Wavelet-based vortical structure detection and length scale estimate for laboratory spilling waves Zhi-Cheng Huang a , Hwung-Hweng Hwung b, ⁎, Kuang-An Chang c a Department of Hydraulic and Ocean Engineering, National Cheng Kung University, Tainan, Taiwan, ROC b Department of Hydraulic and Ocean Engineering, Tainan Hydraulics Laboratory, National Cheng Kung University, Tainan, Taiwan, ROC c Zachry Department of Civil Engineering, Texas A&M University, College Station, Texas 77843, United States abstract article info Article history: Received 15 September 2009 Received in revised form 2 April 2010 Accepted 13 April 2010 Available online 23 May 2010 Keyword: Vortical structure Length scale Turbulence Wave breaking Surf zone Turbulent flow fields under spilling breaking waves are measured by particle image velocimetry and analyzed using the wavelet techniques in a laboratory surf zone. The turbulent vortical structures and corresponding length scales in the flow are detected through the eduction of the most excited mode with local intermittency measure that is found to correlate with the passage of the structure. Distributions and evolution of the educed vortical structures are presented and discussed. Packets of vortical structures with high intermittency is observed to stretch downward below the initially low-intermittency trough level, indicating these structures play a crucial role in turbulent mixing below the trough level. It is found that the probability density functions of the intermittent energy of the educed structures, vorticity and swirl strength display an exponential decay. Ensemble-averaged length scales of the educed vortical structures are found to be about 0.1 to 0.2 times the local water depth, close to the turbulent mixing length reported in the surf zone. The Kolmogorov microscale is evaluated and the turbulent mixing length is estimated using the k -ε relation and mixing length hypothesis. The k -ε relation may overestimate the mixing length scale for energetic descending eddies. © 2010 Elsevier B.V. All rights reserved. 1. Introduction Wave breaking plays an important role in transferring wave energy, momentum, heat, and mass at the air–sea interface. In the process, wave motion is converted from an irrotational flow into a rotational turbulent shear flow, and wave energy is dissipated. Turbulence generated by wave breaking also brings sediment into suspension from the bed and transported by the wave-induced current. Accordingly, turbulence under breaking waves has been an important issue for many researchers such as geophysical scientists, environmental and coastal engineers. Recent advances in wave breaking study have led to better understanding of its mechanism. Descriptive representations of surf zone wave breaking, such as the crest rolling, water splashing and vortex generation, were carried out using flow visualization techni- ques (e.g., Nadaoka et al., 1989; Lin and Hwung, 1992). More advanced quantitative insights for surf zone dynamics were achieved using point measuring techniques such as laser Doppler velocimetry (LDV) (e.g., Stive, 1980; Nadaoka et al., 1989; Ting and Kirby, 1996; Cox and Kobayashi, 2000; Stansby and Feng, 2005; Longo, 2009). However, instantaneous spatial distribution and derivation of certain physical quantities cannot be obtained with LDV, and spatial derivatives were estimated through the Taylor hypothesis (i.e., ∂/ ∂t =-C(∂/∂x) with C being the wave phase speed). This assumption may be questionable in the analysis of turbulence transport in surf zone because turbulent fluctuations are not small if compared to the mean flow (Ting and Kirby, 1995; Kimmoun and Branger, 2007). Recently, more and more flow field and turbulence measurements in surf zones were performed using particle image velocimetry (PIV) due to its full-field advantage of obtaining the entire velocity map (Govender et al., 2002; Kimmoun and Branger, 2007; Ting, 2008; Huang et al., 2009a,b). For flows inside a surf zone, it is known that turbulence is primarily generated in the crest region through the rolling and water splashing process (Peregrine, 1983; Christensen et al., 2002; Watanabe et al., 2005; Kimmoun and Branger, 2007; Huang et al., 2009a). Turbulence in that region is observed to stretch into the interior water column below the trough level by convection and turbulent diffusion after the passing of the developed turbulent bore (Kimmoun and Branger, 2007; Huang et al., 2009a). The downward stretching of turbulence is found to associate with a large-scale eddy motion — the so-called obliquely descending eddy denominated by Nadaoka et al. (1989). The eddy is responsible for excessive mass flux, and it enhances momentum transport in breaking waves. However, such a large turbulent motion occurs intermittently and its instantaneous burst of turbulent kinetic energy and Reynolds stress could not be explained Coastal Engineering 57 (2010) 795–811 ⁎ Corresponding author. Tel.: + 886 6 2757575x50023; fax: + 886 6 2366265. E-mail address: hhhwung@mail.ncku.edu.tw (H.-H. Hwung). 0378-3839/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.coastaleng.2010.04.006 Contents lists available at ScienceDirect Coastal Engineering journal homepage: www.elsevier.com/locate/coastaleng