The equilibrium dynamics and statistics of gravity–capillary waves

Melville, W. Kendall; Fedorov, Alexey V.

doi:10.1017/jfm.2014.740

Cited by 24 publications

(29 citation statements)

References 37 publications

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“…This inertial model, based on a simple physical argument for strong plunging waves, has been confirmed through extensive experimental studies and modeling, well beyond the region of validity of the initial hypothesis (Romero et al 2012;Grare et al 2013;Pizzo & Melville 2013;Melville & Fedorov 2015;Deike et al 2015). Note that proportionality between the initial slope and the slope at breaking is also true in our DNS of steep Stokes waves, and following the definition of Drazen et al (2008) where h is the vertical distance the breaking wave toe travels before impact, hk = −0.05 + S for both the 3D DNS presented here and the 2D results presented in Deike et al (2015).…”

Section: Energy Dissipationmentioning

confidence: 63%

Air entrainment and bubble statistics in breaking waves

2016

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We investigate air entrainment and bubble statistics in three-dimensional breaking waves through novel direct numerical simulations of the two-phase air-water flow, resolving the length scales relevant for the bubble formation problem, the capillary length and the Hinze scale. The dissipation due to breaking is found to be in good agreement with previous experimental observations and inertial-scaling arguments. The air-entrainment properties and bubble-size statistics are investigated for various initial characteristic wave slopes. For radii larger than the Hinze scale, the bubble size distribution, can be described by N (r, t) = B(V 0 /2π)(ε(t − ∆τ )/W g)r −10/3 r −2/3 m during the active breaking stages, where ε(t − ∆τ ) is the time dependent turbulent dissipation rate, with ∆τ the collapse time of the initial air pocket entrained by the breaking wave, W a weighted vertical velocity of the bubble plume, r m the maximum bubble radius, g gravity, V 0 the initial volume of air entrained, r the bubble radius and B a dimensionless constant. The active breaking time-averaged bubble size distribution is described bȳ N (r) = B(1/2π)( l L c /W gρ)r −10/3 r −2/3 m , where l is the wave dissipation rate per unit length of breaking crest, ρ the water density and L c the length of breaking crest. Finally, the averaged total volume of entrained air,V , per breaking event can be simply related to l byV = B( l L c /W gρ), which leads to a relationship to a characteristic slope, S, of V ∝ S 5/2 . We propose a phenomenological turbulent bubble break-up model, based on earlier models and the balance between mechanical dissipation and work done against buoyancy forces. The model is consistent with the numerical results and existing experimental results.

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Section: Energy Dissipationmentioning

confidence: 63%

Air entrainment and bubble statistics in breaking waves

2016

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“…Most recently Melville & Fedorov (2014) using the theory of have shown that the dissipative effects of parasitic capillaries on short, O(1 − 10) cm, gravity-capillary waves may be enough to balance the wind input and also be consistent with the inertial scaling of the breaking parameter, b, presented first for plunging waves by Drazen et al (2008), and extended by Romero et al (2012) to encompass the full range of breaking strengths, including spilling breakers (Pizzo & Melville 2013).…”

Section: Introductionmentioning

confidence: 68%

“…Regarding surface tension effects, boundary layer theory has provided a general description of the appearance of capillary ripples on the front of carrier gravity waves (Longuet-Higgins 1963;Melville & Fedorov 2014) and were first observed numerically by Mui & Dommermuth (1995). Numerical simulations of gravity-capillary waves are based on potential theory with a boundary layer near the interface (Yang & Tryggvason 1998;Furhman et al 2004;Fructus et al 2005), or on Navier Stokes formulation (Mui & Dommermuth 1995;Tsai & Hung 2007, not taking into account the air flow, or the air being modelled by a pressure forcing Melville & Fedorov 2014). They provide qualitative and quantitative comparisons with the various wave patterns and phenomenology observed experimentally.…”

