Correct prediction of particle transport by surface waves is crucial in many practical applications such as search and rescue or salvage operations and pollution tracking and clean-up efforts. Recent results by Deike et al. (J. Fluid Mech., vol. 829, 2017, pp. 364–391) and Pizzo et al. (J. Phys. Oceanogr., vol. 49, no. 4, 2019, pp. 983–992) have indicated transport by deep-water breaking waves is enhanced compared with non-breaking waves. To model particle transport in irregular waves, some of which break, we develop a stochastic differential equation describing both mean particle transport and its uncertainty. The equation combines a Brownian motion, which captures non-breaking drift-diffusion effects, and a compound Poisson process, which captures jumps in particle positions due to breaking. From the corresponding Fokker–Planck equation for the evolution of the probability density function for particle position, we obtain closed-form expressions for its first three moments. We corroborate these predictions with new experiments, in which we track large numbers of particles in irregular breaking waves. For breaking and non-breaking wave fields, our experiments confirm that the variance of the particle position grows linearly with time, in accordance with Taylor's single-particle dispersion theory. For wave fields that include breaking, the compound Poisson process increases the linear growth rate of the mean and variance and introduces a finite skewness of the particle position distribution.@en

Weld-induced squats are a major damage type in high-speed railways as well as in conventional railways. They incur high maintenance costs and endanger operational safety. This paper first presents and analyzes five-year continual field monitoring observations and measurements of squats at rail welds. A hypothesis of the formation and development process of the squats is proposed, which includes three steps. Steps 1 and 2 are pre-cracking, and Step 3 is post-cracking. To verify the pre-cracking process, a three-dimensional (3D) finite element (FE) model is then built up to simulate the vehicle-track interaction with detailed consideration of the local wheel-rail frictional rolling contact. Not only dynamic contact forces but also plastic deformation and wear are calculated. Starting from a smooth rail surface with varying yield stress derived from field-measured hardness, the numerical analysis confirms the hypothesis that the varying hardness at heat-affected zones (HAZs) leads to initial V-shaped irregularities due to differential plastic deformation. Afterward, the surface irregularities excite the dynamic longitudinal contact force, which in turn produces a W-shaped surface pattern through further differential plastic deformation. The growth of the W-shaped pattern leads to the formation of squats. This work provides insight into the squat formation process at rail welds and suggests that welding quality control in terms of hardness variation in the HAZs could reduce or even avoid squats. Early detection of squats with dynamics-based methods is possible.@en