Tsunami generation by paddle motion and its interaction with a beach: Lagrangian modelling and experiment

A 2D Lagrangian numerical wave model is presented and validated against a set of physical wave-flume experiments on interaction of tsunami waves with a sloping beach. An iterative methodology is proposed and applied for experimental generation of tsunami-like waves using a piston-type wavemaker with spectral control. Three distinct types of wave interaction with the beach are observed with forming of plunging or collapsing breaking waves. The Lagrangian model demonstrates good agreement with experiments. It proves to be efficient in modelling both wave propagation along the flume and initial stages of strongly non-linear wave interaction with a beach involving plunging breaking. Predictions of wave runup are in agreement with both experimental results and the theoretical runup law

On transonic viscous-inviscid interaction

The paper is concerned with the interaction between the boundary layer on a smooth body surface and the outer inviscid compressible flow in the vicinity of a sonic point. First, a family of local self-similar solutions of the Karman-Guderley equation describing the inviscid flow behaviour immediately outside the interaction region is analysed; one of them was found to be suitable for describing the boundary-layer separation. In this solution the pressure has a singularity at the sonic point with the pressure gradient on the body surface being inversely proportional to the cubic root dp_w/dx~(−x)^{-1/3} of the distance (−x) from the sonic point. This pressure gradient causes the boundary layer to interact with the inviscid part of the flow. It is interesting that the skin friction in the boundary layer upstream of the interaction region shows a characteristic logarithmic decay which determines an unusual behaviour of the flow inside the interaction region. This region has a conventional triple-deck structure. To study the interactive flow one has to solve simultaneously the Prandtl boundary-layer equations in the lower deck which occupies a thin viscous sublayer near the body surface and the Karman-Guderley equations for the upper deck situated in the inviscid flow outside the boundary layer. In this paper a numerical solution of the interaction problem is constructed for the case when the separation region is entirely contained within the viscous sublayer and the inviscid part of the flow remains marginally supersonic. The solution proves to be non-unique, revealing a hysteresis character of the flow in the interaction region

Lagrangian modelling of extreme wave groups

A 2D Lagrangian numerical wave model is presented and validated against a set of physical wave-flume experiments on focussed wave groups. The Lagrangian calculations demonstrate good agreement with experimental results. The model proves to be efficient in modelling both long-term wave propagation along the flume and strongly-nonlinear waves including initial stages of wave breaking

Lagrangian modelling of fluid sloshing in moving tanks

The paper presents general Lagrangian formulation for sloshing of inviscid fluid in 2D tanks under vertical and horizontal excitation. In the case of a rectangular tank a third-order asymptotic solution for resonant sloshing with a dominating mode is derived using the recursive technique introduced by Buldakov et al. (2006). The problem is also solved numerically using a fully nonlinear finite difference approximation. Both the Lagrangian recursive asymptotic model and the Lagrangian fully nonlinear solver are applied to a problem of high amplitude resonant Faraday waves. Results are compared with experiments of Bredmose et al. (2003) and demonstrate excellent agreement

Wave propagation models for numerical wave tanks

This chapter discusses the importance of efficient wave propagation models for generating boundary conditions for CFD models of wave-structure interaction or as elements of hybrid models. We give a brief review of fully nonlinear wave models based on potential flow theory (FNPT), which are the main candidates for such applications. We then suggest a Lagrangian wave model as an alternative to classical FNPT models. We present a mathematical and numerical formulation of the model, its validation and application to propagation of steep wave groups and to wave groups on sheared currents

Extreme wave groups in a wave flume: Controlled generation and breaking onset

Extreme waves in random seas are usually breaking or close to breaking. Understanding the kinematics and evolution of such waves is important for determining loads on offshore structures. Controlled repeatable generation of realistic breaking waves in wave flume experiments is a difficult but important task. It is rather easy to generate an arbitrary breaking wave, but to the authors’ knowledge there is no methodology for accurate generation of a wave group with a pre-defined spectrum related to a modelled sea state with spilling breaking at a prescribed position. Such waves can be used to model extreme breaking waves in a random sea and their interaction with structures. This paper offers such a methodology. The key feature of the method is the application of an iterative focussing procedure to a linearised amplitude spectrum rather than to a full nonlinear spectrum. The linearised spectrum is obtained using a harmonics separation technique and the general derivation of the method is given for an arbitrary number of components. The procedure is applied to generate focussed wave groups with amplitudes increased in small steps until local crest breaking occurs. As a result, the highest non-breaking waves and weakly breaking waves are generated for otherwise identical conditions. The methodology is applied for four different wave spectra of the same peak frequency: JONSWAP, Pierson-Moskowitz, wide and narrow band Gaussian. It is found that steepness of the limiting breaking wave depends strongly on the choice of wave group spectrum. The results demonstrate that neglecting spectral properties of design waves may lead to misrepresentation of their breaking behaviour

