Coherent Turbulent Structures in a Quasi-steady Spilling Breaker

In this paper, we analyze planar Particle Image Velocimetry (PIV) data of a laboratory hydraulic jump to investigate the large-scale coherence in the turbulent breaker shear layer. Two-point spatial correlations are used at various spatial locations to qualitatively assess the shape of the coherent structures in the different flow regimes. The structures are found to be stretched parallel to the mean surface in the form of ellipses, oriented along the mean strain rate near the foot of the breaker, and further downstream, become increasingly compact and oriented normal to the surface. This indicates the reduced efficiency of the coherent structures away from the foot in extracting energy from the mean flow. In addition, quantitative estimates of length scales are obtained from the correlation coefficients. The average length scales are found to be in the range of previously reported estimates for laboratory generated plunging and spilling breaking waves. INTRODUCTION An understanding of the turbulent flow in breaking waves is essential towards modeling the dynamics of the surf-zone. The post-breaking phase, because of the complexity of the resulting turbulent flow (being two-phase and highly intermittent), remains difficult to investigate, both theoretically (Svendsen and Madsen, 1984) and experimentally (Duncan, 2001; Govender et al., 2002). Owing to the limited knowledge of the detailed dynamics, spilling breakers in the surf-zone are typically modeled as a stagnant eddy or roller riding on the front face of a wave (Madsen and Svendsen, 1983; Cointe and Tulin, 1994). An alternative qualitative description of the breaker shear layer and its turbulence structure suggests the generation of an intense “breaker mixing layer”, which starts from the foot of the breaker (defined according to Brocchini and Peregrine (2001) as the ensemble averaged location of the toe) followed by a wake further downstream (Peregrine and Svendsen, 1978; Battjes and Sakai, 1981). In these “bulk” models, the turbulent structure of the flow, especially the details in the breaker shear layer and in the highly intermittent region near the surface, is either grossly simplified or completely disregarded. 1Center for Applied Coastal Research, University of Delaware, Newark, DE 19711, USA, [email protected] 2D. I. A. M., Universita’ di Genova, Via Montallegro 1, 16145 Genova, Italy 3Graduate College of Marine Studies, University of Delaware 4VIMS Lab, Dept. of Computer and Information Sciences, University of Delaware 1 Misra et al. There are, however, dominant and persisting energy containing scales in turbulent flows that exhibit evident structure, and these are called coherent structures. Laboratory experiments have clearly confirmed the existence of such classes of eddies in breaking waves (Nadaoka, 1986; Chang and Liu, 1998; Stansby and Feng, 2005). Non-intrusive whole-field measurement techniques such as PIV have aided the visualization and characterization of such organized motion in turbulent flows. Further, Melville et al. (2002) have shown that coherent structures in a deep water breaking wave can be studied using a mosaic of PIV images. With a light sheet in the streamwise-spanwise plane, PIV laboratory experiments conducted by Cox and Anderson (2001) on the breaking of regular plunging breakers revealed the nominal diameter (l) of (instantaneous) eddies associated with wave breaking to be around 0.05 m. The breaking wave-height (Hb) was 0.12 m which gives l Hb = 0.42. They noted that they could not detect larger eddies because of the restriction imposed by their target area, which was 10 cm × 10 cm. For many of their tests, they also found complex three-dimensional patterns with no well-defined eddies. Longo (2003), using orthogonal wavelets as a decomposition technique, found that more than 70 % of the total turbulent kinetic energy for spilling breakers were carried by micro (with a length scale in the range 2 mm < l < 10 cm) and mid-size (10 cm < l < 4.0 m) vortices, predominantly below the wave crest, and that most of the energy was transferred from the macroand mid-size vortices to the micro-vortices after the passage of the breaker. The breaking wave-height was 10 cm, giving a maximum and minimum l Hb = 1 for the microand mid-size vortices respectively. Stansby and Feng (2005), with laser Doppler anemometry experiments with laboratory generated bores, found multiple coherent vortices which were elongated along the surface. Motivated by the analogy between quasi-steady surf-zone breakers and bores, recent analysis of a planar (streamwise-cross-stream) PIV study of a turbulent hydraulic jump has shown that the breaker shear layer can be characterized as a mixing layer (Misra et al., 2005a). In this paper, we focus our attention on characterizing the large-scale coherent turbulent motions in the mixing layer. The experimental set-up and flow parameters are described in section 2. The two-point spatial correlation technique used to analyze the structure of the turbulence is described in 3. The results are presented in section 4 followed by conclusions. EXPERIMENTAL SET-UP The experiment was performed in a recirculating Armfield S6 tilting flume that is 4.8 m long and 30 cm wide, with glass side walls (9 mm thick) and an opaque bottom. The jump was set up downstream of a weir. The flow rate and the height of the weir are used to control the upstream flow velocity and water depth, thereby determining the upstream Froude number (Fr = 1.2). After passing the weir, the supercritical flow transitions to a subcritical flow by dissipating energy through the formation of an air-entraining hydraulic jump. The toe of the jump, defined here as the point of maximum surface curvature, was approximately 20 cm downstream of the weir. The flume was kept horizontal throughout the experiments. The PIV set-up consisted of a 120 mj/pulse Nd-Yag New Wave solo laser source with a pulse duration of 3 to 5 nano seconds. This was mounted onto a custom-built submersible waterproof periscope which was lowered into the water. The optics were arranged in such a way that the laser beam emerged as a planar light sheet parallel to the flume wall. The water was seeded with 14 μm diameter silver coated hollow glass spheres with a specific