Advances in Coastal and Ocean Engineering

The following sections are included:

• PREFACE TO THE REVIEW SERIES

• PREFACE TO VOLUME 8

• CONTRIBUTORS

• CONTENTS

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.

Measurements of the cross-stream shape of the crest of gentle spilling breakers are presented. The measurements are obtained with a photographic technique employing a laser light sheet, a high-speed digital camera and a weak concentration of fluorescent dye in the water. In these weak spillers, the breaking process is dominated by surface tension and breaking occurs without overturning of the free surface. As the turbulent flow ensues, ripples aligned with the crest are generated upstream of the crest and travel backwards over the crest. The average crest height versus time shows the passage of these ripples and has a high degree of repeatability from run to run. By the time the ripples reach the crest, there is significant cross-stream structure presumably due to the rapid development of streamwise vorticity. The root-mean square amplitude of the streamwise ripples is as high 60% of the amplitude of the cross-stream ripples.

Interactions between turbulent waters and the atmosphere may lead to some air-water mixing, often called ‘white water’. This study reviews the basic entrainment processes for a wide range of flow situations and presents new evidence leading to a better understanding of the basic multiphase flow dynamics. The focus is on flow situations characterised by very-strong air-water interactions: e.g., vertical plunging jet, stepped chute flow, plunging breaker. The two basic entrainment mechanisms are local and interfacial aerations. In a local aeration process, air is entrapped at the singularity/discontinuity between the impinging jet and the receiving pool of water. At low jet velocities, the bubbles are entrained individually while, at high jet impact velocities, an elongated air cavity is set into motion between the entrained fluid and the jet flow. At impingement, air is entrapped by a Couette flow mechanism. Interfacial aeration occurs when turbulent velocity fluctuations acting next to the free-surface become large enough to overcome surface tension and buoyancy. The sizes of the bubbles and droplets extend over several orders of magnitude. Void fraction distributions may be modelled by advective diffusion models. Turbulence intensity measurements suggest high levels of turbulence across the entire air-water flow, of one to two orders of magnitude greater than in monophase flows. In coastal engineering, air entrainment is characterised by unsteadiness and high levels of aeration. The results demonstrate that air entrainment in coastal and oceanic zones is an important process and cannot be ignored.

The following sections are included:

• Introduction

• The conditional averaging

• The surface layer and the mean air–water interface
  • The mean interface between air and water
  • The intermittency factor for different air–water interfaces

• Integral and differential equations of motion
  • The conservation of mass
  • The conservation of linear momentum
  • The balance equation for the turbulent kinetic energy

• The boundary conditions
  • The kinematic boundary condition
  • The dynamic boundary condition
  • The boundary condition for k

• Closure

• Discussion of simple closures
  • A passive surface layer
  • A simple model for a splashing free surface

• Breaker toe dynamics

• Discussion

• Acknowledgements

• Appendix: the equation for the convection-diffusion of a passive tracer

• References