Researches about the interaction between freak waves and coastal breakwaters are rare. In this paper, the nonlinear freakwaves propagation over a submerged trapezoid breakwater on a flat seabed are investigated both experimentally and numerically, with emphasis on the effect of the breakwater on the hydrodynamic behavior of the breaking and non-breaking freakwaves. A series of experiments are carried out and used to validate a numerical model based on a fully nonlinear Navier-Stokes equations. A spatio-temporal focusing model is employed for freakwave generation. The numerical results of freakwave evolution along the flume are compared with the measured data and good agreement is achieved, which indicates that the present numerical model is capable of accurately predicting the wave-structure interaction. Furthermore, the variation of the freak waves energy structure are conducted to investigate the influence of the breakwater. In the end, the variation of the whole velocity fields near the structure are given to analysis the hydrodynamic characteristics of freak waves during the propagation through the breakwater.
Freak waves, also named rogue waves or giant waves, are extremely large water waves in oceans which are highly nonlinear and may occur unexpectedly due to diverse reasons. Draper (1965) first proposed the concept of freakwave, after that, the physical mechanisms of extremely large water waves have been studied extensively. Numerous studies have shown that the occurrence of freakwave maybe relate to wave energy focusing including a number of processes: wave-current interactions, wave-bottom interactions, wave-wave interactions and wind-wave interactions. These various mechanisms of generation of extreme waves were reviewed in details by Kharif et al.(2003) and Dysthe et al.(2008).
Physical and numerical simulations as the main tools have been carried out by many researchers to represent and research freakwaves. However, modeling of extreme wave events with a random wave series is more challenging as it requires very long simulation time due to the rare probability of occurrence (Kharif et al. 2003). According to the wave-wave interaction, Davis and Zarnick (1964) first proposed the spatio-temporal focusing model in which many wave components appear simultaneously at a specified position in space to generate an extreme wave profile, which is consistent with a random process. From then, there are many investigations using dispersive focused wave groups to generate large transient events both in the laboratory and the numerical flume (Longuet-Higgins, 1980; Baldock et al., 1996; Ning et al., 2009; Huang et al., 2012).
Laboratory experiments have been carried out in a piston-driven wave flume to investigate the solitary wave impact on three types of vertical cylindrical objects, including the vertical cylinder, cone and bell-shaped lighthouse structure. First, the quality of the generated waves is examined by comparing their profiles with the theoretical solutions. The range of piston movements that generates good-quality solitary waves is determined. The scattering of solitary waves around geometrically different vertical structures is then focused on. The wave heights around the structures are measured in detail, from which the wave impact force is derived. The results regarding vertical cylinders agree well with the past research outcomes. It shows that the vertical cone structure experiences the largest impact force. Although the bellshaped lighthouse structure incurs slightly larger impact force than the vertical cylinder, it has a much larger and thus more stable base to resist the overturning moment. The findings confirm the good mechanical performance of some of the old lighthouse structures, which have existed for around 200 years.
A solitary wave is described by Goring (1978) as a single “hump” of water that is entirely above still water level with an infinite wavelength. Solitary waves were first identified by Russell (1845) and have been the subject of considerable research ever since. Theoretical and experimental work by Hammack and Segur (1974) showed that from any water displacement above still water level at least one solitary wave shall emerge followed by a number of dispersive waves.
The Boxing Day tsunami of 2004 will go down in history as being one of the worst natural disasters ever recorded as it claimed the lives of more than 150,000 people, left millions homeless and caused billions of dollars’ worth of damage (Briggs et al. 2005). Although the Boxing Day tsunami shall be remembered for the devastating amount of damage it caused, it is important that it is not classed as being a “freak event of nature”. The tsunami itself was fairly typical of other tsunamis that have occurred in the past and are likely to strike again as shown recently by the tsunami that struck the north-east coast of Japan on the 11th March 2011. Solitary waves are not only used to model tsunamis but are also used to model large storm surges that commonly occur as a result of hurricanes.
