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.

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.

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,” engulfment of a single, well-formed air bubble is typical of a “mode (b)” event, while the generation of a fine-scale air-water mixing occurs for a “mode (c)” event. Upward accelerations of the flip-through jet exceeding 1500g have been measured and the generation/collapse process of a small air cavity is described in conjunction with the available pressure time histories. Predictions of the vertical pressure distributions made with the pressure-impulse model of Cooker and Peregrine [M. J. Cooker and D. H. Peregrine, “Pressure-impulse theory for liquid impact problems,” J. Fluid Mech. 297, 193 (1995)] show good agreement with the experimental data.

[1] We describe a simple mathematical model capable of reproducing the main features of sand wave inception and growth. In particular we focus on the prediction of the migration rates that sand waves undergo because of tidal and residual currents. The model adequately predicts migration rates even for the cases of upstream-propagating sand waves, i.e., for sand waves which migrate in the direction opposite to that of the residual current. We show that upstream/downstream propagation is mainly controlled by the relative strength of the residual current with respect to the amplitude of the quarter-diurnal tide constituent and by the phase shift between the semi-diurnal and quarter-diurnal tide constituents. Therefore, to accurately predict field cases, a detailed knowledge of the direction, strength, and phase of the different tide constituents is required.

[1] 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.Citation: Brocchini, M., and T. E. Baldock (2008), Recent advances in modeling swash zone dynamics: Influence of surf-swash interaction on nearshore hydrodynamics and morphodynamics, Rev. Geophys., 46, RG3003,