Maurizio Brocchini

The dynamics of strong turbulence at free surfaces. Part 1. Description

A free surface may be deformed by fluid motions; such deformation may lead to surface roughness, breakup, or disintegration. This paper describes the wide range of free-surface deformations that occur when there is turbulence at the surface, and focuses on turbulence in the denser, liquid, medium. This turbulence may be generated at the surface as in breaking water waves, or may reach the surface from other sources such as bed boundary layers or submerged jets. The discussion is structured by consideration of the stabilizing influences of gravity and surface tension against the disrupting effect of the turbulent kinetic energy. This leads to a two-parameter description of the surface behaviour which gives a framework for further experimental and theoretical studies. Much of the discussion is necessarily heuristic, and is often limited by a lack of appropriate experimental observations. It is intended that such experiments be stimulated, to test the value or otherwise of our two-parameter description.

Recent advances in modeling swash zone dynamics: Influence of surf-swash interaction on nearshore hydrodynamics and morphodynamics

The role of the swash zone in influencing the whole nearshore dynamics is reviewed with a focus on the interaction between surf and swash zone processes. Local and global hydromorphodynamic phenomena are discussed in detail, and a description of the overall swash zone operation is given. The effects of swash zone boundary conditions are highlighted, together with the importance of surf zone boundary conditions. Major emphasis is placed on illustrating the interactions of various hydrodynamic modes which, in turn, control the swash and surf zone morphology. Finally, methods to account for swash zone processes in coastal models with different temporal and spatial resolutions are proposed.

Wave impact loads: The role of the flip-through

The impact of waves upon a vertical, rigid wall during sloshing is analyzed with specific focus on the modes that lead to the generation of a flip-through [M. J. Cooker and D. H. Peregrine, “A model for breaking wave impact pressures,” in Proceedings of the 22nd International Conference on Coastal Engineering (ASCE, Delft, 1990), Vol. 2, pp. 1473–1486]. Experimental data, based on a time-resolved particle image velocimetry technique and on a novel free-surface tracking method [M. Miozzi, “Particle image velocimetry using feature tracking and Delaunay tessellation,” in Proceedings of the 12th International Symposium on Applications of Laser Techniques to Fluid Mechanics (2004)], are used to characterize the details of the flip-through dynamics while wave loads are computed by integrating the experimental pressure distributions. Three different flip-through modes are observed and studied in dependence on the amount and modes of air trapping. No air entrapment characterizes a “mode (a) flip-through,” engulfm...

An efficient solver for nearshore flows based on the WAF method

Abstract We describe an efficient and robust flow solver for the integration of the classic Nonlinear Shallow Water Equations (NSWE) on a beach of arbitrary topography. On the basis of the ‘shock capturing’ Weighted Average Flux (WAF) method, a numerical code is implemented which employs a space-splitting technique to integrate the NSWE over a horizontally two-dimensional domain (2DH). Special care is put in handling the moving shoreline and a new, efficient formulation of the shoreline boundary conditions is presented. This is based on the hydrodynamic equivalent of the cavitation condition used in gas dynamics. Model capabilities are illustrated by means of a number of tests (both 1DH and 2DH). These reveal that, though primarily conceived for modelling nearshore hydrodynamics, the solver can be successfully adopted even for studying the run-up of large tsunami waves.

The dynamics of strong turbulence at free surfaces. Part 2. Free-surface boundary conditions

Strong turbulence at a water–air free surface can lead to splashing and a disconnected surface as in a breaking wave. Averaging to obtain boundary conditions for such flows first requires equations of motion for the two-phase region. These are derived using an integral method, then averaged conservation equations for mass and momentum are obtained along with an equation for the turbulent kinetic energy in which extra work terms appear. These extra terms include both the mean pressure and the mean rate of strain and have similarities to those for a compressible fluid. Boundary conditions appropriate for use with averaged equations in the body of the water are obtained by integrating across the two-phase surface layer. A number of ‘new’ terms arise for which closure expressions must be found for practical use. Our knowledge of the properties of strong turbulence at a free surface is insufficient to make such closures. However, preliminary discussions are given for two simplified cases in order to stimulate further experimental and theoretical studies. Much of the turbulence in a spilling breaker originates from its foot where turbulent water meets undisturbed water. A discussion of averaging at the foot of a breaker gives parameters that may serve to measure the ‘strength’ of a breaker.

A reasoned overview on Boussinesq-type models: the interplay between physics, mathematics and numerics.

