Reflected Wave Height Research Articles

Study on the hydraulic effect of Tesla valve structure on the end roadway of abandoned coal mine pumped storage

The use of abandoned mine for pumped storage has garnered significant attention as a novel energy storage technology. The hydraulics of utilizing underground reservoirs constructed in mine roadways represent a key issue for the application of abandoned mines in pumped storage. This study focuses on the practical situation of the Longdong Coal Mine in Jiangsu Province, China. By employing numerical simulation methods, the research investigates the phenomenon of water wave reflection at the end of the roadway in an abandoned mine pumped storage station, as well as the improvement effect of the Tesla valve structure on the reflected water waves. It was found that under the condition of the hydraulic turbine, the reflected wave height at the end of the roadway could reach 1–1.5 times that before reflection. The Tesla valve structure was found to be an effective means of reducing the water level height at the end of the roadway. The average water level was reduced by 0.55 m and 0.35 m under the two flow rates of 1 m/s and 1.4 m/s, respectively. Under the pump condition, the Tesla valve structure has little obstruction to the reverse flow of water. This study has to a certain extent addressed the issue of excessive wave height from water wave reflections at the end of the roadway, thereby enhancing the operational stability of the abandoned mine pumped storage station.

Roles of breaking and reflection in wave energy attenuation on the shoreface-nourished beach

Shoreface nourishments with the artificial sandbar are effective strategies to mitigate coastal erosions mainly by wave breaking and reflection. Thus, a better understanding of the contributions of breaking and reflection in wave energy loss is important for the prediction and description of the performance of the shoreface nourishment. Experiments are conducted in a wave flume, and data analysis is complemented with numerical simulations performed with a phase-resolving model. Both incident and reflected wave heights are well reproduced by the numerical model. The ratio of reflection to reflection-plus-breaking energy loss ranges from 4% to 11%, implying the dominant role of breaking-induced dissipation over reflection in present cases. The wave transmission coefficient decreases with the decrease in the bar crest depth and onshore implementation of the artificial sandbar. The trapezoidal artificial sandbar promotes an intense wave breaking over the berm width and is more effective in eliminating waves than the triangular artificial sandbar. Due to the erodible nature of the artificial sandbar, future works will consider the use of a hydro-morphological coupled approach to study the time-varying characteristics of wave breaking and reflection during morphological evolution.

Numerical Study on Compound-Slope Seawalls with Different Types of Protective Facings

Zeng, C.-S.; Zhan, J.-M., and Hu, W.-Q., 2022. Numerical study on compound-slope seawalls with different types of protective facings. Journal of Coastal Research, 38(1), 182–195. Coconut Creek (Florida), ISSN 0749-0208. The compound seawall is an important infrastructure to protect the coast effectively against tide and wave impacts. In this paper, a hybrid realizable k – ∊/laminar model and a volume of fluid interface capture method were used to study compound-slope seawalls with different types of protective facings. An analytical method was used to separate the incident wave and the reflected wave, and the numerical results for a compound-slope seawall with a hollow-block protective facing structure were verified by experimental results. The monitored wave surface, incident wave, and reflected wave data in the numerical simulation were compared with the experimental results, and the results show that the numerical model can simulate the interaction process of waves and compound-slope seawalls well. Furthermore, a series of numerical simulation studies on compound-slope seawalls under different protective facing structures with different wave heights, wave periods, water depths, and structure slopes was conducted. The results show that the hollow-block protective facings have a significant weakening effect on the reflected wave height, wave run-up, and wave force when the wave is moderate, which is important for the safety of seawall and onshore building structures.

Parametric modelling of nearshore wave reflection

The importance of wave reflection on nearshore hydrodynamics has recently been acknowledged by an increasing number of studies, yet it is difficult to simulate by the conventional parametric wave transformation models widely used in coastal engineering practice. Here, we propose a simple and efficient semi-empirical method to deal with this issue. The proposed method considers wave reflections resulted from both the underwater sloping bottom and the shoreline. The former is represented by a local underwater reflection-induced energy transfer term, based on a similarity analysis of the bulk wave reflection from equivalent sloping steps. The latter is calculated as the shoreline boundary condition by utilizing a simple empirical formula of wave reflection coefficient for an emerged coastal structure. Model verifications against the previous theoretical/empirical formulas, experimental data and numerical results suggest a promising predictability of the proposed method for the cross-shore reflected wave height transformation with various bathymetry configurations. Three different formulas of the bulk reflection coefficient for an underwater sloping step are tested and compared, indicating the importance of considering slope effects in these formulas. Model results also suggest that wave reflection along a steep beach profile can be quantitatively comparable to the shoreline reflection, and it is important to include reflections of both sources in numerical modelling. The simple method can be extended and incorporated into the existing operational parametric wave models. It serves as a possible approach to simulate wave reflection with low computational demand and reasonable accuracy, and to include wave reflection influences in studying coastal processes on a broad range of time and spatial scales.

