Hydrodynamic performance of vertical porous structures under regular waves

The hydrodynamic efficiency of the vertical porous structures is investigated under regular waves by use of physical models. The hydrodynamic efficiency of the breakwater is presented in terms of the wave transmission (kt ), reflection (kr) and energy dissipation (kd ) coefficients. Different wave and structural parameters affecting the breakwater efficiency are tested. It is found that, the transmission coefficient (kt ) decreases with the increase of the relative water depth (h/L), the wave steepness (Hi/L), the relative breakwater widths (B/L, B/h), the relative breakwater height (D/h), and the breakwater porosity (n). The reflection coefficient (kr) takes the opposite trend of kt when D/h=1.25 and it decreases with the increasing h/L, Hi/L and B/L when D/h 1.0. The dissipation coefficient (kd) increases with the increasing h/L, Hi/L and B/L when D/h 1.0 and it decreases when D/h=1.25. In which, it is possible to achieve values of kt smaller than 0.3, krlarger than 0.5, and kd larger than 0.6 when D/h=1.25, B/h=0.6, h/L 0.22, B/L 0.13, and Hi/L 0.04. Empirical equations are developed for the estimation of the transmission and reflection coefficients. The results of these equations are compared with other experimental and theoretical results and a reasonable agreement is obtained.     

Effect of under connected plates on the hydrodynamic efficiency of the floating breakwater

In this paper, the hydrodynamic efficiency of a floating breakwater system is experimentally studied by use of physical models. Regular waves with wide ranges of wave heights and periods are tested. The efficiency of the breakwater is presented as a function of the wave transmission, reflection, and energy dissipation coefficients. Different parameters affecting the breakwater efficiency are investigated, e.g. the number of the under connected vertical plates, the length of the mooring wire, and the wave length. It is found that, the transmission coefficient kt decreases with the increase of the relative breakwater width B/L, the number of plates n and the relative wire length l/h, while the reflection coefficient kr takes the opposite trend. Therefore, it is possible to achieve kt values smaller than 0.25 and kr values larger than 0.80 when B/L is larger than 0.25 for the case of l/h-1.5 and n=4. In addition, empirical equations used for estimating the transmission and reflection coefficients are developed by using the dimensionless analysis, regression analysis and measured data and verified by different theoretical and experimental results.     

Testing and calibrating parametric wave transformation models on natural beaches

To provide coastal engineers and scientists with a detailed inter-comparison of widely used parametric wave transformation models, several models are tested and calibrated with extensive observations from six field experiments on barred and unbarred beaches. Using previously calibrated (“default”) values of a free parameter γ, all models predict the observations reasonably well (median root-mean-square wave height errors are between 10% and 20%) at all field sites. Model errors can be reduced by roughly 50% by tuning γ for each data record. No tuned or default model provides the best predictions for all data records or at all experiments. Tuned γ differ for the different models and experiments, but in all cases γ increases as the hyperbolic tangent of the deep-water wave height, H_o. Data from two experiments are used to estimate empirical, universal curves for γ based on H_o. Using the new parameterization, all models have similar accuracy, and usually show increased skill relative to using default γ.     

The effect of relative crest submergence on wave breaking over submerged slopes

Experiments were performed in a wave flume to measure the intensity, transmission and reflection of waves breaking over a submerged reef with an offshore gradient of 1:10. The results demonstrate that the relative water depth over the reef crest (h_c/H_o) is a dominant factor affecting the breaking characteristics. In particular it is found that as the relative crest submergence is reduced, there is a considerable increase in the intensity of wave breaking over the reef that can be quantified through measurements of the air cavity enclosed beneath the plunging jet. It is also shown that there is a corresponding decrease in wave transmission and reflection as the submergence is reduced.     

