unique solution to the problem. Instead, a reasonable approach valid for practical engineering must be applied, and the article outlines one viable solution that can be used to transform a wave spectrum from encounter to absolute domain. Specifically, two pseudo algorithms are presented, and good performance is achieved with both algorithms when they are tested at different operational scenarios.     

平直斜坡上破波带内质量输移流对污染物输移影响的数值研究

破波带内外都有质量输移流存在,其对破波带内污染物输移有怎样的影响,需要进一步深入研究。本文基于实验以及考虑质量输移流的对流扩散数学模型研究了平直斜坡上破波带内质量输移流对污染物输移影响。数学模型包括波浪模型、近岸流模型以及对流扩散模型。首先建立了破波带内污染物输移数学模型,其中波浪场基于波能守恒方程来计算,波导流场基于Longuet-Higgins提出的辐射应力模拟,污染物对流扩散方程中考虑了质量输移流的影响,并利用算例验证该数学模型。其次简要介绍了平直斜坡上破波带内污染物输移实验,并分析了污染物输移特性。连续投放污染物会形成污染带,本文分析了两种波况下不同时刻污染带与岸线夹角的变化,以及污染物在垂直岸线和沿岸线方向的输移速度,结果表明对两种波况来说在初始10-40s污染团向岸线方向输移速度分别约为0.05m/s、0.017m/s,之后速度分别减小为0.001m/s、0.011m/s。数值模拟结果与实验结果比较表明：考虑质量输移流的模拟结果与实验更为吻合。因而,通过实验以及数模研究表明破波带内质量输移流对破波带内污染物在垂直岸线方向的输移有重要影响,而对沿岸方向的输移则影响较小。     

Numerical simulation of wave overtopping at coastal dikes and low-crested structures by means of a shock-capturing Boussinesq model

In this paper, a shock-capturing numerical model, based on the combined solution of Boussinesq and nonlinear shallow water equations is applied to the simulation of wave runup, overtopping and wave train propagation over impermeable, emerged and low-crested, structures. In order to improve the performances of the scheme at wet–dry interfaces, a numerical treatment is introduced to provide well-balancing of advective fluxes and source terms. One- and two-dimensional test cases are presented to validate the performances of the model under both regular and irregular wave conditions.     

NearCoM-TVD — A quasi-3D nearshore circulation and sediment transport model

The newly developed nearshore circulation model, SHORECIRC, using a hybrid finite-difference finite-volume TVD-type scheme, is coupled with the wave model SWAN in the Nearshore Community Model (NearCoM) system. The new modeling system is named NearCoM-TVD and the purpose of this study is to report the capability and limitation of NearCoM-TVD for several coastal applications. For tidal inlet applications, the model is verified with the semi-analytical solution of Keulegan (1967) for an idealized inlet-bay system. To further evaluate the model performance in predicting nearshore circulation under intense wave–current interaction over complex bathymetry, modeled circulation patterns are validated with measured data during RCEX field experiment (MacMahan et al., 2010). For sediment transport applications, two sediment transport models are applied to predict three sandbar migration events at Duck, NC, during August to October 1994 (Gallagher et al., 1998). The model of Kobayashi et al. (2008) incorporates wave-induced onshore sediment transport rate as a function of the standard deviation of wave-induced horizontal velocities. The modeled beach profile evolution for two offshore events and one onshore event agrees well with the measured data. The second model investigated here combines two published sediment transport models, namely, the total load model driven by currents under the effect of wave stirring (Soulsby, 1997) and the wave-driven sediment transport model due to wave asymmetry/skewness (van Rijn et al., 2011). The model study with limited field data suggests that the parameterization of wave stirring is appropriate during energetic wave conditions. However, during low energy wave conditions, the effect of wave stirring needs to be re-calibrated.     

Ekman Convective Layer Flow of a Viscous Incompressible Fluid

Analytical solutions for generalizing the Ekman stationary flow of a viscous incompressible fluid in an infinite layer are obtained. The solution of an overdetermined system of the Oberbeck–Boussinesq equations is considered. It is suggested to use a class of exact solutions for this problem. It is shown that the structure of the solutions allows one to preserve the advective derivative in the heat-conductivity equation; this makes it possible to model the stratification of the temperature and pressure fields and describe the oceanic countercurrents.     