Modeling studies on the behavior of single and double rubble mound breakwaters using genetic programming tool

Experimental investigation on wave transmission, reflection and dissipation characteristics of rubble mound breakwater models are time consuming and expensive. However, such studies are required for designing the rubble mound breakwaters for marine structures in an optimal condition. In order to overcome such problems many researchers used various soft computing techniques such as Artificial Neural Network (ANN), Adaptive Neuro Fuzzy Interference System (ANFIS), Genetic Programming (GP), Support Vector Machine (SVM) etc, in order to predict the design factors in the field of coastal engineering. The current work proposes Genetic Programming (GP) as a modeling tool to evolve mathematical models for the behavior of single and double breakwaters. Based on the detailed experimental data, GP models were performed to predict the reflected wave height (H r ), wave height on the breakwater (H 5 ) and transmitted wave height (H t ) by considering with and without trigonometric effects of those breakwaters. The quality of predictability of the present model is measured by the statistical parameter, RMSE (Root Mean Square Error). Since the waves were more complex in nature, it is very essential in considering the trigonometric function’s effect in the modeling aspects. It is evident that, the GP model accurately described the non linear complex effects.

Modeling impact pressure on the surface of porous structure by macroscopic mesh-free method

In this study, the impacting force on the face of porous structure is investigated by using the mesh-free macroscopic model. To achieve this, the mesh-free macroscopic approach of Moving Particle Semi-implicit method (MPS) is redeveloped. Firstly, a stabilization technique is used in the method to eliminate numerical noise. Secondly, the spatial discretization operators employ a porosity-based coefficient to account for the representative volume to model fluid flows in the porous media. More importantly, an improved numerical technique is proposed to overcome abrupt porosity change at the boundary between the porous and non-porous regions. The numerical model is validated by the dam-breaking waves through porous blocks and flows over porous weirs, in which the simulated free-surface profiles are in good agreement with experimental measurements. By applying the method, how the porosity and mean diameter of porous materials play a role in impacting pressure and wave height for dam-breaking flow through porous block is investigated. It is found that the porous materials with a larger porosity or larger mean diameter are able to easily permit water penetration through the porous media while the impacting pressure at the interface and reflected wave height can be reduced.

Approximate analytical solutions for a solitary wave interacting with a partially submerged porous wall

This study presents the development of an approximate analytical model for the investigation of the hydrodynamic interactions between a solitary wave and a partially submerged thin porous wall. Analytical solutions of the velocity potentials are derived according to the Fourier integral and solution superposition procedure along with satisfying the formed boundary and matching conditions. The free-surface elevations are also formulated. The hydrodynamic forces are computed by integrating the pressure distributions along the structural surfaces. Laboratory experiments were carried out to measure the free-surface elevations at locations upstream and downstream of the porous walls tested for the verification of the derived analytical solutions. It is demonstrated through result comparisons that the present analytical model can provide nicely matched predictions on the time varying transmitted waves including wave peak but slightly overestimated reflected wave heights. The horizontal hydrodynamic forces from the present analytical solutions are also in good agreement with other published experimental data when a special case of non-porous wall is considered. The variations of wave run-up, overall transmission coefficient, and maximum horizontal force under different conditions are presented and discussed to evaluate the performance of a partially submerged thin porous wall subject to an encountering solitary wave.

Uphill filling system for a bar-like casting

Bar-like sand mould tilted angle reduced free surface fluctuations. The primary and secondary reflected wave heights decreased with the scaling of Re0.8 and Re0.55, respectively. These heights were reduced by 54% and 51% when θ was increased from 0° to 5°. A larger tilted angle was found to generate an air cavity in the cast, the size of which was observed to vary with Reynolds number (Re). An optimised range of tilted angle (2°–3°) was proposed as a compromise to reduce the free surface fluctuations and maintain a perfect casting shape at the end of the filling stage.

Comparison of Artificial Neural Network and Regression Approaches for Evaluation of Hydrodynamic Performance of Quarter Circular Break Water

Quarter-circle Break Water (QBW) is a modified semi-circular breakwater, which are similar to caisson consists of a quarter circular surface facing incident waves, with horizontal bottom and a rear vertical wall and are generally placed on a rubble mound foundation. QBW may be constructed as emerged with and without perforations that may be one side or on either sides. By these perforations, the energy is dissipated owing to the formation of eddies and turbulence is created inside the hollow chamber. In this paper, the data collected from the experimental work carried out at National Institute of Technology, Surathkal is analysed by plotting the non-dimensional graphs of reflection coefficient, reflected wave height and incident wave height for various values of wave steepness. These values are used for prediction of QBW adopting Artificial Neural Network (ANN) and Regression (REG) approaches. In ANN, Multi-Layer Perceptron (MLP) and Radial Basis Function networks are considered for training the network data. Goodness-of-Fit (GoF) test viz., Kolmogorov-Smirnov test statistic and Model Performance Analysis (MPA) viz., correlation coefficient, mean absolute error and model efficiency are applied for checking the adequacy of ANN and REG approaches to the observed data. The results of GoF test and MPA indicates the MLP is better suited for evaluation of hydrodynamic performance of QBW.