Shoreline variability via empirical orthogonal function analysis: Part II relationship to nearshore conditions

The method of empirical orthogonal function (EOF) or principal component analysis (PCA) was used to investigate the spatial and temporal variability of shoreline data sets from Duck, North Carolina, the Gold Coast, Australia, and the United States Pacific Northwest. In the present work, an attempt is made to relate the individual modes of shoreline variability identified by the EOF analyses to select parameterizations of the nearshore environment. The parameters considered include the wave energy (E), the cross-shore and longshore wave energy fluxes (F_x and F_y), the wave steepness (H_o/L_o), the non-dimensional fall velocity parameter (Ω), the profile parameter (P), the surf-similarity parameter (ζ), and a surfzone Froude number (F_r). Correlation analyses were used to evaluate the linear relationship between each of these parameters and the temporal eigenfunctions, c_k(t), associated with individual modes of shoreline change. Typically, strong correlations were observed between longshore uniform modes and the monthly means of several of the nearshore parameters.     

X-波段雷达近海海浪频谱反演的神经网络模型

X-波段雷达作为国内海浪观测的一种新工具,在海浪频谱获取和有效波高反演方面仍存在较多问题.本文利用非线性回归方法,将现场实测浮标数据频谱和雷达一维图像谱分别与标准频谱模型进行拟合,发现浮标频谱和一维图像谱具有标准频谱的特征,能够较准确地获取相应的谱参数.提出了建立由雷达一维图像谱参数反演海浪频谱参数的神经网络模型,同时在模型中加入影像序列信噪比,进而反演有效波高,并将反演结果与现场实测数据和传统算法(建立影像序列信噪比与有效波高之间的线性回归方程)进行了对比,结果表明,获取谱参数的误差和反演有效波高的平均误差在20％以内,而传统算法计算有效波高平均误差在20％以上.     

Wave set-up on coral reefs. 1. Set-up and wave-generated flow on an idealised two dimensional horizontal reef

Wave set-up may be significant in determining water levels on coral reefs particularly in microtidal environments and hence is an important factor for the design of reef-top structures and for the stability of reef-top islands. Laboratory experiments have been made on a two dimensional model of an idealised horizontal reef under two different conditions corresponding to a fringing reef (or closed lagoon) situation and a platform reef (or open lagoon) situation. Both wave set-up on the reef-top and the wave-generated flow across the reef were measured and related to wave and tide level conditions.All other factors being the same, wave set-up is greatest at low tide levels whereas wave-generated flow is greater at higher tide levels. The magnitude of the set-up on a platform reef with a wave-generated flow is less than on a fringing reef without any net flow by an amount equal to the velocity head of the flow across the reef. Dimensionless parameters and q/√gH_o³ are found to be functions of relative submergence parameters h_r/H_o or . For values of ( ) H_o > 1 waves break on the reef-top and radiation stress theory can be used to calculate set-up. For ( )H_o < 0.7 waves break on the reef-face and set-up is determined by broadcrested weir control at the reef-edge. (The symbols are defined as follows: g is gravitational acceleration; h_r is still water depth over horizontal reef-top; H_o is offreef wave height (equivalent deep water value); q is discharge per unit length of reef edge; T is wave period and is maximum wave set-up on reef-top.)     

随机波浪中畸形波在三维岛礁地形上的试验研究

在试验水池中，开展了波浪在岛礁地形上演化问题的研究。首先在实验水池中建立了西太平洋某岛礁地形的模型，然后采用改进的JONSWAP谱，由造波机产生不同周期、波高的随机波浪。试验中观察到了不同类型畸形波生成的过程及不同波面形态的畸形波。对偏度、峰度及水深与畸形波要素H_m/H_s（H_m表示波列中的最大波高， H_s为有效波高）的关系进行了详细的分析，同时，对畸形波波高H_fr与偏度的关也进行了分析。通过对试验结果分析，发现峰度与畸形波要素i>H_m/H_s呈正相关， H_fr增大时相应的偏度也会呈现增大的趋势。此外，水深的变化剧烈时（如斜坡、海山位置）有助于畸形波的发生。     

