A spherical particle’s acceleration fall through still fluid was investigated analytically and experimentally using the Basset‐Boussinesq‐Oseen equation. The relationship between drag coefficient and Reynolds number was studied, and various parameters in the drag coefficient equation were obtained with respect to the small, medium, and large Reynolds number zones. Next, some equations were used to derive the finite fall time and distance equations in terms of certain assumptions. A simple experiment was conducted to measure the fall time and distance for a spherical particle falling through still water. Sets of experimental data were used to validate the relationship between fall velocity, time, and distance. Finally, the initial velocity effect on the total fall time and distance was discussed with different terminal Reynolds numbers, and it was determined that the initial velocity plays a more important role in the falling motion for small terminal Reynolds numbers than for large terminal Reynolds number scenarios.

The behavior of a vertical plunging jet was numerically investigated using the coupled Level Set and Volume of Fluid method. The computational results were in good agreement with the experimental results reported in the related literature. Vertical plunging jet characteristics, including the liquid velocity field, air void fraction, and turbulence kinetic energy, were explored by varying the distance between the nozzle exit and the still water level. It was found that the velocity at the nozzle exit plays an unimportant role in the shape and size of ascending bubbles. A modified prediction equation between the centerline velocity ratio and the axial distance ratio was developed using the data of the coupled Level Set and Volume of Fluid method, and it showed a better predicting ability than the Level Set and Mixture methods. The characteristics of turbulence kinetic energy, including its maximum value location and its radial and vertical distribution, were also compared with that of submerged jets.

Integrating coastal vegetation into sea dikes is a nature-based approach aimed at combining disaster prevention with ecological sustainability in coastal areas. This study investigates the impact of vegetation on the wave run-up on dikes through numerical analysis. The numerical model used in the study solves the Reynolds-averaged Navier–Stokes equations by adding a vegetation resistance force to account for momentum loss. A stabilized k–ω shear stress transport model considering the vegetation effect was adopted for turbulence closure. A series of numerical simulations was carried out on the wave run-up (Ru) on dikes, focusing on the effects of different vegetation heights, densities, zone lengths, and dike slopes under various wave conditions. The results indicate that vegetation can significantly decrease Ru and may cause the wave to change from breaking to nonbreaking on dikes. The Ru behaviors depend on whether waves break and can be well characterized by the Iribarren number and dimensionless wave momentum flux parameter under breaking and nonbreaking conditions, respectively. Finally, the multivariate non-linear regression (MNLR) and artificial neural network (ANN) methods were adopted to explore a prediction model for evaluating Ru. Comparisons showed that the prediction performance of the ANN model is superior to that of the MNLR model. The ANN model has the potential as a promising predictive tool for obtaining wave run-up on dikes with vegetated foreshores under breaking and nonbreaking conditions.