A numerical model is presented to simulate the interaction between waves and a moored floating tank coupling with internal liquid. A strong coupling algorithm for fluid-structure interaction has been developed to overcome the unstable problem. The impact of internal liquid on tank motion is converted to the external force acting on the empty floating tank. The numerical model is validated by the experimental results with good agreements for the motion responses and water surface elevations. The numerical results of moored floating liquid tank are compared with the floating tank without internal sloshing. The effects of liquid sloshing on the tank motion are also presented.
In recent years, the floating storage systems have attracted favorable attention with the ever-growing need for oil storage and liquefied natural gas reserves. Compared with the traditional oil storage facilities constructed on the land, the floating storage systems offer designers good alternatives with the advantages of cost reduction and land area saving. Furthermore, profiting from being constructed offshore, they are ideal in keeping explosive oil and liquefied natural gas away from earthquakes and thunder strikes. However, the safety of the floating storage structures could be influenced by the internal sloshing liquid coupling with external water waves during loading and offloading operations. The motion responses of floating structure may be violent under extreme sea conditions, which will result in large mooring force and fatigue damage. Moreover, the highly localized impact pressure acting on tank walls may cause structural damages. Therefore, the research on floating liquid storage systems coupling with internal sloshing are in progress.
Traditionally, the sloshing problem and the seakeeping problem for floating liquid storage structure are studied separately. For example, Faltinsen (1978) derived the linear analytical solution for liquid sloshing in a 2-D rectangular tank. Faltinsen and Timokha (2001) developed a multimodal approach to describe the sloshing phenomenon in a rectangular tank. Akyildiz and Ünal (2005) carried out a series of model tests of rectangular tank in pitch motion to assess the sloshing loads on the walls. Besides the analytical and experimental methods, numerical simulations were also applied for sloshing mechanism study. Nakayama and Washizu (2010) applied the boundary element method to analyze the non-linear liquid sloshing in a 2-D rectangular tank. Cho and Lee (2004) analyzed the large amplitude sloshing phenomenon using finite element method. However, for real condition of coastal and offshore engineering applications, such as floating oil storage systems and LNG ships, the internal sloshing flow generated by moving liquid tank walls would affect the motion responses of the floating body in return. So it is necessary to explore the interaction between the sloshing flow and the floating body, which means the motion dynamics and the sloshing phenomenon should be considered simultaneously. Francescutto and Contento (1994) presented an experimental investigation on the coupling between the roll motion of a ship in a regular beam sea and the sloshing flow in a compartment. Kim et.al. (2007) found that the nonlinearity of sloshing flow is very important in coupling analysis between ship motion and sloshing. Rognebakke and Faltinsen (2009) studied the effect of sloshing on the motion response of a floating tank restricted to sway motion under regular beam sea waves. They found that the sway response tended to a minimum value, when the first mode sloshing frequency equalled to the external wave frequency. Similar studies have also been given by Nasar et al. (2010).
A series of wave flume experiments are carried out to investigate the pore pressure distribution around twin pipelines in fine-sandy seabed. Typical characteristics of the pore-water pressures have been summarized for different wave periods, burial depths and the interval spacing. The differences between single and twin pipeline conditions are also studied. Results show that the identical cylinder close to the existing pipeline has significant impacts on the distribution of pore-water pressures around the pipelines. The pore-water pressures increase with the increase of wave period, while the amplitude of pore pressure decreases with the increasing interval spacing and the burial depth.
With the rapid development of fossil energy exploitation in the ocean, submarine pipelines have been playing a significant role in the offshore transportation of oil and gas in the past decades. Pipelines placed on an erodible seabed may undergo several kinds of destroys when exposed to sufficiently strong waves/currents. One potential danger is the wave-induced liquefaction in a porous seabed, which may cause damaging instability of buried pipelines, like sinking or floatation (Dunlap et al., 1979; Herbich et al., 1984). Thus, the evaluation of the pore pressure response in seabed is of great importance to pipeline engineers involved in the design of offshore pipelines.
