Tian-Jian Hsu

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].

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.

Vortex generation and evolution in water waves propagating over a submerged rectangular obstacle. Part II: Cnoidal waves

Vortex generation and evolution due to flow separation around a submerged rectangular obstacle under incoming cnoidal waves is investigated both experimentally and numerically. The Particle Image Velocimetry (PIV) technique is used in the measurement. Based on the PIV data, a characteristic velocity, phrased in terms of incoming wave height, phase speed, dimension of the obstacle, and a local Reynolds number are proposed to describe the intensity of vortex. The numerical model, which solves the two dimensional Reynolds Averaged Navier Stokes (RANS) equations, is used to further study the effects of wave period on the vortex intensity. Measurements for the mean and turbulent velocity fields further indicate that the time history of the intensity of fluid turbulence is closely related to that of the vortex intensity.

Toward modeling turbulent suspension of sand in the nearshore

[1] We present two depth- and phase-resolving models, based on single- and two-phase approaches for suspended sediment transport under water waves. Both models are the extension of a wave hydrodynamic model Cornell Breaking Wave and Structure (COBRAS). In the two-phase approach, dilute two-phase mass and momentum equations are calculated along with a fluid turbulence closure based on balance equations for the fluid turbulence kinetic energy k f and its dissipation rate ∈ f . In the single-phase approach the fluid flow is described by the Reynolds-Averaged Navier-Stokes equations, while the sediment concentration is calculated by an advection-diffusion equation for the conservation of sediment mass. The fluid turbulence is calculated by k f -∈ f equations that incorporate the essential influence of sediment, which can also be consistently deduced from the two-phase theory. By adopting a commonly used sediment flux boundary condition near the bed the proposed models are tested against laboratory measurements of suspended sediment under nonbreaking skewed water waves and shoaling broken waves. Although the models predict wave-averaged sediment concentrations reasonably well, the corresponding time histories of instantaneous sediment concentration are less accurate. We demonstrate that this is due to the uncertainties in the near-bed sediment boundary conditions. In addition, we show that under breaking waves the near-bed sediment pickup cannot be solely parameterized by the bottom friction, suggesting that other effects may also influence the near-bed sediment boundary conditions.

A numerical investigation of fine particle laden flow in an oscillatory channel: the role of particle-induced density stratification

Studying particle-laden oscillatory channel flow constitutes an important step towards understanding practical application. This study aims to take a step forward in our understanding of the role of turbulence on fine-particle transport in an oscillatory channel and the back effect of fine particles on turbulence modulation using an Eulerian–Eulerian framework. In particular, simulations presented in this study are selected to investigate wave-induced fine sediment transport processes in a typical coastal setting. Our modelling framework is based on a simplified two-way coupled formulation that is accurate for particles of small Stokes number ( St ). As a first step, the instantaneous particle velocity is calculated as the superposition of the local fluid velocity and the particle settling velocity while the higher-order particle inertia effect neglected. Correspondingly, only the modulation of carrier flow is due to particle-induced density stratification quantified by the bulk Richardson number, Ri . In this paper, we fixed the Reynolds number to be Re Δ = 1000 and varied the bulk Richardson number over a range ( Ri = 0, 1 × 10 −4 , 3 × 10 −4 and 6 × 10 −4 ). The simulation results reveal critical processes due to different degrees of the particle–turbulence interaction. Essentially, four different regimes of particle transport for the given Re Δ are observed: (i) the regime where virtually no turbulence modulation in the case of very dilute condition, i.e. Ri ~ 0; (ii) slightly modified regime where slight turbulence attenuation is observed near the top of the oscillatory boundary layer. However, in this regime a significant change can be observed in the concentration profile with the formation of a lutocline; (iii) regime where flow laminarization occurs during the peak flow, followed by shear instability during the flow reversal. A significant reduction in the oscillatory boundary layer thickness is also observed; (iv) complete laminarization due to strong particle-induced stable density stratification.

On the dynamics of wave-mud interaction: A numerical study

[1] Many previous studies consider wave attenuation over muddy seabeds and bottom boundary layer fluid-mud transport as two distinct research topics. Hence, various processes related to the physics of wave-mud interaction, such as turbulence-sediment interactions, rheological stresses, and nonlinear wave-wave interactions are incorporated rather artificially. The aim of this work is to present a new modeling approach which allows for the resolution of nonlinear wave propagation and bottom boundary layer mud transport with a single set of governing equations and closures. By adopting a fluid-mud modeling framework, a well-validated depth/phase-resolving wave propagation model, based on the Reynolds-Averaged Navier-Stokes (RANS) equations, is extended to model cohesive sediment transport. The numerical model consists of a set of governing equations based on the equilibrium Eulerian approach accurate for the fine sediment limit. The numerical model reduces to the clear fluid RANS equations when the sediment concentration approaches zero. Hence, the model is able to calculate continuously and consistently the nonlinear wave propagation, wave boundary layer processes, and fluid-mud transport without the need to prescribe the mud layer characteristics. Numerical simulations reveal several important physical processes that are critical for understanding the water-wave dynamics over muddy seabeds: (i) an enhancement of the wave boundary layer thickness due to the presence of the fluid-mud and rheological stress, which leads to a scaling relation between the enhanced wave boundary-layer and the fluid-mud layer and (ii) a direct wave amplitude dissipation due to rheological effects and clear evidences of low- and high-frequency wave attenuation via nonlinear energy transfer.