Section: Introductionmentioning

confidence: 99%

“…They provide qualitative and quantitative comparisons with the various wave patterns and phenomenology observed experimentally. The enhancement of dissipation by parasitic capillaries has also been described, both experimentally (Zhang 1995;Caulliez 2013) and numerically Tsai & Hung 2007Melville & Fedorov 2014). Numerical simulations of the complete two-phase flow remain relatively rare and have focused on the resolution of the wave breaking and post impact dynamics, which are numerically challenging (Chen et al 1999;Song & Sirviente 2004;Iafrati 2009Iafrati , 2011Iafrati et al 2013).…”

Section: Introductionmentioning

confidence: 99%

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Capillary effects on wave breaking

2015

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We investigate the influence of capillary effects on wave breaking through direct numerical simulations of the Navier-Stokes equations for a two-phase air-water flow. A parametric study in terms of the Bond number, Bo, and the initial wave steepness, , is performed at a relatively high Reynolds number. The onset of wave breaking as a function of these two parameters is determined and a phase diagram in terms of ( , Bo) is presented that distinguishes between non-breaking gravity waves, parasitic capillaries on a gravity wave, spilling breakers and plunging breakers. At high Bond number, a critical steepness c defines the wave stability. At low Bond number, the influence of surface tension is quantified through two boundaries separating, firstly gravity-capillary waves and breakers, and secondly spilling and plunging breakers; both boundaries scaling as ∼ (1 + Bo) −1/3 . Finally the wave energy dissipation is estimated for each wave regime and the influence of steepness and surface tension effects on the total wave dissipation is discussed. The breaking parameter b is estimated and is found to be in good agreement with experimental results for breaking waves. Moreover, the enhanced dissipation by parasitic capillaries is consistent with the dissipation due to breaking waves.

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“…According to this approach, appropriate transfer functions can be used to determine wave kinematics at different nodes of an offshore structure from a simulated surface elevation record. However, this method has shown unacceptable results near free surface, especially for unrealistically high-frequency wave components [8][9][10]. To cope with the offshore industrial practice, reasonable results of wave kinematics near-surface zone are considered essential.…”

Section: Introductionmentioning

confidence: 99%

Various methods of simulating wave kinematics on the structural members of 100-year responses

Husain¹,

Zaki²,

Najafian³

2017

J. MECH. ENG. SCI.

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The main force acting on an offshore structure is usually due to wind-generated random waves. According to the Morison equation, the wave force on a cylindrical member of an offshore structure depends on wave kinematics at the centre of the element. It is therefore essential to accurately estimate the magnitude of wave-induced water particle kinematics at all points in a random wave field. Linear random wave theory (LRWT) is the mostfrequently used theory to simulate water particle kinematics at different nodes of an offshore structure. Several empirical techniques have been suggested to provide a more realistic representation of the near-surface wave kinematics. The empirical techniques popular in the offshore industry include Wheeler stretching and vertical stretching. Most recently, two new effective methods (effective node elevation and the effective water depth) have been recently introduced. The problem is that these modified methods differ from one another in their predictions. Hence, the aim of this study is to investigate the effects of predicting the 100-year responses from various methods of simulating wave kinematics accounting for the current effect. In this paper, four versions of the wave kinematics procedure have been tested by comparing the short-term probability distributions of extreme responses. For all current cases, the highest vertical ratios for zero, positive and negative current cases are 1.414, 1.175 and 1.831, respectively. It is observed that even for positive-current cases, the difference between Wheeler and vertical stretching predictions is quite high and cannot be neglected. Thus, further investigation is necessary to resolve this problem and the outcomes in providing useful design information for the oil and gas industry.

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The equilibrium dynamics and statistics of gravity–capillary waves

Cited by 24 publications

References 37 publications

Air entrainment and bubble statistics in breaking waves

Air entrainment and bubble statistics in breaking waves

Capillary effects on wave breaking

Various methods of simulating wave kinematics on the structural members of 100-year responses

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