Yamamoto et al. (1978) proposed and verified an analytical solution for the pore pressure and the displacements of the porous medium in a poroelastic seabed exposed to the propagating waves on the basis of Biot's model (Biot, 1941), and concluded that the permeability and stiffness ratio of the soil are significant parameters in investigating the seabed response. A one-dimensional model was developed by Magda (1990) to analyze the phase delay in pore pressure in consideration of the saturation and compressibility of both water and soil skeleton, and Magda (1996) further promoted this model to a two-dimensional one. Zen and Yamazaki (1990) introduced a new concept of “oscillatory” excess pore pressure and developed a one-dimensional criterion for liquefaction with this new concept, while Jeng (1997) further developed this criterion to three-dimensional. In order to study the complete sequence of sediment behavior under progressive waves, Sumer et al. (2006a) conducted a series of experiments and divided the whole liquefaction process into four parts including pressure buildup, liquefaction, dissipation of pore pressure and the generation of ripples.
Numerical simulations of debris flow events provide a useful tool for investigating, within realistic geological contexts, the dynamics of these phenomena. One application of such numerical models is to evaluate and forecast impact loading on protection barriers. Most of these models are uncoupled methods: this means that it is necessary to use different codes for analysing the motion phase and for evaluating impact forces. In this way, the uncertainties related to the barrier design are increased and difficult to quantify. In this paper the combined finite-discrete element method, FEMDEM is employed to back-analyse experimental impact tests of debris flow interacting against rigid and waterproof barrier. This methodology allows the simultaneous determination of flow characteristics (velocity and thickness) and impact load on the barrier structure. Two different numerical set-ups were adopted to reproduce laboratory experiments. In the first case, we defined a priori the size and the shape of the impacting particles. In the second case, the unstable mass was hypothesised as a unique block with fracture joint elements behaviour, cohesionless, and very low tensile strength. In this way the gravity and friction forces led the particles flowing into the flume. The results were compared in order to quantify the effects of the set-up schemes and material characteristics on the simulations. Limitations and future developments on the application of FEMDEM methodology to this type of geotechnical problem are discussed.
Forecasting debris flow motion characteristics and impact loads on obstacles is an essential component of landslide risk assessment, but it is still a big challenge. The runout prediction provides a mean of defining the susceptible areas, estimating the debris flows intensity and working out the information for the individuation and design of appropriate protective measures (Pirulli and Sorbino, 2008). Concerning the evaluation of debris flow motion characteristics, numerical simulations can provide a useful tool. In the attempt of modelling landslide dynamics, many methods based on continuum (Savage and Hutter, 1989; Hungr, 1995; Pirulli, 2005; Pastor et al., 2009) or discontinuum (Will and Konietzky, 1998; Richefeu et al., 2012) mechanics have been developed. The outputs of these models are fundamental for the design of countermeasures and they are used as inputs in codes (e.g Brighenti, Segalini, and Ferrero, 2013; Hungr and Kellerhals, 1984) for evaluating impact forces on structures.
The numerical wave flume using first order wavemaker theory has been well established and widely used for a long time. But the existing numerical models based on the first order wave-maker theory will lose accuracy as the nonlinear effects enhance. Because of the different propagation velocities of the spurious harmonic waves and the primary waves, the simulated waves with the first order wave-maker theory have an unstable wave profile. In this paper, a numerical wave flume with piston-type wave maker is established. The comparison of the surface elevation using first order and second order wave-maker theory proves that second order wave-maker theory can make stable wave profile in both temporally and spatially. Harmonic analysis is applied to prove the superiority of second order wave-maker theory.