Cross-Section Model Test on Shelter Effect of Pile Jetty on Revetment

Pile jetty is a typical type of wharf in construction of port engineering and was often built in front of revetment. The reflected wave height, wave overtopping and pressure were usually reduced because of the barrier effect of upper platform and piles. Cross-section model test was in common use for the verification of structure design. The shelter effect of pile jetty on revetment was tested through cross-section wave physical model. Model scale was 1:20. The results show that the shelter effect is fairly obvious in high design water level. The reduction percentage was 33% of reflected wave height, 50% of wave overtopping and 30-50% of wave loading.

Decomposition of Incident and Reflected Waves Using a Single Moving Wave Gauge

Abstract A new method of splitting regular or irregular waves into reflected and transmitted waves using a single moving wave gauge was developed. Water surface elevations at several locations and times were measured with one wave gauge, and the incident and reflected wave heights were obtained using the fast Fourier transformation and the least-square method. The accuracy and efficiency of the proposed method were validated using numerical tests for regular and irregular waves. Good agreement was observed between the target and the prediction values.

Using time-stack overlooking images to separate incident and reflected waves in wave flume

A time-stack wave image technique for separating incident and reflected waves in wave flumes is presented for normally incident waves propagating over a submerged breakwater with arbitrary 2D bathymetry. The wavenumber-frequency spectra from the time-stack wave image were used to determine the directions of incident and reflected waves, and the inverse Fourier transform method was used to derive the spatial variations and the time series of incident and reflected wave. The time series of separated incident and reflected wave and the wave reflection coefficients with the various wave phases between the incident waves and the reflected waves were fairly close to the values reported by Baldock and Simmonds, and the mean deviations in this study are slightly smaller than theirs. Furthermore, according to the profile of reflected wave heights, the reflection wave heights in this study case are not the constant, due to the incident waves encounter the various structures and sloping bathymetry. Additionally, existing 2D methods for separating incident and reflected waves over the sloping bathymetry; the water depths at the wave gauges must be known in order to calculate the linear shoaling coefficients. The present method, in contrast, does not require knowledge of the water depth, making it more practical than existing methods.

The Boundary Value Problem for the Nonlinear Shallow Water Equations

We propose an approximate analytical solution of the boundary value problem (BVP) for the nonlinear shallow waters equations. Our work, based on the Carrier and Greenspan [1] hodograph transformation, focuses on the propagation of nonlinear nonbreaking waves over a uniformly plane beach. Available results are briefly discussed with specific emphasis on the comparison between the Initial Value Problem and the BVP; the latter more completely representing the physical phenomenon of wave propagation on a beach. The solution of the BVP is achieved through a perturbation approach solely using the assumption of small waves incoming at the seaward boundary of the domain. The most significant results, i.e., the shoreline position estimation, the actual wave height and velocity at the seaward boundary, the reflected wave height and velocity at the seaward boundary are given for three specific input waves and compared with available solutions.

Simplified analytical solutions for wave interaction with absorbing-type caisson breakwaters

Simplified analytical solutions are presented to model the interaction of linear waves with absorbing-type caisson breakwaters, which possess one, or two, perforated or slotted front faces which result in one, or two, interior fluid regions (chambers). The perforated/slotted surfaces are idealized as thin porous plates. Energy dissipation in the interior fluid region(s) inside the breakwater is modelled through a damping function. Under the assumption of potential flow and linear wave theory a boundary-value problem may then be formulated to describe wave interaction with the idealized structure. A solution to this simplified problem may be obtained by an eigenfunction expansion technique and an explicit analytical expression may be obtained for the reflected wave height. Using the experimental work of previous authors, damping coefficients are determined for both single and double chamber absorbing-type caisson breakwaters. Based on the damping for a single perforated-wall breakwater, a methodology is proposed to enable the estimation of the damping coefficients for a breakwater with two chambers. The theoretical predictions of the reflection coefficients for the two-chamber structures using the present model are compared with those obtained from laboratory experiments by other authors. It is found that the inclusion of the damping in the interior fluid region gives rise to improved agreement between theory and experiment.