Focusing unidirectional wave groups on finite water depth with and without currents

Focused waves are often used in physical and numerical studies as a representative condition for extreme waves or as a mean to generate very steep and breaking waves at a desired location in space and time. A focused wave is in theory created when all the components in a transient wave group come in phase. In the past, linear wave theory and empirical iterative methodologies have been suggested in order to achieve the required phase and amplitude focusing. Nevertheless, their effectiveness decreases as the non-linearity of the wave group increases and thus the generation of very high focused waves was a challenging task. Here, an empirical iterative methodology is suggested which can focus waves of any height at a predetermined temporal and spatial location. The methodology has been successfully applied to wave groups travelling on still water but also on sheared currents and it has been implemented in both physical and numerical wave flumes. The results presented here refer to linear, weakly non-linear and strongly non-linear focused waves generated with a realistic target spectrum

A numerical study of wave-current interaction in the bottom boundary layer

In the present work, a numerical wave-current flume has been developed, based on a standard k-εmodel. The numerical flume was 12.86m in length, with a numerical beach at one end of the flume. The Volume of Fluid (VOF) method was used to capture the free surface in the flume. The velocity profile obtained at the test section from the numerical simulation has then been compared with experimental data and good agreement found. Periodic velocities in the bottom boundary layer have been obtained which agree well with the experimental data. The model provides an insight to the changes in bed shear stress time histories that characterise wave current interaction

Simulating breaking focused waves in CFD: Methodology for controlled generation of first and second order

A new methodology is proposed for the generation of breaking focused waves in computational fluid dynamics (CFD) simulations. The application of the methodology is illustrated for a numerical flume with a piston-type wavemaker built in the CFD model olaFlow. Accurate control over the spectral characteristics of the wave group near the inlet and the location of focus/breaking are achieved through empirical corrections in the input signal. Known issues related to the spatial and temporal downshift of the focal location for focusing wave groups are overcome. Focused wave groups are produced with a first- and second order-paddle motion, and the propagation of free and bound waves is validated against the experimental results. A very good overall degree of accordance is reported, which denotes that the proposed methodology can produce waves breaking at a focused location

Experimental Generation of Focusing Wave Groups on Following and Adverse-Sheared Currents in a Wave-Current Flume

Focused waves are often used in physical and numerical studies as a representative condition for extreme waves or as a means to generate very steep and breaking waves at a prescribed location in space and time. They have also been combined with depth-varying currents in investigations of incipient wave breaking, wave breaking–induced energy dissipation, and wave–current induced loads on marine structures. A focused wave is created when all the components in a transient wave group come into phase. In the past, linear wave theory and iterative methodologies coupled with the linear Doppler-shifted dispersion relationship have been suggested to account for the presence of a current and achieve the required phase and amplitude focusing. In the majority of cases, linear or constant steepness spectra are used, which, compared to measured or theoretical spectra like the Joint North Sea Wave Project (JONSWAP), Gaussian, and Pierson-Moskowitz (PM) can be termed unrealistic. The effectiveness of these methodologies also decreases as the nonlinearity increases; therefore, in most studies, either weakly nonlinear conditions are used or the focus location is determined empirically. Here, an iterative methodology is suggested that can focus waves of any height at a predetermined temporal and spatial location even for wave groups propagating on a strong following or adverse current. An experimental apparatus developed to generate relatively stable sheared velocity profiles is also described. The depth-varying profile of the resulting currents diverges from that of classical wind-driven currents and comes closer to profiles measured in field sites important for the deployment of, for instance, tidal and wind energy converters. The methodology is successfully applied to wave groups traveling on still water, following, and adverse currents, and the results presented refer to linear, weakly nonlinear, and strongly nonlinear–focused waves generated for a range of realistic target spectra. The capability to generate wave groups with the same amplitude spectrum at a fixed location for a variety of flow conditions—still water, following, and adverse sheared currents—is also illustrated