Hweng Hwung

Structural permeability effects on the interaction of a solitary wave and a submerged breakwater

Abstract The unsteady two-dimensional Navier–Stokes equations and Navier–Stokes type model equations for porous flows were solved numerically to simulate the interaction between a solitary wave and a submerged porous breakwater. The free surface boundary conditions and the interfacial boundary conditions between the water and the porous media are in complete form. A piston-type wavemaker, set-up in the computational domain, generated the incident solitary wave. The accuracy of the numerical model was verified by comparing the numerical results with the experimental data. Having verified the accuracy of the numerical model, the effects of several parameters on the interaction of a solitary wave and a submerged breakwater were systematically investigated. These parameters include the incident wave height, the aspect ratio of the breakwater, and the porosity including the impermeable case. The flow fields near the breakwater are discussed in terms of the velocity vectors, the vortex shedding and the trajectories of the fluid particles. The pressure drag acting on the breakwater was also calculated. The numerical results reveal that if the breakwater width is small compared with the effective wave length, the structure permeability has no apparent effect on wave transformation. For wide porous breakwaters, if the structure porosity is small, the increase in the porosity results in the reduction of the transmission coefficient; otherwise the transmission coefficient increases with porosity.

ENERGY DISSIPATION AND AIR BUBBLES MIXING INSIDE SURF ZONE

The first part of this article gives an overview of the development works that have been carried out to date along the French coast, covering types, operating principles and impacts. A philosophy is identified with regard to the schemes implemented so far and those recommended for the future: rather than static structures that resist the action of the sea, it would often be preferable to substitute dynamic structures and schemes that work in harmony with it. Much research is being carried out on designs of this type. An analysis and summary of this work is given in the second part of this article. Most such work is currently at the experimental stage and no miracle solution has been found so far. Local conditions must be examined carefully before deciding to use any of the new alternatives being proposed.

Observations on the evolution of wave modulation

A series of laboratory experiments on the long-time evolution of nonlinear wave trains in deep water was carried out in a super wave flume (300×5.0×5.2u200am) at Tainan Hydraulics Laboratory of National Cheng Kung University. Two typical wave trains, namely uniform wave and imposed sideband wave, were generated by a piston-type wavemaker. Detailed discussions on the evolution of modulated wave trains, such as transient wavefront, fastest growth mode and initial wave steepness effect, are given and the results are compared with existing experimental data and theoretical predictions. Present results on the evolution of initial uniform wave trains cover a wide range of initial wave steepness () and thus, greatly extend earlier studies that are confined only to the larger initial wave steepness region (). The amplitudes of the fastest growth sidebands exhibit a symmetric exponential growth until the onset of wave breaking. At a further stage, the amplitude of lower sideband becomes larger than the carrier wave and upper sideband after wave breaking, which is known as the frequency downshift. The investigations on the evolution of initial imposed sideband wave trains for fixed initial wave steepness but different sideband space indicate that the most unstable mode of initial wave train will manifest itself during evolution through a multiple downshift of wave spectrum for the wave train with the smaller sideband space. It reveals that the spectrum energy tends to shift to a lower frequency as the wave train propagates downstream due to the sideband instability. Experiments on initial imposed sideband wave trains with varied initial wave steepness illustrate that the evolution of the wave train is a periodic modulation and demodulation at post-breaking stages, in which most of the energy of the wave train is transferred cyclically between the carrier wave and two imposed sidebands. Meanwhile, the wave spectra show both temporal and permanent frequency downshift for different initial wave steepness, suggesting that the permanent frequency downshift induced by wave breaking observed by earlier researchers is not permanent. Additionally, the local wave steepness and the ratio of horizontal particle velocity to linear phase velocity at wave breaking in modulated wave group are very different from those of Stokes theory.

Extended Boussinesq Equations for Water-Wave Propagation in Porous Media

This paper presents a new Boussinesq-type model equations for describing nonlinear surface wave motions in porous media. The mathematical model based on perturbation approach reported by Hsiao et al. is derived. The drag force and turbulence effect suggested by Sollitt and Cross are incorporated for observing the flow behaviors within porous media. Additionally, the approach of Chen for eliminating the depth-dependent terms in the momentum equations is also adopted. The model capability on an applicable water depth range is satisfactorily validated against the linear wave theory. The nonlinear properties of model equations are numerically confirmed by the weakly nonlinear theory of Liu and Wen. Numerical experiments of regular waves propagating in porous media over an impermeable submerged breakwater are performed and the nonlinear behaviors of wave energy transfer between different harmonics are also examined.

Evolution of sidebands in deep-water bichromatic wave trains

Numerical and physical experiments on bichromatic wave trains were conducted in deep water. The evolution of wave trains and corresponding spectra were investigated in this paper. The results indicate that the evolution of bichromatic wave trains strongly depends on the wave steepness and frequency difference between the imposed wave components. The evolutions of wave trains including breaking and non-breaking types were analyzed for different combination of wave steepness and frequency difference. Specifically, for non-breaking cases, the wave trains evolve modulation and demodulation periodically in the experimental data. This phenomenon can be better predicted by the nonlinear Schrödinger (NLS) equation. However, for the free surface displacement, the multi-layer Boussinesq model gives better phase agreement with experimental data. For breaking case, the amplitude of lower sideband frequency is selectively amplified through the breaking process, which can be qualitatively simulated in the NLS model by adding an additional proper damping function. The experimental data also show weak evolution of induced bound long wave during the breaking process

NONLINEAR WATER WAVES OVER A THREE-DIMENSIONAL POROUS BOTTOM USING BOUSSINESQ-TYPE MODEL

Nonlinear water waves propagating over a three-dimensional submerged porous bottom are investigated using depth-integrated model developed by Hsiao et al. In particular, the case of waves over porous submerged trapezoidal mounds is discussed and the results are compared with the experimental data of Cruz et al. The overall comparisons are reasonably good, suggesting that the model equations used in this study can describe diffraction, reflection and refraction effects well.