半潮堤前的反射形态与时均流速场分析

采用模型试验和数值模拟研究了不同水深工况下半潮堤前的反射形态及时均流速场。基于Hilbert变换建立了叠合波的时频分离技术,同时获取了入射波和反射波的波面过程及相位关系,通过试验数据证明其适用于不同反射程度的波浪信号分析。不同水深工况下,半潮堤前形成了部分立波系统,腹点和节点分别以四分之一波长的偶数倍和奇数倍交替增加。半潮堤前底床水质点水平速度包络图与波面包络图相差四分之一周期的相位,水平速度的极大值和极小值分别出现在波面包络图的节点和腹点,意味着节点处易形成冲刷,腹点处易形成淤积。3种工况的周期平均速度场均在迎浪基床上方的堤脚处存在一个小型环流系统,可能引起局部冲刷,此处需加强防护。淹没工况下,半潮堤前的周期平均速度场形成一个大型环流系统,表层水流向堤后,中下层水流向海侧,意味着底床悬起的泥沙很可能向离岸方向流失。     

Quantification of changes in current intensities induced by wave overtopping around low-crested structures

The phenomenon of overtopping is traditionally studied for well-emerged harbour structures and often focuses on safety and stability. In this paper laboratory tests are presented and analysed to sharpen the hypothesis that overtopping is capable of changing the horizontal circulation pattern around low-crested structures. A unique data set from laboratory experiments was acquired in the wave basin at Delft University of Technology. The experiments were performed using an emerged impermeable low-crested structure (three freeboards and three different wave conditions for each freeboard) and yielded nine different combinations of set-up and overtopping driving forces. Using this information it was possible to quantify the changes in cross-shore and longshore velocity induced by the overtopping and the set-up changes under the different freeboard and wave conditions described. It is found that overtopping enhances the outgoing flows (longshore velocities parallel to the structure) away from the lee side of the structure and dampens the water level gradient driven flow towards the structure.     

A practical alternative to the “mild-slope” wave equation

The “mild-slope” equation which describes wave propagation in shoaling water is normally expressed in an elliptic form. The resulting computational effort involved in the solution of the boundary value problem renders the method suitable only for small sea areas. The parabolic approximation to this equation considerably reduces the computation involved but must omit the reflected wave. Hence this method is not suited to the modelling of harbour systems or areas near to sea walls where reflections are considerable. This paper expresses the “mild-slope” equation in the form of a pair of first-order equations, which constitute a hyperbolic system, without the loss of the reflected wave. A finite-difference numerical scheme is described for the efficient solution of the equations which includes boundaries of arbitrary reflecting power.     

On an Advective Model of a Ventilated Thermocline

Oceanology - A model of an advective thermocline is proposed for the case of continuously stratified Sverdrup circulation with a ventilated layer caused by the divergence of flows in the Ekman...     

New model to determine forces at on-bottom slender pipelines

The present paper proposes a numerical model to determine horizontal and vertical components of the hydrodynamic forces on a slender submarine pipeline lying at the sea bed and exposed to non-linear waves plus a current. The new model is an extension of the Wake II type model, originally proposed for sinusoidal waves (Soedigdo et al., 1999) and for combined sinusoidal waves and currents (Sabag et al., 2000), to the case of periodic or random waves, even with a superimposed current. The Wake II type model takes into account the wake effects on the kinematic field and the time variation of drag and lift hydrodynamic coefficients. The proposed extension is based on an evolutional analysis carried out for each half period of the free stream horizontal velocity at the pipeline. An analytical expression of the wake velocity is developed starting from the Navier–Stokes and the boundary layer equations. The time variation of the drag and lift hydrodynamic coefficients is obtained using a Gaussian integration of the start-up function. A reduced scale laboratory investigation in a large wave flume has been conducted in order to calibrate the empirical parameters involved in the proposed model. Different wave and current conditions have been considered and measurements of free stream horizontal velocities and dynamic pressures on a bottom-mounted pipeline have been conducted. The comparison between experimental and numerical hydrodynamic forces shows the accuracy of the new model in evaluating the time variation of peaks and phase shifts of the horizontal and vertical wave and current induced forces.     