Moored structures in waves and currents

The present paper provides a brief review of the analysis of moored floating structures in waves and currents. A hydrodynamic analysis is required in order to predict wave and current effects on floating structures, and corresponding numerical models for determining transmitted and reflected wave heights, added masses, damping coefficients, and wave exciting forces are summarized. A mooring analysis is required in conjunction with the hydrodynamic analysis in order to calculate the restraint provided by the mooring system, as well as the structure motions, mooring line and anchor loads, and mooring line configurations. Various aspects of static, dynamic, and nonlinear responses are discussed and illustrated with example applications. Key words: coastal engineering, currents, floating structures, hydrodynamics, mooring forces, ocean engineering, wave forces, waves.

Estimation of incident and reflected waves in regular wave experiments

This paper presents a laboratory technique for measurement of reflected waves by a submerged horizontal plate. A simple method is proposed to decompose the composite wave record obtained from the wave reflection experiments in the wave flume. The data collected were used to compute the reflected wave height by means of two and three probe methods proposed by other investigators and compared with the directly computed reflected wave using the measured incident wave. The experiment was carried out for a horizontal plate of 1 m length spanning the full width of the flume with wave periods ranging from 0.8 to 1.8 sec with 0.1 sec increments and wave heights of 5, 10 and 15 cm. The methods using two and three probes with phase measurement yield better results than the three probe method without phase measurement, and in general they have a wider range of application. The method using three probes without the phase measurement generally fails due to numerical instability of the scheme. The results obtained by the proposed method are compared with the two and three probe methods and a comparative analysis of the four methods is presented and discussed.

Prediction of Field Swash And Reflected Wave Distributions

ABSTRACTA prediction model of the distribution of reflected wave height and period in the swash zone is developed. The model is combined with a swash distribution model which considers waves merging on the swash slope. Verifications using field data on several kinds of beaches show fairly good agreement.

Model Experiments on Waves and Nearshore Currents around Floating Wave Power Plant in Coastal Waters in Comparison with Detached Breakwater

The role of a floating wave power plant in the environmental control of coastal waters for coastal fisheries is discussed. An experimental investigation was carried out into the physical characteristics, i.e. waves and wave induced nearshore current around a model of a floating wave power plant on an inclined bottom in comparison with a model of a detached breakwater. The results are summarised as follows: (1) The floating wave power plant can be utilised for environmental conservation and the progress of coastal fisheries to create calm sea areas, improve water quality, control nearshore currents and provide power for aeration and dipping out of bottom waters. (2) The calm water area behind the floating power plant model where wave transmission ratio is less than 0.5 in three dimensional condition is almost the same as behind the detached breakwater. (3) The calm water area becomes wider near the shore line as the bottom slope becomes more gentle. (4) The reflected wave height at the front of the floating power plant model is much smaller than the detached breakwater. (5) Circulating current on free surfaces from the centre of the model to the outer side of the floating power plant model is dominant near water surface, it is dominant from the outer side to the centre of the model of the detached breakwater. In particular, strong currents toward the shore line just behind the floating wave power plant model was observed. (6) Water exchange near the floating wave power plant model is larger than the detached breakwater. It becomes larger as the bottom slope becomes more gentle for both models.

LABORATORY STUDY ON PERVIOUS CORE BREAKWATERS

Effects of permeable core layer installed in trapezoidal and rectangular breakwaters have been studied experimentally and analytically. As the materials for armour and core use of the lattice composed of circular cylinders was made in addition to rocks. Perforated plates were also applied as a kind of very thin core. Expermental results show that the reflected wave heights from breakwater could be reduced considerably by locating the core layer shoreward within it while core thickness controls the transmitted wave heights in the protected water area. Harmonic analysis about the water surface in lattice armour reveals that the second harmonic waves take a pattern of standing wave distribution having a node at the seaward face of breakwater. Thin perforated plates work success-- fully for reducing the transmitted wave heights when they are installed at the rear face of breakwater. An analytical approach to predict the transmission and the reflection coefficients is applied for the present experimental data and shown to be useful.

ESTIMATION OF INCIDENT AND REFLECTED WAVES IN RANDOM WAVE EXPERIMENTS

A technique to resolve the incident and reflected waves from the records of composite waves is presented. It is applicable to both regular and irregular trains of waves. Two simultaneous wave records are taken at adjacent locations, and all the amplitudes of Fourier components are analyzed by the FFT technique. The amplitudes of incident and reflected wave components are estimated from the Fourier components, and the incident and reflected wave spectra are constructed by smoothing the estimated periodograms. The wave resolution is effective in the range outside the condition of the gauge spacing being even integer of half wavelength. The ratio of incident and reflected wave energies in the effective resolution range is employed in estimating the overall reflection coefficient. The incident and reflected wave heights are estimated from the composite wave heights by energy consideration.