This paper, which is largely the fruit of an invited talk on the topic at the latest International Conference on Coastal Engineering, describes the state of the art of modelling by means of Boussinesq-type models (BTMs). Motivations for using BTMs as well as their fundamentals are illustrated, with special attention to the interplay between the physics to be described, the chosen model equations and the numerics in use. The perspective of the analysis is that of a physicist/engineer rather than of an applied mathematician. The chronological progress of the currently available BTMs from the pioneering models of the late 1960s is given. The main applications of BTMs are illustrated, with reference to specific models and methods. The evolution in time of the numerical methods used to solve BTMs (e.g. finite differences, finite elements, finite volumes) is described, with specific focus on finite volumes. Finally, an overview of the most important BTMs currently available is presented, as well as some indications on improvements required and fields of applications that call for attention.

Topographically controlled, breaking-wave-induced macrovortices. Part 1. Widely separated breakwaters

In this and the companion paper (Part 2) we examine experimentally, computationally, and analytically the behaviour of breaking-wave-induced macrovortices during startup conditions. Widely separated breakwaters and rip current topographies are chosen as opposite ends of the parameter space. Part 1 examines generation mechanisms using phase-resolving and phase-averaged approximations, and suggests several simple predictive relations for general behaviour. Vortex trajectories and shedding periods for wave breaking on widely spaced breakwaters are also considered in detail. Results show broad agreement with theoretical trajectories. Predictions of vortex shedding periods on breakwater heads show excellent agreement with computations. Part 2 examines startup macrovortices on rip current topographies using computations and laboratory experiments, and changes in behaviour as the system transitions from wide to narrow gap width.

Evolution of the air cavity during a depressurized wave impact. II. The dynamic field

The present paper on wave-impact events in depressurized environments completes the analysis of Part I by focusing on the dynamical features of the impacts and on the influence of the ambient pressure. Connection is made between the impact regimes typically described in the literature and the stages described in Part I [C. Lugni, M. Miozzi, M. Brocchini, and O. M. Faltinsen, “Evolution of the air cavity during a depressurized wave impact. I. The kinematic flow field,” Phys. Fluids 22, 056101 (2010)]. The stages of isotropic/anisotropic compression and expansion of the air cavity are of particular interest. The impact duration at the wall is almost independent of its height above the undisturbed surface level, but its intensity rapidly decreases in the body of the fluid (the peak pressure halves within the first two compression/expansion cycles). The time evolution of the pressure loads on the wall is analyzed by means of the Hilbert transform and an empirical mode decomposition of the signals. This enable...

Evolution of the air cavity during a depressurized wave impact. I. The kinematic flow field

This paper describes a systematic experimental study of the role of the ambient pressure on wave impact events in depressurized environments. A wave impact event of “mode (b)” [see Lugni et al., “Wave impact loads: The role of the flip-through,” Phys. Fluids 18, 122101 (2006)] causes entrapment of an air cavity. Here the topological and kinematic aspects of its oscillation and evolution toward collapse into a mixture of water and air bubbles are studied, while Part II [Lugni et al., “Evolution of the air cavity during a depressurized wave impact. II. The dynamic field,” Phys. Fluids 22, 056102 (2010)] focuses on the dynamic features of the flow. Four distinct stages characterize the flow evolution: (1) the closure of the cavity onto the wall, (2) the isotropic compression/expansion of the cavity, (3) its anisotropic compression/expansion, and (4) the rise of the cavity up the wall. The first two stages are mainly governed by the air leakage, the last two by the surrounding hydrodynamic flow, which contrib...

Experimental investigation and numerical modelling of steep forced water waves

Steep forced water waves generated by moving a rectangular tank are investigated both experimentally and numerically. Our main focus is on energetic events generated by two different types of external forcing. Horizontal motions are arranged to give wave impact on the sidewall. Steep standing waves forced by vertical acceleration can result in spectacular breaking modes similar to, and more energetic than, those reported by Jiang, Perlin & Schultz (1998, hereinafter J98). Among them we find thin sheets derived from sharp-crested waves, (‘mode A’ of J98) and the ‘flat-topped’ crest or ‘table-top’ breaker (‘mode B’ of J98). We report here on experimental observations of ‘table-top’ breakers showing remarkably long periods of free fall motion. Previously such breakers have only been observed in numerical computations. Both types of breakers often thin as they fall to give thin vertical sheets of water whose downward motion ends in either a small depression and a continuing smooth surface, or air entrainment to appreciable depths. Experimental results are compared graphically with numerical results of two theoretical models. One is an extended set of Boussinesq equations following Wei et al. (1995), which are successful up to wave slopes of O (1). The other numerical comparison is with a fully nonlinear irrotational flow solver (Dold 1992) which can follow the waves to breaking.