Philip L.-F. Liu

A numerical study of breaking waves in the surf zone

This paper describes the development of a numerical model for studying the evolution of a wave train, shoaling and breaking in the surf zone. The model solves the Reynolds equations for the mean (ensemble average) flow field and the k –e equations for the turbulent kinetic energy, k , and the turbulence dissipation rate, e. A nonlinear Reynolds stress model (Shih, Zhu & Lumley 1996) is employed to relate the Reynolds stresses and the strain rates of the mean flow. To track free-surface movements, the volume of fluid (VOF) method is employed. To ensure the accuracy of each component of the numerical model, several steps have been taken to verify numerical solutions with either analytical solutions or experimental data. For non-breaking waves, very accurate results are obtained for a solitary wave propagating over a long distance in a constant depth. Good agreement between numerical results and experimental data has also been observed for shoaling and breaking cnoidal waves on a sloping beach in terms of free-surface profiles, mean velocities, and turbulent kinetic energy. Based on the numerical results, turbulence transport mechanisms under breaking waves are discussed.

Runup of solitary waves on a circular island

This is a study of the interactions of solitary waves climbing up a circular island. A series of large-scale laboratory experiments with waves of different incident height-to-depth ratios and different crest lengths is described. Detailed two-dimensional run-up height measurements and time histories of surface elevations around the island are presented. A numerical model based on the two-dimensional shallow-water wave equations including runup calculations was developed. Numerical model predictions agreed very well with the laboratory data and the model was used to study wave trapping and the effect of slope. Under certain conditions, enhanced runup and wave trapping on the lee side of the island were observed, suggesting a possible explanation for the devastation reported by field surveys in Babi Island off Flores, Indonesia, and in Okushiri Island, Japan.

Modeling wave runup with depth-integrated equations

A telescoping boom crane having a multi-sectioned, telescopically extending boom and an extensible pendant support system. The extending boom includes boom sections that are extensibly receivable within the adjacent boom section. The boom sections are made of a sheet material. A releasable locking mechanism may be attached to the boom sections to secure the boom sections.The extensible pendant support system includes a plurality of pendants. The pendants are extensibly receivable within an adjacent pendant. The pendant support system at least partially supports the boom when a load is applied to the boom. Further, the support system may include a forestay length locking device functioning to prohibit extension of a subsequent pendant from an adjacent pendant once the former pendant achieves an extended position.

Waves over Soft Muds: A Two-Layer Fluid Model

Abstract The problem of water waves propagating over a mud bottom, characterized as a laminar viscous fluid, is treated in several ways. First, two complete models are present, each valid for different lower (mud) layer depths, and second, a boundary layer model is presented as an appendix for the case where the lower layer is thick with respect to the boundary layer. These models are compared to the shallow water model and experimental results of Gade (1957, 1958) and agree well. The results show that extremely high wave attenuation rates are possible when the thickness of the lower layer is the same order as the internal boundary layer thickness and when the lower layer is thick.

A numerical study of submarine-landslide-generated waves and run-up

A mathematical model is derived to describe the generation and propagation of water waves by a submarine landslide. The model consists of a depth–integrated continuity equation and momentum equations, in which the ground movement is the forcing function. These equations include full nonlinear, but weak frequency–dispersion, effects. The model is capable of describing wave propagation from relatively deep water to shallow water. Simplified models for waves generated by small seafloor displacement or creeping ground movement are also presented. A numerical algorithm is developed for the general fully nonlinear model. Comparisons are made with a boundary integral equation method model, and a deep–water limit for the depth–integrated model is determined in terms of a characteristic side length of the submarine mass. The importance of nonlinearity and frequency dispersion in the wave–generation region and on the shoreline movement is discussed.

A numerical model for wave motions and turbulence flows in front of a composite breakwater

Abstract A mathematical model based on the Volume-Averaged/Reynolds Averaged Navier-Stokes (VARANS) equations is developed to describe surface wave motions in the vicinity of a coastal structure, which could be either a rigid solid structure or a permeable structure or a combination of both. In the VARANS equations, the volume-averaged Reynolds stress is modeled by adopting the nonlinear eddy viscosity assumption. The model equations for the volume-averaged turbulent kinetic energy and its dissipation rate are derived by taking the volume-average of the standard k−ϵ equations. Because of the volume-averaging process, the effects of the small-scale turbulence in porous media are introduced. The performance of the model is checked by comparing numerical solutions with the experimental data related to a composite breakwater reported by Sakakiyama and Liu [Coast. Eng. 121 (2001) 117].

