Effect of Mooring Lines on the Hydroelastic Response of a Floating Flexible Plate Using the BIEM Approach

A boundary integral equation method (BIEM) model for the problem of surface wave interaction with a moored finite floating flexible plate is presented. The BIEM solution is obtained by employing the free surface Greens function and Green’s theorem, and the expressions for the plate deflection, reflection, and transmission coefficients are derived from the integro-differential equation. Furthermore, the shallow water approximation model and its solution is obtained based on the matching technique in a direct manner. The accuracy of the present BIEM code is checked by comparing the results of deflection amplitude, reflection, and transmission coefficients with existing published results and experimental datasets as well as the shallow water approximation model. The hydroelastic response of the moored floating flexible plate is studied by analyzing the effects of the mooring stiffness, incidence angle, and flexural rigidity on the deflection amplitude, plate deformations, reflection, and transmission coefficients. The present analysis may be helpful in understanding the different physical parameters to model a wave energy conversion device with mooring systems over BIEM formulations.

Cuspon-type Waves and Their Properties

The general Degasperis-Prosesi equation (gDP) describes the evolution of the water surface in a unidirectional shallow water approximation. We consider essentially non-integrable versions of this model and analyze their cuspon-type solutions, that is continuous traveling waves with the unbounded first derivative.

Mega-Ship-Generated Tsunami: A Field Observation in Tampa Bay, Florida

The displacement of a large amount of water in a moderate-sized estuary by a fast-moving mega-ship can generate tsunami-like waves. Such waves, generated by cruise ships, were observed in Tampa Bay, Florida, USA. Two distinct, long tsunami-like waves were measured, which were associated with the passage of a large cruise ship. The first wave had a period of 5.4 min and a height of 0.40 m near the shoreline. The second wave had a period of 2.5 min and was 0.23 m high. The peak velocity of the onshore flow during the second wave reached 0.65 m/s. The shorter, second wave propagated considerably faster than the first wave in the breaking zone. The measured wave celerity was less than 50% of the calculated values, using the shallow water approximation of the dispersion equation, suggesting that nonlinear effects play an important role. A fundamental similarity among the generation of tsunamis, as induced by mega-ships, landslides or earthquakes, is a process that causes a vertical velocity at the sea surface, where a freely propagating wave is produced. This mega-ship-generated tsunami provides a prototype field laboratory for systematically studying tsunami dynamics, particularly the strong turbulent flows associated with the breaking of a tsunami wave in the nearshore, and tsunami–land interactions. It also provides a realistic demonstration for public education, which is essential for the preparation and management of this unpreventable hazard.

Impact Force of a Geomorphic Dam-Break Wave against an Obstacle: Effects of Sediment Inertia

The evaluation of the impact force on structures due to a flood wave is of utmost importance for estimating physical damage and designing adequate countermeasures. The present study investigates, using 2D shallow-water approximation, the morphodynamics and forces caused by a dam-break wave against a rigid obstacle in the presence of an erodible bed. A widely used coupled equilibrium model, based on the two-dimensional Saint–Venant hydrodynamic equations combined with the sediment continuity Exner equation (SVEM), is compared with a more complex two-phase model (TPM). Considering an experimental set-up presented in the literature with a single rigid obstacle in a channel, two series of tests were performed, assuming sand or light sediments on the bottom. The former test is representative of a typical laboratory experiment, and the latter may be scaled up to a field case. For each test, two different particle diameters were considered. Independently from the particle size, it was found that in the sand tests, SVEM performs similarly to TPM. In the case of light sediment, larger differences are observed, and the SVEM predicts a higher force of about 26% for both considered diameters. The analysis of the flow fields and the morphodynamics shows these differences can be essentially ascribed to the role of inertia of the solid particles.

Generalised Serre–Green–Naghdi equations for open channel and for natural river hydraulics

In this paper, we present a new non-linear dispersive model for open channel and river flows. These equations are the second-order shallow water approximation of the section-averaged (three-dimensional) incompressible and irrotational Euler system. This new asymptotic model generalises the well-known one-dimensional Serre–Green–Naghdi (SGN) equations for rectangular section on uneven bottom to arbitrary channel/river section.

On the Connection Between Step Approximations and Depth-Averaged Models for Wave Scattering by Variable Bathymetry

Summary Two popular and computationally inexpensive class of methods for approximating the propagation of surface waves over two-dimensional variable bathymetry are ‘step approximations’ and ‘depth-averaged models’. In the former, the bathymetry is discretised into short sections of constant depth connected by vertical steps. Scattering across the bathymetry is calculated from the product of $2 \times 2$ transfer matrices whose entries encode scattering properties at each vertical step taken in isolation from all others. In the latter, a separable depth dependence is assumed in the underlying velocity field and a vertical averaging process is implemented leading to a second-order ordinary differential equation (ODE). In this article, the step approximation is revisited and shown to be equivalent to an ODE describing a depth-averaged model in the limit of zero-step length. The ODE depends on how the solution to the canonical vertical step problem is approximated. If a shallow water approximation is used, then the well-known linear shallow water equation results. If a plane-wave variational approximation is used, then a new variant of the mild-slope equations is recovered.