Profiles of fully developed (Airy) waves in different water depths

Airy waves have a sinusoidal profile in deep water that can be modeled by a time series at any point x and time t, given by η(x,t) = (H_o/2) cos[2πx/L_o − 2πt/T_w], where H_o is the deepwater height, L_o is the deepwater wavelength, and T_w is the wave period. However, as these waves approach the shore they change in form and dimension so that this equation becomes invalid. A method is presented to reconstruct the wave profile showing the correct wavelength, wave height, wave shape, and displacement of the water surface with respect to the still water level for any water depth.     

Wave run-up on slender piles in design conditions — Model tests and design rules for offshore wind

Wave run-up on foundations is a very important factor in the design of entrance platforms for offshore wind turbines. When the Horns Reef 1 wind turbine park in Denmark was designed the vertical wave run-up phenomenon was not well known in the industry, hence not sufficiently considered in the design of Horns Reef 1. As a consequence damage was observed on the platforms. This has been the situation for several sites and design tools for platform loads are lacking. As a consequence a physical model test study was initiated at Aalborg University to clarify wave run-up on cylindrical piles for different values of diameter to water depth ratios (D/h) and different wave heights to water depth ratios (H/h) for both regular and irregular waves. A calculation model is calibrated based on stream function theory for crest kinematics and velocity head stagnation theory. Due to increased velocities close to the pile an empirical factor is included on the velocity head. The evaluation of the calculation model shows that an accurate design rule can be established even in breaking wave conditions. However, calibration of a load model showed that it was necessary to increase the run-up factor on the velocity head by 40% to take into account the underestimation of run-up for breaking or nearly breaking waves given that they produce thin run-up wedges and air entrainment, two factors not coped with by the measurement system.     

Shoreline response to a single shore-parallel submerged breakwater

Submerged breakwaters (SBWs) are becoming a popular option for coastal protection, mainly due to their low aesthetic impact on the natural environment. However, SBWs have rarely been employed for coastal protection in the past and therefore, their efficacy remains largely unknown. The main objective of the present study was to investigate the structural and environmental conditions that govern the mode of shoreline response (i.e shoreline erosion vs shoreline accretion) to SBWs. The relative importance of the key structural and environmental parameters governing the response mode to a single shore parallel SBW is investigated through a combination of theoretical analysis and numerical modelling. Using physical considerations, a theoretical response-function model is derived under several simplifying assumptions including parallel depth contours, linear wave theory, shore normal waves, and no wave–current interaction. Numerical modelling is undertaken with the Mike21 model suite to simulate the depth averaged velocity fields (without morphological updating) due to waves acting on a single shore-parallel SBW located on a schematised beach with parallel depth contours. In total 92 coupled wave–current simulations were undertaken. The results indicate that the mode of shoreline response to the SBW can be expressed in terms of the two non-dimensional parameters h_B/H₀ and (s_B/h_B)^3/2(L_B/h_B)²(A³/h_B)^1/2 (variables defined in the text).     

On the estimation of surface gravity waves from subsurface pressure records for estuarine basins

According to small-amplitude theory, the surface gravity-wave spectrum can be estimated from a subsurface pressure-fluctuation spectrum by applying a factor (K) that compensates for the attenuation of surface-wave amplitude as the depth below the water surface and the wave frequency increase.There are a number of factors, however, that cause K to be inaccurate over a large portion of the spectrum's frequency range. Numerous attempts have been made to derive an empirical correction factor (n) that could be applied to K to provide a better estimate of the surface-wave spectrum. This paper evaluates some of these empirical factors, specifically for use in an estuarine environment, and recommends Graces' (1978) equation for n as a function of the non-dimensional frequency parameter kh (where $\text{k =}\text{2π}\text{L}$ is the local wavenumber, h the local depth and L the wavelength).The paper also evaluates the maximum limit (K_max) on the magnitude of K suggested by Esteva & Harris (1970), where relative depth $\text{d}\text{h}$ (d is the pressure transducer height above the bottom) and k_oh (a parameter directly related for large values of kh to wave frequency by the dispersion relation) are the independent variables. The choice of K_max may be made unimportant if d is selected beforehand using an equation (Knowles, 1981a) for the minimum $\text{d}\text{h}$ limit affected by the choice of K_max.     

