Abstract
Axisymmetric standing waves occur across a wide range of free surface flows. When these waves reach a critical height (steepness), wave breaking and jet formation occur. For travelling surface gravity waves, wave breaking is generally considered to limit wave height and reversible wave motion. In the ocean, the behaviour of directionally spread waves lies between the limits of purely travelling (two dimensions) and axisymmetric (three dimensions). Hence, understanding wave breaking and jet formation on axisymmetric surface gravity waves is an important step in understanding extreme and breaking waves in the ocean. We examine an example of axisymmetric wave breaking and jet formation colloquially known as the ‘spike wave’, created in the FloWave circular wave tank at the University of Edinburgh, UK. We generate this spike wave with maximum crest amplitudes of 0.15–6.0 m (0.024–0.98 when made non-dimensional by characteristic radius), with wave breaking occurring for crest amplitudes greater than 1.0 m (0.16 non-dimensionalised). Unlike two-dimensional travelling waves, wave breaking does not limit maximum crest amplitude, and our measurements approximately follow the jet height scaling proposed by Ghabache et al. (J. Fluid Mech., vol. 761, 2014, pp. 206–219) for cavity collapse. The spike wave is predominantly created by linear dispersive focusing. A trough forms, then collapses producing a jet, which is sensitive to the trough's shape. The evolution of the jets that form in our experiments is predicted well by the hyperbolic jet model proposed by Longuet–Higgins (J. Fluid Mech., vol. 127, 1983, pp. 103–121), previously applied to jets forming on bubbles.
Highlights
Wave breaking is commonly considered to be the process that limits the height that surface gravity waves may reach
We have examined axisymmetric wave breaking and jet formation in a 25 m diameter, 2 m deep circular wave tank
In seminal experiments (Guthrie 1875; Rayleigh 1876; Honda & Matsushita 1913; Fultz & Murty 1963), in which axisymmetric waves were generated by sub-harmonic Faraday resonance in cylindrical containers, the predominant focus was on generation and nonlinear changes to the frequency of oscillation at amplitudes well below wave breaking (A/r0 0.07)
Summary
Wave breaking is commonly considered to be the process that limits the height (steepness) that surface gravity waves may reach. Faraday resonance can create axisymmetric waves (Miles 1984), and axisymmetric jetting behaviour is common when features with rotational symmetry, such as bubbles and droplets, encounter a free surface or wall (e.g., Blake & Gibson 1981; Longuet-Higgins & Oguz 1997; Zeff et al 2000) See Tab. 1 in Basak et al (2021) for a comprehensive overview of theoretical, numerical, and experimental studies involving such behavior These examples occur across a range of scales with varying relative importance of the effects of viscosity, capillarity, and gravity. As suggested by Longuet-Higgins (1983), some features such as jet formation may be ubiquitous
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