Piston-type wave-maker has been widely used to generate waves in laboratory flume or basin. Havelock (1929), Svendsen (1985) and Dean & Dalrymple (1991) had well established first order wave-maker theory. Flick & Guza (1980) and Ursell et al. (1960) had verified the first order wave-maker theory by experiments in the laoratory (see also Galvin, 1964; Keating & Webber, 1977). Small-amplitude assumption is the basic assumption of first order wave-maker theory. The small-amplitude waves will decompose into a primary wave and spurious superharmonic wave, which will affect the stability of the wave profile (see Gōda and Kikuya, 1964; Multer and Galvin, 1967; Iwagaki and Sakai, 1970), when the motion of the wave-maker is sinusoidal. In early 1847, Stokes found the superharmonic wave by regular wave in terms of a perturbation series using the wave steepness as the small ordering parameter. But the problem of generated nonlinear wave was gave a solution by Fontanet (1961). He found the spurious superharmonic wave by piston-type wave-maker with sinusoidal motion in Lagrangian coordinates and suggested that it can be restrained using wave paddle control signal with an addition component.
Further, Moubayed & Williams (1994) extended second order wave-maker theory from the regular wave to the bichromatic wave. For the irregular waves, second order wave-maker theory has both sum and difference frequencies in the interaction terms. Longuet-Higgins & Stewart (1962, 1964) deduced the subharmonics generated by wave components interaction under the narrow band assumption. Flick & Guza (1980) pointed out that spurious long wave will be generated by a first order bichromatic control signal. Barthel et al. (1983) used the second order difference frequencies wave paddle control signal to restrain spurious long wave and expended the theory to the flap-type wave-maker. Schaffer (1996) derived second order wave-maker theory including sum frequencies and difference frequencies components without the narrow band assumption. The theory was applied to the piston-type and flap-type wave-makers and was verified by experiments. Schaffer & Steenberg (2003) extended the second order wave-maker theory to multidirectional waves.
A non-reflection internal wave-maker using a momentum source function is coupled with a CIP-based model. The momentum source term derived from the Boussinesq water wave theory equations is employed and added to the Navier-Stokes equations for wave generations. The influence of reflected waves, which is a big problem for a boundary wave maker when containing the interaction of waves and structures, can be avoided by using the internal wave-maker method, because the waves generated by the source function do not interact with reflected waves. A constrained interpolation profile (ClP)-based model is employed to solve the incompressible Navier-Stokes equations with the free surface boundary condition to deal with the water-air-structure interactions. In addition, the VOF-type tangent of hyperbola for interface capturing/slope weighting (THINC/SW) method is used to capture the free surface. The structure is treated by an immersed boundary method. A series of numerical simulations using the momentum source wave-maker are compared with the analytical solution to verify the applicability in a two dimensional numerical wave flume. Furthermore, a more challenging wave decomposition process over a submerged trapezoid breakwater is presented. The numerical results of wave surface profile show a good agreement with the experimental results. It indicates that the CIP-based model with the non-reflection internal wave-maker can provide a more robust modeling of wave generation and wave-structure interaction without being affected by the reflected wave.
Wave generation plays an significant role in numerical wave flumes. During the development of wave simulation, three types of numerica methods for wave generation have been developed based on continuity and Naiver-Stokes equations: internal generation of waves, static boundary wave generation, and moving boundary wave generation. A key challenge for numerical models is to maintain the incident wave and minimize unwanted reflected waves from structures. The static boundary wave generation and moving boundary wave generation usually need an special treatment in generation boundary in order to avoid reflected waves. The internal wave-maker, which generates wave from a region inside the numerical flume and absorbs wave at two ends of the flume, provides a good non-reflecting property. The reflected wave propagates over the wave maker zone without affecting the wave generation and is finally absorbed by the sponge layers.
The gravity collapse in density stratification fluid, as one kind of excitation sources for large amplitude internal solitary waves (ISWs), is studied by constructing the initial step-like rectangular disturbance for a two-layer fluid system in both stratified fluid flume and numerical model respectively. The characteristics of excitation source, the conditions of the stable propagation and the existence of the large-amplitude ISWs are brought insight in detail. The characteristics of the larger-amplitude ISWs tend to be predicted by the eKdV or MCC theories, and the prediction is selective for the different value between the upper and lower layers in a two-layer fluid system.