Motion responses of barge carrying liquid tank

The interaction between the liquid sloshing in a rectangular tank equipped inside the barge and the barge responses has been investigated through a comprehensive experimental program. The barge was subjected to both regular and random wave excitations under beam sea condition. Three relative fill levels (h_s/l) with liquid fill depth (h_s) to length of tank (l) ratio of 0.163, 0.325 and 0.488 were considered. In addition, the barge responses of equivalent dry weight condition corresponding to each fill level were measured to understand the influence of sloshing. While the excitation wave frequency equals to first mode natural sloshing frequency, a noticeable decrease in the sway response has been observed. However, the effect of sloshing oscillation on the heave response is insignificant. A split up of roll resonance was observed for the aspect ratio of 0.163 due to the coupling effect of roll motion and sloshing.     

A morphodynamic model to simulate the seasonal closure of tidal inlets

Seasonally open tidal inlets usually occur in microtidal, wave-dominated coastal environments where strong seasonal variations of streamflow and wave climate are experienced. These inlets are closed to the ocean for a number of months every year due to the formation of sand bars across their entrances. The annual closure of these inlets inhibits ocean access for boats and could also cause deterioration of water quality in the estuary/lagoon connected to the inlet. As these estuaries/lagoons are commonly used as harbours or recreational facilities there is increased interest in keeping the inlets permanently open. A process-based numerical model capable of simulating inlet closure is invaluable in terms of identifying the natural processes governing inlet closure. As a further step, this type of model could also be used to determine the effect of any proposed engineering solutions to keep the inlet open on the adjacent beaches. A morphodynamic model capable of simulating the seasonal closure of inlets, which includes both longshore (LST) and cross-shore transport (CST) processes, was developed in this study. Application of the model to two idealised scenarios indicated that cross-shore processes govern inlet behaviour when LST rates were low. The Dean's criterion [Dean, R.G., 1973. Heuristic models of sand transport in the surf zone. Proc. Conf. on Eng. Dynamics in the Surf Zone, Sydney, pp. 208–214.] for on–offshore transport was employed to show that, for small offshore wave incidence angles, onshore transport aided inlet closure when the offshore wave steepness (H_o/L_o) was less than the critical wave steepness (H_o/L_o)_crit, while offshore transport helped to keep the inlet open when (H_o/L_o) was greater than (H_o/L_o)_crit. LST was found to be the dominant process leading to inlet closure when (H_o/L_o) was much larger than (H_o/L_o)_crit or when the offshore wave incidence angle was large.     

Experimental study of wave–wave nonlinear interactions using the wavelet-based bicoherence

The wavelet-based bicoherence, which is a new and powerful tool in the analysis of nonlinear phase coupling, is used to study the nonlinear wave–wave interactions of breaking and non-breaking gravity waves propagating over a sill. Two cases of mechanically generated random waves based on Jonswap spectra are used for this purpose. Values of relative depth, k_ph (k_p is the wave number of the spectral peak and h is the water depth) for this study range between 0.38 and 1.22. The variations of wavelet-based total bicoherence for the test cases indicate that the degree of quadratic phase coupling increases in the shoaling region consistent with a wave profile that is pitched shoreward, relative to a vertical axis as seen in the experiments, but decreases in the de-shoaling region. For the non-breaking case, the degree of quadratic phase coupling continues to increase until waves reach the top of the sill. Breaking waves, however, achieve their highest level of quadratic phase coupling immediately before incipient breaking and the degree of phase coupling decreases sharply following breaking. In addition the wavelet-based bicoherence spectra provide evidence of the harmonics' growth which is reflected in the energy spectra. The bicoherence spectra also show that quadratic phase coupling between modes within the peak frequency as well as between modes of the peak frequency and its higher harmonics are dominant in the shoaling region, even though there are relatively high levels of quadratic phase coupling occurring between other frequencies. Furthermore, using the temporal resolution property of the wavelet-based bicoherence, we find that the quadratic wave interactions occur more readily during segments of time with large change of wave amplitude, rather than those segments having large wave amplitudes, but small gradients in amplitude.     