FLOW CHARACTERISTICS OF SPILLING AND PLUNGING BREAKERS IN THE SURF ZONE

Fundamental flow characteristics in the surf zone of spilling (SP) and plunging (PL) breakers are compared using a well-validated numerical model named COBRAS. The main objective is to investigate how beach slope affects flow characteristics (streamline topography, vorticity evolution processes, TKE dynamics and reverse flow) in the surf zone of plunging (PL) and spilling (SP) breakers. The major results are of four categories: (1) the streamline topography of PL waves is mostly similar to that of SP. For both types of breaker, a convergent stagnation point (CSP) always appears in the offshore direction after the generation of a divergent stagnation point (DSP). The location of a DSP is generally underneath the front face of wave crest. Both DSP and CSP move to the inner surf zone following wave propagation. (2) the main difference of vortices evolution is that clockwise (CW) vortices after wave breaking are stronger for PL waves but mild for SP waves . The CW vortices of SP decay upstream directly but those of PL waves advect toward the bottom slope and then degenerate upstream. (3) The TKE generated by PL waves is much larger than that generated by SP waves. The distributions of generated TKE values of SP and PL waves are similar to the corresponding vortex motions. (4) The maximum magnitude of reverse flow in surf-zone of PL waves is around 1.4 times that of SP waves.

Combination Mode of Internal Waves Generated by Surface Wave Propagating over Two Muddy Sea Beds

When surface wave propagating over the two layer system usually induces internal wave in three different modes: they are external, internal and combination. In the present study, the nonlinear response of an initially flat sea bed, with two muddy sections, to a monochromatic surface progressive wave was investigated. From this theoretical result, it shows that a surface water wave progressing over two different muddy sections, the surface wave will excite two opposite-traveling short interfacial waves, forming a nearly standing wave at the interface of the fresh water and the muddy layer. Meanwhile, two opposite-outgoing “mud” waves each with very long wavelength will be simultaneously induced at the interface of two muddy sections. As a result, the amplitudes of the two short internal waves are found to grow exponentially in time. Furthermore, it will be much difficult to excite the internal waves when surface water wave progressing over two muddy sections with the large density gap.

Intermittent slipping of landslide regulated by dilatancy evolution and velocity-weakening friction law: an efficient numerical scheme

When a block of dense sandy soil moves downhill, the shear-induced soil dilatancy along the basal shear boundary produces a negative value of excess pore pressure that increases the basal frictional resistance. Dilatancy angle, Ψ, the degree to which the basal soil dilates due to the shear, normally evolves during slope failure. A study by other researchers shows that if Ψ is constant, the block of dense soil will remain stable (or unstable) sliding when the velocity-weakening rate of the basal friction coefficient of the block is small (or large) enough. Moreover, during unstable sliding processes, the block of dense soil exhibits “periodic” patterns of intermittent slipping. Here, we used a more efficient and accurate numerical scheme to revisit that study. We expanded their model by assuming Ψ evolves during slope failure. Consequently, we acquired completely different results. For instance, even though the velocity-weakening rate of the friction coefficient is fixed at the same smaller (or larger) value that those researchers use, the stable (or unstable) steady states of landslide they predict will inversely change to unstable (or stable) when Ψ decreases (or increases) with the increase of slide displacement to a value small (or large) enough. Particularly, in unstable processes, the soil block exhibits “aperiodic” styles of intermittent slipping, instead of “periodic”. We found out that the stick states appearing later last longer (or shorter) in the case of decreasing (or increasing) Ψ. Moreover, because the basic states of landslides with impacts of dilatancy evolution are not steady nor periodic, traditional stability-analysis methods cannot be “directly” used to analyze the stability of such landslides. Here, we broke through this technical problem to a degree. We showed that combining a concept called “quasi-steady-state approximation” with a traditional stability-analysis technique can qualitatively predict the instability onset of the landslides. Through this study, we demonstrated that the combination of Chebyshev collocation (CC) and 4th-order Runge-Kutta methods is more accurate and efficient than the numerical scheme those researchers use.

Feasibility study on an integrated offshore wind turbine and mariculture cage facility

A 1:36 scale model tests are carried out in the Near-shore Wave Basin (NSWB) at Tainan Hydraulics Laboratory (THL) with the jacket type offshore wind turbine foundation under the location of soft scour protection in the test area. The scour around the jacket type offshore wind turbine foundation exposed to wave and current was conducted in the NSWB with the mobile bed experiment. Two locations (water depth 12m and 16m) of the foundations are separately simulated in this study. From the experimental result, it shows that the scour protection effect of an integrated offshore wind turbine and cage net aquaculture facility as a soft countermeasure for scour protection of jacket type offshore wind turbine foundation is further evaluated in this study. Meanwhile, the detail analysis for stakeholders opinions on the integration of offshore wind farm and coastal aquaculture is also considered to obtain the important experience and knowledge; furthermore to understand the real demand for adjusting the feasibility of this soft countermeasure.