Eulerian–Lagrangian analysis for particle velocities and trajectories in a pure wave motion using particle image velocimetry

Abstract

This paper investigates the velocity and the trajectory of water particles under surface waves, which propagate at a constant water depth, using particle image velocimetry (PIV). The vector fields and vertical distributions of velocities are presented at several phases in one wave cycle. The third-order Stokes wave theory was employed to express the physical quantities. The PIV technique's ability to measure both temporal and spatial variations of the velocity was proved after a series of attempts. This technique was applied to the prediction of particle trajectory in an Eulerian scheme. Furthermore, the measured particle path was compared with the positions found theoretically by integrating the Eulerian velocity to the higher order of a Taylor series expansion. The profile of average travelling distance is also presented with a solution of zero net mass flux in a closed wave flume.

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

“…The theoretical considerations by Constantin (2006) and Constantin & Strauss (2010), the numerical simulations performed by Clamond (2012) and the experimental feedback provided by Umeyama (2012) show that for a symmetric travelling wave with a profile that is monotone between successive wave troughs and crests, the maximum M(t) of the horizontal fluid velocity is attained at the crest and does not exceed the propagation speed c of the wave. Kinematic wave breaking criteria based on numerical simulations, laboratory experiments and field observations indicate that with the onset of breaking the maximal horizontal fluid velocity rapidly increases during the overturning process from below 0.85c to almost 30 % greater than c, cf.…”

Turbulence-particle interactions under surface gravity waves

“…Several theoretical, numerical, and experimental studies have shown that the point particles underneath linear and nonlinear periodic waves experience non-closed orbits with horizontal drifts, and particles acquire a non-looping single arc during the passage of nonlinear solitary waves (LonguetHiggins 1953;Bakhoday-Paskyabi 2015;Umeyama 2012). Nevertheless, the inertial particles extract momentum from the wave orbital motions near the air-sea interface and accelerate in the form of sinking/rising helix (Constantin 2006;Eames 2008;Santamaria et al 2013).…”

A Hamiltonian approach to wave-current interactions in two-layer fluids

“…13 In the setting of travelling waves propagating in irrotational flow with no stratification, the Hamiltonian structure was essential in uncovering the flow pattern beneath the surface waves: theoretical studies 14,15 were confirmed numerically 16 and experimentally. 17 In this special context, the presence of an underlying current -that can only be uniform in these circumstances -increases considerably the dynamical complexity. For a two-layer fluid with a non-uniform underlying current, numerical and experimental data suggest an even richer dynamics, highlighted by the possible appearance of critical levels.…”