Wave evolution over submerged sills: tests of a high-order Boussinesq model

A Boussinesq model accurate to O(μ)⁴, μ=k₀h₀ in dispersion and retaining all nonlinear effects is derived for the case of variable water depth. A numerical implementation of the model in one horizontal direction is described. An algorithm for wave generation using a grid-interior source function is derived. The model is tested in its complete form, in a weakly nonlinear form corresponding to the approximation δ=O(μ²), δ=a/h₀, and in a fully nonlinear form accurate to O(μ²) in dispersion [Wei, G., Kirby, J.T., Grilli, S.T., Subramanya R. (1995). A fully nonlinear Boussinesq model for surface waves: Part 1. Highly nonlinear unsteady waves. J. Fluid Mech., 294, 71–92]. Test cases are taken from the experiments described by Dingemans [Dingemans, M.W. (1994). Comparison of computations with Boussinesq-like models and laboratory measurements. Report H-1684.12, Delft Hydraulics, 32 pp.] and Ohyama et al. [Ohyama, T., Kiota, W., Tada, A. (1994). Applicability of numerical models to nonlinear dispersive waves. Coastal Engineering, 24, 297–313.] and consider the shoaling and disintegration of monochromatic wave trains propagating over an elevated bar feature in an otherwise constant depth tank. Results clearly demonstrate the importance of the retention of fully-nonlinear effects in correct prediction of the evolved wave fields.     

Hydrodynamic efficiency of partially immersed caissons supported on piles

The efficiency of the breakwater, which consists of caissons supported on two or three rows of piles, was studied using physical models. The efficiency of the breakwater is presented as a function of the transmission, reflection and the wave energy dissipation coefficients. Regular waves with wide ranges of wave heights and periods and constant water depth were used. Different characteristics of the caisson structure and the supporting pile system were also tested. It was found that, the transmission coefficient (k_t) decreases with increasing the relative breakwater draft D/L, increasing the relative breakwater width B/h, and decreasing the piles gap-diameter ratio G/d. It is possible to achieve k_t values less than 0.25 when D/L≥0.1. The reflection coefficient takes the opposite trend especially when D/L≤0.15. The proposed breakwater dissipates about 10-25% of the incident wave energy. Also, simple empirical equations are developed for estimating the wave transmission and reflection. In addition, the proposed breakwater model is efficient compared with other floating breakwaters.     

Discussion of “Analytic solution of long wave propagation over a submerged hump” by Niu and Yu (2011)

Recently, Niu and Yu (2011) presented an analytical solution of the long wave refraction by a submerged circular hump. The geometry of the hump was assumed to be axi-symmetric and the water depth over the hump region was described by a positive constant plus a power function of the radial distance with an arbitrary value of the power exponent, i.e., h = h₁ + βr^s, where h₁ is the water depth at the crest of the hump. Their general hump is an extension of the paraboloidal hump (i.e., s = 2) studied by Zhang and Zhu (1994) and Zhu and Harun (2009). Because of this extension in the topography of the hump, the problem to seek a general analytical solution to the long-wave equation becomes much more complicated and the solution technique need to be more skillful, especially for the case with the exponent s being a rational, see Eq. (17) in Niu and Yu (2011).