The time evolution of the maximal horizontal surface fluid velocity for an irrotational wave approaching breaking

Constantin, Adrian

doi:10.1017/jfm.2015.112

Cited by 11 publications

(9 citation statements)

References 17 publications

(24 reference statements)

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“…Since the variation along the arc length σ is such that |U | goes on increasing as we approach the point 2, and given that the horizontal velocity |U | decreases dramatically at point 1, the maximum necessarily occurs in the vicinity of point 2. These results are quite in line with those of Constantin [6].…”

Section: Identification Of the Velocity At The Free Surfacesupporting

confidence: 93%

Wave Kinematics in a Two-Dimensional Plunging Breaker

Scolan

Guilcher

2019

Water Waves

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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.

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Section: Identification Of the Velocity At The Free Surfacesupporting

confidence: 93%

Wave Kinematics in a Two-Dimensional Plunging Breaker

Scolan

Guilcher

2019

Water Waves

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“…Constantin & Strauss [14] proved that the pressure strictly decreases horizontally away from a crest line towards its neighbouring trough lines and increases with depth provided the maximum angle of inclination of the free surface is at most 45°. Recently, using an exact equation relating the time evolution of the maximum and minimum horizontal fluid velocities at the surface, Constantin [15] found that the derivative of the pressure is negative on the forward face of a wave, while it is positive on the rear face. More recently, Constantin [16] and Martin [17] proved mathematically that, for irrotational waves, the maximum and minimum of the dynamic pressure occur at the wave crest and wave trough, respectively.…”

Section: Introductionmentioning

confidence: 99%

Dynamic-pressure distributions under Stokes waves with and without a current

Umeyama¹

2017

Phil. Trans. R. Soc. A.

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To investigate changes in the instability of Stokes waves prior to wave breaking in shallow water, pressure data were recorded vertically over the entire water depth, except in the near-surface layer (from 0 cm to -3 cm), in a recirculating channel. In addition, we checked the pressure asymmetry under several conditions. The phase-averaged dynamic-pressure values for the wave-current motion appear to increase compared with those for the wave-alone motion; however, they scatter in the experimental range. The measured vertical distributions of the dynamic pressure were plotted over one wave cycle and compared to the corresponding predictions on the basis of third-order Stokes wave theory. The dynamic-pressure pattern was not the same during the acceleration and deceleration periods. Spatially, the dynamic pressure varies according to the faces of the wave, i.e. the pressure on the front face is lower than that on the rear face. The direction of wave propagation with respect to the current directly influences the essential features of the resulting dynamic pressure. The results demonstrate that interactions between travelling waves and a current lead more quickly to asymmetry.This article is part of the theme issue 'Nonlinear water waves'.

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“…Assuming the natural physical condition that initially the normal derivative of the pressure is negative on the smooth free surface, the short-time existence of a smooth subsequent free surface is ensured by the considerations in [12,31]. While the solution generated by such an initial state might develop into a breaking wave (see the discussion in [8]), in which case our considerations refer to any time up to the breaking time, it is known (see [24]) that small localized data ensure the longtime existence of solutions even outside the class of travelling waves. Let us also point out that smooth surface wave profiles of constant-vorticity flows are quite common: in particular, a travelling wave profile that is Hölder continuously differentiable must be real analytic (see [9]).…”

Section: The Mean Flow Beneath the Surface Wavesmentioning

confidence: 99%

On the decrease of kinetic energy with depth in wave–current interactions

Aleman

Constantin

2019

Math. Ann.

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We study wave-current interactions in two-dimensional water flows with constant vorticity over a flat bed. We establish decay rates for the velocity beneath spatially periodic surface waves without any restrictions on the wave amplitude. The approach relies on complex function theory and overcomes the intricacies inherent to nonlinear flow patterns by taking advantage of specific structural properties of the governing equations for water waves.

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The time evolution of the maximal horizontal surface fluid velocity for an irrotational wave approaching breaking

Cited by 11 publications

References 17 publications

Wave Kinematics in a Two-Dimensional Plunging Breaker

Wave Kinematics in a Two-Dimensional Plunging Breaker

Dynamic-pressure distributions under Stokes waves with and without a current

On the decrease of kinetic energy with depth in wave–current interactions

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