Runup and rundown generated by three-dimensional sliding masses

To study the waves and runup/rundown generated by a sliding mass, a numerical simulation model, based on the large-eddy-simulation (LES) approach, was developed. The Smagorinsky subgrid scale model was employed to provide turbulence dissipation and the volume of fluid (VOF) method was used to track the free surface and shoreline movements. A numerical algorithm for describing the motion of the sliding mass was also implemented. To validate the numerical model, we conducted a set of large-scale experiments in a wave tank of 104 m long, 3.7 m wide and 4.6 m deep with a plane slope (1:2) located at one end of the tank. A freely sliding wedge with two orientations and a hemisphere were used to represent landslides. Their initial positions ranged from totally aerial to fully submerged, and the slide mass was also varied over a wide range. The slides were instrumented to provide position and velocity time histories. The time-histories of water surface and the runup at a number of locations were measured. Comparisons between the numerical results and experimental data are presented only for wedge shape slides. Very good agreement is shown for the time histories of runup and generated waves. The detailed three-dimensional complex flow patterns, free surface and shoreline deformations are further illustrated by the numerical results. The maximum runup heights are presented as a function of the initial elevation and the specific weight of the slide. The effects of the wave tank width on the maximum runup are also discussed.

On two-phase sediment transport: sheet flow of massive particles

A model is presented for concentrated sediment transport that is driven by strong, fully developed turbulent shear flows over a mobile bed. Balance equations for the average mass, momentum and energy for the two phases are phrased in terms of concentration–weighted (Favre averaged) velocities. Closures for the correlations between fluctuations in concentration and particle velocities are based on those for collisional grain flow. This is appropriate for particles that are so massive that their fall velocity exceeds the friction velocity of the turbulent fluid flow. Particular attention is given to the slow flow in the region of high concentration above the stationary bed. A failure criterion is introduced to determine the location of the stationary bed. The proposed model is solved numerically with a finite–difference algorithm in both steady and unsteady conditions. The predictions of sediment concentration and velocity are tested against experimental measurements that involve massive particles. The model is further employed to study several global features of sheet flow such as the total sediment transport rate in steady and unsteady conditions.

An analysis of 2004 Sumatra earthquake fault plane mechanisms and Indian Ocean tsunami

The 2004 Sumatra earthquake and the associated tsunamis are one of the most devastating natural disasters in the last century. Several fault plane models have been suggested to represent the rupture mechanism of the earthquake. During this tsunami event, two satellites flew over Bay of Bengal and provided measurements for sea surface elevation with accuracy better than 4.2 cm. The satellite data provide an opportunity to further calibrate and validate the fault mechanism and tsunami propagation models as well. Thus, based on the proposed fault plane models, a series of numerical simulations for tsunami generation and propagation in the Bay of Bengal have been carried out. In comparison with the satellite data, the numerical results show that although the length of the entire ruptured zone is up to 1300 km long for this earthquake, the duration of slip and the rupture speed are still relatively short in comparison with the time scale and the propagation speed of tsunami and the impulsive fault plane model simulates reasonably well the tsunamis in the deep ocean.An inverse method is developed to optimize the seafloor displacement on the fault plane based on the measurements of satellite Jason-1. Finally, employing the optimized fault plane model, we demonstrate that the tsunami simulation model can produce results that match very well with the measurements of sea surface level by satellite TOPEX/Poseidon and available tidal gage measurements at Maldives.

Turbulence transport, vorticity dynamics, and solute mixing under plunging breaking waves in surf zone

Plunging breaking waves generate turbulence and vorticity, which are of great importance for the solute and sediment transport in surf zone. In this paper the complex breaking processes are simulated by using an accurate numerical model that solves the Reynolds equations for the mean flow and modified k-e equations for the turbulence field. A solute transport model is employed to investigate the solute mixing under plunging waves. After validation of the numerical model by comparing numerical results with available experimental data, the numerical model is further utilized to study the detailed mechanisms of turbulence transport and vorticity dynamics. The differences between spilling and plunging breaking waves are discussed. The impact of the wave breaking on solute mixing in the surf zone is also examined.