Study on Earthquake-Induced Sloshing Waves in Moraine-Dammed Lakes

Large surface water waves can be triggered in moraine-dammed lakes during earthquakes and may lead to the overtopping failure of moraine dams. In the earthquake-prone Himalayas, there are thousands of moraine-dammed lakes; their outburst may lead to catastrophic disasters (e.g. floods and debris flow), posing severe threats to humans and infrastructures downstream. This paper experimentally studied earthquake-induced water waves (EWWs) in moraine-dammed lakes and examined the effects of several factors (e.g. water depth, earthquake parameters, and uneven lake basin). The experimental results suggest that the EWWs positively correlate to the earthquake wave, and the maximum height of the EWWs increases by 10%–15% when the effect of the uneven lake basin is considered. Based on the experiment data, we derived a calculation equation to estimate the maximum amplitude of EWWs considering the basin effect, and proposed a fast risk assessment method for moraine lakes due to overtopping EWWs. Finally, based on the method, we assessed the failure risk of the moraine lakes located in the Gyirong river basin where the China–Nepal corridor crosses. The study broadens understandings of the risk source of moraine-dammed lakes.

USE OF GALERKIN TECHNIQUE TO THE ROLLING OF A PLATE IN DEEP WATER

The classical problems of surface water waves produced by small oscillations of a thin vertical plate partially immersed as well as submerged in deep water are reinvestigated here. Each problem is reduced to an integral equation involving horizontal component of velocity across the vertical line outside the plate. The integral equations are solved numerically using Galerkin approximation in terms of simple polynomials multiplied by an appropriate weight function whose form is dictated by the behaviour of the fluid velocity near the edge(s) of the plate. Fairly accurate numerical estimates for the amplitude of the radiated wave at infinity due to rolling and also for swaying of the pate in each case are obtained and these are depicted graphically against the wave number for various cases.

WATER WAVE SCATTERING BY A THIN VERTICAL SUBMERGED PERMEABLE PLATE

An alternative approach is proposed here to investigate the problem of scattering of surface water waves by a vertical permeable plate submerged in deep water within the framework of linear water wave theory. Using Havelock’s expansion of water wave potential, the associated boundary value problem is reduced to a second kind hypersingular integral equation of order 2. The unknown function of the hypersingular integral equation is expressed as a product of a suitable weight function and an unknown polynomial. The associated hypersingular integral of order 2 is evaluated by representing it as the derivative of a singular integral of the Cauchy type which is computed by employing an idea explained in Gakhov’s book [7]. The values of the reflection coefficient computed with the help of present method match exactly with the previous results available in the literature. The energy identity is derived using the Havelock’s theorems.

Controllability and stabilization of gravity-capillary surface water waves in a basin

<p style='text-indent:20px;'>The paper concerns the controllability and stabilization of surface water waves in a two-dimensional rectangular basin under the forces of gravity and surface tension. The surface waves are generated by a wave-maker placed at the left side-boundary and it is physical relevant to see whether the surface waves are controllable or can be stabilized using appropriate motion of the wave-maker. Due to the surface tension, an edge condition must be imposed at the contact point between the free surface and a solid boundary. Two types of wave-makers are considered: "flexible" or "rigid". It is shown that the surface waves are approximately controllable, but not exactly controllable, for both "flexible" and "rigid" wave-makers. In addition, under a static feedback to control a "rigid" wave-maker, the strong stability of feedback control system is obtained.</p>

The Role of Non-Hydrostatic Effects in Nonlinear Dispersive Wave Modeling

Surface water waves is an important research topic in coastal and ocean engineering due to its influences on various human activities. In this study, our purpose is to gain a deeper insight on the effects of non-hydrostatic (NHS) pressure on surface wave motions and its role in numerical modeling, based upon the high-order NHS model and optional vertical accelerations. The relative contribution of non-hydrostatic effects (Pnhs/Phs) and its sensitivity on phase celerity and amplitude of dispersive waves are quantified. The vertical structure of Pnhs/Phs clearly indicates stronger NHS effects in deeper waters and its significance near the surface. The NHS effects mainly slow down wave celerity and maintain incident amplitude for linear dispersive waves. The NHS effects are also responsible for increased amplitude and phase speed under strong non-linearity. The inter-relation between (un)realistic physical responses and model errors is discussed. Further, four experimental conditions for waves with complicated interactions are examined. Overall, the NHS effects play a critical role in side-band generation of bi-chromatic waves, and increased celerity and amplitude during nonlinear shoaling, as well as velocity moderation under co-existence of depth-varying currents. Possibly owing to weaker wave–wave interactions, however, wave directionality does not strongly interfere with FNHS/QNHS (Fully/Quasi Non-HydroStatic) effects on a fast-modulated nonlinear evolution of spatial focusing or diffraction waves.

Adaptive Numerical Modeling of Tsunami Wave Generation and Propagation with FreeFem++

A simplified nonlinear dispersive Boussinesq system of the Benjamin–Bona–Mahony (BBM)-type, initially derived by Mitsotakis (2009), is employed here in order to model the generation and propagation of surface water waves over variable bottom. The simplification consists in prolongating the so-called Boussinesq approximation to bathymetry terms, as well. Using the finite element method and the FreeFem++ software, we solve this system numerically for three different complexities for the bathymetry function: a flat bottom case, a variable bottom in space, and a variable bottom both in space and in time. The last case is illustrated with the Java 2006 tsunami event. This article is designed to be a pedagogical paper presenting to tsunami wave community a new technology and a novel adaptivity technique, along with all source codes necessary to implement it.