A numerical investigation of wave‐breaking‐induced turbulent coherent structure under a solitary wave

To better understand the effect of wave-breaking-induced turbulence on the bed, we report a 3-D large-eddy simulation (LES) study of a breaking solitary wave in spilling condition. Using a turbulence-resolving approach, we study the generation and the fate of wave-breaking-induced turbulent coherent structures, commonly known as obliquely descending eddies (ODEs). Specifically, we focus on how these eddies may impinge onto bed. The numerical model is implemented using an open-source CFD library of solvers, called OpenFOAM, where the incompressible 3-D filtered Navier-Stokes equations for the water and the air phases are solved with a finite volume scheme. The evolution of the water-air interfaces is approximated with a volume of fluid method. Using the dynamic Smagorinsky closure, the numerical model has been validated with wave flume experiments of solitary wave breaking over a 1/50 sloping beach. Simulation results show that during the initial overturning of the breaking wave, 2-D horizontal rollers are generated, accelerated, and further evolve into a couple of 3-D hairpin vortices. Some of these vortices are sufficiently intense to impinge onto the bed. These hairpin vortices possess counter-rotating and downburst features, which are key characteristics of ODEs observed by earlier laboratory studies using Particle Image Velocimetry. Model results also suggest that those ODEs that impinge onto bed can induce strong near-bed turbulence and bottom stress. The intensity and locations of these near-bed turbulent events could not be parameterized by near-surface (or depth integrated) turbulence unless in very shallow depth.

Direct numerical simulations of transition and turbulence in smooth-walled Stokes boundary layer

Stokes boundary layer (SBL) is a time-periodic canonical flow that has several environmental, industrial, and physiological applications. Understanding the hydrodynamic instability and turbulence in SBL, therefore, will shed more light on the nature of such flows. Unlike its steady counterpart, the flow in a SBL varies both in space and time, which makes hydrodynamic instability and transition from laminar to turbulent state highly complicated. In this study, we utilized direct numerical simulations (DNS) to understand the characteristics of hydrodynamic instability, the transition from laminar to turbulent state, and the characteristics of intermittent turbulence in a smooth SBL for ReΔ in the range of 500–1000. Simulation results show that nonlinear growth plays a critical role on the instability at ReΔ=500 and 600. However, the nonlinear growth does not warrant sustainable transition to turbulence and the outcome is highly dependent on the amplitude and spatial distribution of the initial velocity dist...

Large‐eddy simulation of wave‐breaking induced turbulent coherent structures and suspended sediment transport on a barred beach

To understand the interaction between wave-breaking induced turbulent coherent structures and suspended sediment transport, we report a Large-Eddy Simulation (LES) study of wave breaking processes over a near-prototype scale barred beach. The numerical model is implemented using the open-source CFD toolbox, OpenFOAM®, in which the incompressible three-dimensional filtered Navier-Stokes equations for the water and air phases are solved with a finite volume scheme. A Volume of Fluid (VOF) method is used to capture the evolution of the water-air interface. The numerical model is validated with measured free surface elevation, turbulence averaged flow velocity, turbulent intensity, and for the first time, the intermittency of breaking wave turbulence. Simulation results confirm that as the obliquely descending eddies (ODEs) approach the bottom, significant bottom shear stress is generated. Remarkably, the collapse of ODEs onto the bed can also cause drastic spatial and temporal changes of dynamic pressure on the bottom. By allowing sediment to be suspended from the bar crest, intermittently high sediment suspension events and their correlation with high turbulence and/or high bottom shear stress events are investigated. The simulated intermittency of sediment suspension is similar to previous field and large wave flume observations. Coherent suspension events account for only 10% of the record but account for about 50% of the sediment load. Model results suggest that about 60∼70% of coherent bottom stress events are associated with surface-generated turbulence. Nearly all the coherent sand suspension events are associated with coherent turbulence events due to wave-breaking turbulence approaching the bed. This article is protected by copyright. All rights reserved.

Convective instability in sedimentation: 3‐D numerical study

To provide a probable explanation on the field observed rapid sedimentation process near river mouths, we investigate the convective sedimentation in stably stratified saltwater using 3-D numerical simulations. Guided by the linear stability analysis, this study focuses on the nonlinear interactions of several mechanisms, which lead to various sediment finger patterns, and the effective settling velocity for sediment ranging from clay (single-particle settling velocity V0 = 0.0036 and 0.0144 mm/s, or particle diameter d = 2 and 4 μm) to silt (V0 = 0.36 mm/s, or d = 20 μm). For very fine sediment with V0 = 0.0036 mm/s, the convective instability is dominated by double diffusion, characterized by millimeter-scale fingers. Gravitational settling slightly increases the growth rate; however, it has notable effect on the downward development of vertical mixing shortly after the sediment interface migrates below the salt interface. For sediment with V0 = 0.0144 mm/s, Rayleigh-Taylor instabilities become dominant before double-diffusive modes grow sufficiently large. Centimeter-scale and highly asymmetric sediment fingers are obtained due to nonlinear interactions between different modes. For sediment with V0 = 0.36 mm/s, Rayleigh-Taylor mechanism dominates and the resulting centimeter-scale sediment fingers show a plume-like structure. The flow pattern is similar to that without ambient salt stratification. Rapid sedimentation with effective settling velocity on the order of 1 cm/s is likely driven by convective sedimentation for sediment with V0 greater than 0.1 mm/s at concentration greater than 10–20 g/L.