Vorticity and intermittency within the pre-breaking region of spilling breakers S. Longo ⁎ Department of Civil Engineering, University of Parma, Viale G.P. Usberti,181/A, 43100 Parma, Italy abstract article info Article history: Received 25 March 2008 Received in revised form 2 September 2008 Accepted 10 September 2008 Available online 14 October 2008 Keywords: Waves Breakers Turbulence Vorticity Wavelets This paper presents measurements and analysis of fluid velocity within the context of spilling waves. The data have been collected using 2-D Laser Doppler Velocimetry in pre-breaking monochromatic waves generated in a wave tank. The analysis is performed using orthogonal wavelets and, in addition to the classical criterion adopted in applying Taylor's hypothesis, a new algorithm is proposed for the eduction of eddies at different length scales. The contribution of different scale vortices is computed, and phase is resolved. Microvortices (smaller than the breaker height but larger than the dissipative vortices) and mid- size vortices (with length ranging from the breaker height to the wave length) carry out most turbulence energy under wave crest. The phase average vorticity and strain rate is computed at different wave lengths, with the analysis of intermittence. The intermittency factor shows spikes in the wave crest, especially for turbulence in small vortices. © 2008 Elsevier B.V. All rights reserved. 1. Introduction In recent years it has become customary to describe turbulent fields as a mixing of coherent structures of different length scales. Turbulence, instead of a continuum in the flow field, seems to be organised in spatial structures. Without detailing the nature and aspect of a coherent structure, we simply regard it as a recognisable pattern, with a certain degree of determinism. Most of the known coherent structures have a specific capacity for transporting momen- tum, and hence play important roles in the overall dynamics. Nadaoka et al. (1989) demonstrated that large-scale eddy motion is responsible for the excessive mass flux and enhanced momentum transport in breaking waves. In addition, they demonstrated that vorticity related to large eddies also reduces the wave height favouring the transforma- tion of energy into kinetic energy instead of potential energy. Our interest in coherent structures in waves is motivated by the important role they play in free surface flows with a movable bottom, as they strongly modify the free surface and affect sediment transport. Coherent structures are intimately related to intermittency, whose pattern is a sequence of intervals of evident strong turbulent fluctuations and intervals of much weaker turbulent fluctuations. Sediment transport in suspension is essentially organised in intermittent events, with sediment being lifted from the bottom and then moved by the mean current. Intermittent events are intimately related to coherent structures. Many experiments have clearly confirmed the existence of eddies of different length scales in breaking waves (Nadaoka et al. 1989; Chang and Liu, 1998), with large eddies that once generated by the breaking process rotate and assume appearance of oblique vortices. The oblique vortices are the most effective in extracting energy from the mean motion. Lin and Rockwell (1994) studied the evolution of a quasi-steady breaking wave in terms of vorticity. Chang and Liu (1998) studied velocity and vorticity under a breaking wave using Particle Image Velocimetry. Coherent structure and turbulence under breaking waves was experimentally analysed using Digital Particle Image Velocimetry by Melville et al. (2002). Their experiments essentially refer to waves breaking in deep water. As a consequence, many of their results cannot be compared with the results of the present study, but we can learn from their investigation that coherent structures and mean flow generated by breaking waves, and readily identified in the laboratory, may be very difficult to isolate in the field. The detection of coherent structure relies on an ad hoc experimental technique that is often supported by algorithms during data analysis. Large eddies can be easily detected using photographs or visualisation techniques, whilst the smaller eddies can be detected using proper analysis of the velocity signal, as pattern-recognition methods and conditional sampling. In a 2-D perspective a coherent structure is defined as a region with local swirling motion. Techniques used for extracting eddies in a flow field include: (1) a direct analysis of the vorticity field; (2) a Galilean decomposition, which consists in translat- ing the velocity field by an amount equal to the advection velocity of the coherent structure under identification; (3) low-pass filtering the velocity signal in order to remove the small scale contribution; (4) analysis of the velocity gradient tensor; (5) algorithms based on a wavelet transform of the velocity vector field (Camussi, 2002). Coherent structures are strictly related to intermittency, with a large degree of intermittency expected at all length scales. The concept of intermittency and coherent structures involves considering Coastal Engineering 56 (2009) 285–296 ⁎ Tel.: +39 0521 905157; fax: +39 0521905924. E-mail address: sandro.longo@unipr.it. 0378-3839/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.coastaleng.2008.09.003 Contents lists available at ScienceDirect Coastal Engineering journal homepage: www.elsevier.com/locate/coastaleng