Wave Reflection from Nearshore Depressions (original) (raw)
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Coastal Engineering, 2001
The linear Mild-Slope equation (MSE) is examined in the limit of very shallow water. This is done by means of a series comparison with the more 'exact' linear classical theory (E) valid over arbitrary uniform slopes and known to have a "minimum norm" solution basis pair respectively regular and logarithmically singular at the shore line. It is shown that the agreement between E and MSE is exact for the first three terms for the regular wave and the first two for the singular wave. It is further demonstrated, by application of this example, that the Mild-Slope equation represents a better approximation than does the classical linearised shallow water equation (SWE) in the case of extremely small depth. In particular, if solutions to each are tuned to the same finite wave height at the shore line, then MSE predicts the correct curvature of wave height there whereas SWE does not. The work of Booij [1983] is supported and varied to allow performance on very steep beds to be tested against exact values rather than those of numerical simulation. Those tests are carried out both as Boundary Value Problems (Scheme A) and Initial Value Problems (Scheme B) with matching results on global error. Methods are found of specifying phase and group velocity which are consistent with linear wave beach theory and lead to improvements in solving the mild slope equation over steep flat beaches. The improvements are found generally superior, in the case considered, to those of some recently developed 'modified' and 'extended' MSEs. Finally, it is demonstrated, and confirmed by both asymptotic theory and calculation, that the addition of evanescent modes constitutes improvement only in intermediate depths and is not recommended in depths of the order of only a wavelength on a steep (e.g. 45 o) beach.
Obliquely incident wave reflection and runup on steep rough slope
Journal of Coastal Research, 2001
A two-dimensional, time-dependent numerical model for finite amplitude, shallow-water waves with arbitrary incident angles is developed to predict the detailed wave motions in the vicinity of the still waterline on a slope. The numerical method and the seaward and landward boundary algorithms are fairly general but the lateral boundary algorithm is limited to periodic boundary conditions. The computed results for surging waves on a rough 1:2.5 slope are presented for the incident wave angles in the range 0-80°. The time-averaged continuity, momentum and energy equations are used to check the accuracy of the numerical model as well as to examine the cross-shore variations of wave setup, return current, longshore current, momentum fluxes, energy fluxes and dissipation rates. The computed reflected waves and waterline oscillations are shown to have the same alongshore wavelength as the specified nonlinear incident waves. The computed variations of the reflected wave phase shift and wave runup are shown to be consistent with available empirical formulas. More quantitative comparisons will be required to evaluate the model accuracy.
Procedia Engineering, 2016
This paper presents and discusses the results of experimental investigations using both vertical and sloping seawalls configurations to determine the optimal wave reflection characteristics of seawalls for protecting beaches against erosion under a variety of hydrodynamic conditions. The different experiments include both of rectangular or triangular serrated blocks and slotted seawalls with or without triangular serrations as energy dissipaters. The linear wave theory is utilized. Moreover, the Dalrymple method is considered to predict the ordinates of the resultant standing wave due to the partial wave reflection. Using the dimensional analysis, lab measurements, and SPSS, predictive formulae are proposed to predict the reflection coefficient for the five tested models by using SPSS software. The findings of the present investigation could be applied to optimize the design criteria of shore protection structures.
Low crested breakwaters are used to protect beaches from wave action. A series of large scale 3D laboratory experiments were carried out to investigate the effects in wave characteristics (disturbance) around a system of two non-parallel, permeable, low crested breakwaters by oblique wave incidence. The transmission and reflection coefficients were calculated and compared to existing formulae. The existing formulae, for both phenomena, transmission and reflection, had good relation in some cases. The angle of wave incidence did not show important influence for the wave transmission while is affected the wave reflection. The influence of wave period must be investigated in wave transmission and the influence of wave height in wave reflection.
Simulation of surface waves generated by an underwater landslide moving over an uneven slope
Russian Journal of Numerical Analysis and Mathematical Modelling, 2011
This paper is focused on the study of the effect of an underwater slope unevenness on the wave mode characteristics caused by the motion of a landslide over this slope. Using the simplest model representation of a landslide in the form of a rigid body, the authors consider two model reliefs, taking to some extent into account the peculiarities of the Mediterranean coast of Israel. The simulation of wave processes is performed within the framework of the equations of the shallow water theory. The results of the comparison of wave modes are discussed, the dependences of the characteristics of these modes on geometric and physical parameters of the studied phenomena, such as the landslide bedding depth, its length and thickness, the geometry of the slope, and the friction force are analyzed.