Wave Kinematics in a Two-Dimensional Plunging Breaker
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Wave Kinematics in a Two-Dimensional Plunging Breaker Yves-Marie Scolan1 · Pierre-Michel Guilcher1 Received: 22 January 2019 / Accepted: 12 July 2019 © Springer Nature Switzerland AG 2019
Abstract In the wake of theoretical, numerical and experimental advances by a large number of contributors, we revisit here some aspects of the fluid kinematics in a two-dimensional plunging breaker occurring in shallow water. In particular, we propose a simplified identification of the velocity distribution at the free surface in terms of the velocity at some characteristic points. We can then simply explain the reasons for which the velocity is maximum inside the barrel at its roof. We also show that the relative velocity field calculated in a coordinate system centered to a point where the velocity is maximum may have a possible analytic representation. Keywords Potential flow · Nonlinear wave kinematics · Plunging breaker
1 Introduction The kinematics in the fluid of a plunging breaker has been abundantly studied in the past. The pioneering works by John [13] for the theoretical developments and by Miller [18] for the experimental observations are often cited in the papers that appeared in 70s and early 80s. The literature on the kinematics in breaking waves became more and more abundant as soon as the available computational resources have yielded the first numerical results with robust enough algorithms. The corresponding numerical models appeared in the late 70s and early 80s; they were mainly formulated in Potential Theory for two-dimensional configurations. Since the pioneering works by LonguetHiggins and Cokelet [16], Vinje and Brevig [28] and Dold and Peregrine [8], many studies have been achieved. Since then, Potential Theory remains undoubtedly the right framework to analyse the fine details of a breaker as long as no rotational effects predominate (see [12]). Indeed, that is the case during the early stages of the flow in a
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Yves-Marie Scolan [email protected] Pierre-Michel Guilcher [email protected]
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ENSTA Bretagne IRDL UMR 6027, 2 Rue François Verny, 29806 Brest Cedex 9, France
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Y.-M. Scolan, P.-M. Guilcher
sloshing tank as shown in Karimi et al. [14]. Obviously, when dealing with overturning crest thus leading to an entrapped gas pocket, it is a drastic approximation to neglect the influence of the gas dynamics above the liquid. Indeed, the obtained results must always be commented having in mind how these results will be influenced by the presence of gas which interacts more or less strongly with the liquid provided that both fluids (liquid and gas) are non-miscible. Since the recent work by Song and Zhang [26], we know that the inner surface of the gas pocket may have complicated shape. Before that, it is also observed that the formation of the pocket close to wall is delayed by the presence of the entrapped gas and the crest is much less sharp due to the strong gas flow occurring when the pocket closes up, the gas being compressible or not. For low density
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