A second-order solution of waves passing porous structures

Only linear theoretical analyses of wave interaction with porous structures exist, mainly due to both the complexities of flows inside the porous medium, and the mathematical inhomogeneous boundary-value problem. Since the hydrodynamic flow mechanism is non-linear a non-linear analysis can better describe the characteristic nature of the problem. In this paper, a generalized potential theory is used to describe both the internal and external water flows. An implicit non-linear model is used to describe flow mechanism inside the porous medium. The perturbation method is used to solve the problem analytically up to the second order. The second-order solution is decomposed into time-dependent and time-independent parts. And, correspondingly, the inhomogeneous boundary-value problems are solved analytically. In the analysis, the second-order characteristics of the problem, including the dispersion equation, wave numbers and friction coefficient, as well as wave reflection and transmission, are investigated in detail. It is shown that the mode swapping of the second-order wave numbers only occurs among the evanescent modes. The second-order friction effects become important in shallow-water cases. The comparison of the results of present theory with experimental results shows that the second-order solution is good correction to the linear theory.     

Three dimensional application of the complementary mild-slope equation

The complementary mild-slope equation (CMSE) is a depth-integrated equation, which models refraction and diffraction of linear time-harmonic water waves. For 2D problems, it was shown to give better agreements with exact linear theory compared to other mild-slope (MS) type equations. However, no reference was given to 3D problems. In contrast to other MS-type models, the CMSE is derived in terms of a stream function vector rather than in terms of a velocity potential. For the 3D case, this complicates the governing equation and creates difficulties in formulating an adequate number of boundary conditions. In this paper, the CMSE is re-derived using Hamilton's principle from the Irrotational Green–Naghdi equations with a correction for the 3D case. A parabolic version of it is presented as well. The additional boundary conditions needed for 3D problems are constructed using the irrotationality condition. The CMSE is compared with an analytical solution and wave tank experiments for 3D problems. The results show very good agreement.     

An Analytical Solution for Nearshore Circulation Driven by Focused/Defocused Waves

An offshore shoal or bar refracts ocean surface waves and causes wave focusing/defocusing on the adjacent beach.Wave focal patterns characterized by alongshore variations in wave height, wave angle, and breaking location induce alongshore non-uniformities of wave setup and nearshore circulation, e.g., rip currents and alongshore currents, in the surfzone. A simplified analytic model for nearshore circulation generated by focused/defocused waves on a planar beach is developed and theoretical solutions are obtained using transport stream function and perturbations in alongshore distributions of wave height and wave angle at the breaker line. The analytic model suggests that alongshore currents are strongly affected by a pair of counter-rotating vortices generated shoreward of the wave focal zone. The vortices are persistent, and their strengths depend on the amplitudes of alongshore variations in wave height and wave angle. The alongshore gradient in wave height tends to intensify the vortices while the convergence of wave angle tends to weaken the vortices. Divergent flows associated with the vortices in the surfzone are intense,strengthening alongshore currents in the downstream of the wave focal zone and weakening alongshore currents or causing flows reversal in the upstream. Alongshore currents are modulated by rip currents associated with the wave focusing/defocusing patterns.     

Effects of currents on interpretation of sub-surface pressure spectra

Ocean waves are often measured using sub-surface pressure transducers. The transfer function, relating pressure fluctuations to variations in water-surface elevation, is usually based on linear wave theory, with an empirical correction factor being applied to account for non-linearities.This paper is concerned with the determination of surface-elevation spectra from pressures recorded beneath irregular waves travelling on a current. Predicted spectra are compared with spectral densities calculated from measurements using a surface-piercing wave gauge. Results show that significant errors arise if the Doppler effect, associated with the presence of the current, is ignored. The importance of selecting appropriate values of the empirical correction factor is also demonstrated.