Manifold sources may excite the internal waves in the stratified ocean, such as surface wind and ship motion, undulating terrain and undersea earthquake, tide current and submarine motion which can be summarized as disturbances from its surface, bottom and interior respectively (Chen, 2007). Internal solitary wave (ISW) is a special form of waves in the ocean, which is usually induced by the gravitational collapse of the mixed density pycnocline due to the tidal flow over the rugged terrain such as the margins ridge, the continental shelf break, the island and the strait (Stastna, 2005; Li, 2011). The large-amplitude ISWs accompanied with tremendous energy and strong currents may affect the change of marine environment and threaten the safety of marine engineering structures (Si,2012; Cai,2014). The physical characteristics of source as well as the validity of theory for the large-amplitude ISWs have always been concerned.
Due to the complexity of marine stratified environment and the uncertainty of large-amplitude ISW generation, the field observation is extremely hard for both generation and evolution of the ISW. The development of the modern experiment and measurement technologies in a stratified fluid provides an effective method. Wu (1969) first introduced this principle of gravity collapse into the ISW-making experiments. Maxworthy (1980) experimentally studied the gravitational collapse of mixed region induced by the immersion of gravity flow in a two-layer fluid system. Michallet et al (1998) conducted the experiment on the characteristics of ISWs generated by the gravity collapse in two immiscible fluids (water/petrol). Chen et al (2007) qualitatively presented the process of the ISWs generation by the gravity collapse in laboratory experiments. Wei et al (2014) improved the traditional gravity collapse wave-maker device and began to apply it in engineering. In addition, lots of the relevant numerical studies (Lin, 2102; Zhu, 2014; Terez, 1998) also provided further comprehensions on the gravity collapse and its exciting ISW. But the evolution of the gravity collapse and the generation mechanism of ISW due to the disturbance have not been widely comprehended.
Ma, Yuxiang (Dalian University of Technology) | Song, Yongbo (Dalian University of Technology) | Liao, Bo (Dalian University of Technology) | Ma, Xiaozhou (Dalian University of Technology) | Dong, Guohai (Dalian University of Technology)
The Peregrine breather (PB) is a rational solution of the nonlinear Schrödinger equation (NLS). PB is localized in both space and time, culminates in the amplification that is three times the initial wave amplitude. Therefore, it is often considered to be an appropriate prototype of rouge waves in ocean. However, until now, there are some researches on the evolution of PB of ocean gravity waves, but experimental observation of the PB in a wave flume is still lacking, especially investigations on the influence of water depth on the evolution of PB. In the present study, detailed measurements for propagation of PB with different initial steepness were conducted in a wave flume. Higher harmonics significantly contribute the surface elevations at the place where the PB solution reaches the maximum amplitude. But the contribution of higher harmonics on surface elevations reduces with increasing water depth. The experimental results are in a very good agreement with the PB up to the short distance from the wave maker, at further distances, differences between the theory and the experiment start to appear. The third order solution of the NLS agrees well with experiments. The maximum envelope amplification in the experiments is slightly below that predicted by the PB; the discrepancy reduces with increasing water depth.
Freak waves, which appear nowhere and disappear without trace, can cause ships and offshore structures in danger due to their extraordinary large wave heights (Lavrenov, 2003; Lechuga, 2006; Akhmediev et al. 2009). A freak wave is often identified if its height reach to twice the significant wave height (Kharif and Pelinovsky, 2003; Mori, 2004; Kharif et al. 2009). Usually, freak waves were always reported after accidents and the wave heights were accessed by visual inspection. Until now, however, there are limited freak waves, which were directly recorded in ocean. There are several possible physical mechanisms for generating freak waves (Lavrenov, 1998; Kharif and Pelinovsky, 2003). In offshore regions, one of the most likely mechanisms is the modulational instability, which relates to the detuning four wave interactions (Janssen, 2003). The modulational instability of gravity waves can well be modelled by the nonlinear Schrödinger equations (NLS). Therefore, NLS type equations are often used to study the characteristics of freak waves (Osborne et al. 2000; Onorato et al. 2001; Chabchoub et al. 2012c). Peregrine breather (PB) is the simplest theoretical solution of the NLS. PB can present a double spatial- temporal localization and the amplitude can reach three times the initial value, therefore, it can be considered as a prototype of freak waves (Shrira and Geogjaev, 2010). The PB was observed in optics (Kibler et al. 2010), water waves (Chabchoub et al. 2011; Shemer and Alperovich, 2013), and plasma (Bailung et al. 2011). Theoretically there are higher order breather solutions that are also localized both in space and time, and have been observed experimentally (Chabchoub et al. 2012a; Chabchoub et al. 2012b; Frisquet et al. 2013; Frisquet et al. 2014). It could be that most of the parameters of wave flume, in particular its limited length, not long enough to exhibit the fully evolution of breather from a quite low initial frequency. In fact, the data of marine observations and laboratory demonstrate experiments that freak waves may appear in arbitrary depth (Kharif and Pelinovsky, 2003). Our present experimental study uses a wide range of parameters of the background carrier wave. The paper is arranged as following: In Sec. 2 we introduce the breather solutions of NLS, and the experimental setup is described in Sec. 3. Experimental results and discussion are presented in Sec. 4. Conclusions are presented in Sec. 5.
Majd, Soheil Farazi (Istanbul Technical University) | Yagci, Oral (Istanbul Technical University) | Kirca, V.S. Ozgur (Istanbul Technical University) | Kitsikoudis, Vasileios (Istanbul Technical University) | Lentsiou, Elpida (Aristotle University of Thessaloniki)
The present experimental study investigates the generated flow field in the presence of a bottom mounted cylinder with a downstream inclination. The experiments were conducted in an 18 m × 0.50 m × 0.50 m flume under steady flow conditions. A cylinder with a diameter of 7.5 cm served as a disturbance to the flow under several inclination angles, parallel to the flow direction. Specifically, 0°, 15°, 30°, 40°, and 50° inclination, with respect to the vertical, were tested separately under three different approach velocities. Instantaneous flow velocities were measured with an acoustic Doppler velocimeter, while the upstream separation distance in the cylinder proximity was visualized with the aid of a laser sheet. Results show that once the pile is inclined, the flow features change considerably. Generally, inclination renders the pile to be more hydrodynamic in shape with the suppression of the vortex shedding. At the same time, inclination makes the cross-sectional area of the pile to become elliptical, leading to an increase in the friction area and turbulence production on the cylinder boundary layer. Also, the upstream separation distance of the cylinder near the bed was significantly altered with the inclination, which would presumably affect the generation and strength of the horseshoe vortices to be generated due to this separation.
Flow around and wake behind bottom-mounted cylinders (piles) is an important topic in coastal/offshore engineering as well as many other disciplines. Thus, the subject has been studied quite extensively from many different aspects, such as forces on cylindrical piles, turbulence and mixing in the wake, scour around the pile, effect of pile grouping, etc. The imposition of a bottom-mounted cylindrical element into a flow field induces a complicated alteration of the flow field (Sumer and Fredsoe, 2006), which may cause serious problems to the structure due to potential excessive scouring on its basis. In the presence of a cylinder the approaching flow decelerates in its proximity and a strong downflow occurs, which leads to separation at the cylinder basis. Spirals are formed at the basis, which are carried away downstream forming the horseshoe vortices (Sumer and Fredsoe, 2002). At the side of the cylinder the streamlines are contracted and due to adverse pressure gradient the boundary layer separates since inertia is dominant compared to viscous forces. This triggers increased turbulence production and the generation of lee-wake vortices, which are propagated downstream, usually with the occurrence of vortex shedding. The interaction between flow and bottom-monted circular cylinders has been extensively studied both experimentally (e.g., Graf and Yulistiyanto, 1998; Unger and Hager, 2007) and numerically (e.g., Roulund et al., 2005) and has been evolved to a prominent fluid mechanics problem.