Scour around submarine pipes due to high-amplitude transient waves

Estimation of scour dimensions below submarine pipelines is a vital step in designing offshore infrastructure.Extreme events like tsunami waves produce strong erosive forces below the underwater pipes,apt to create scour holes,jeopardizing the safety of the structure.Despite the importance of this issue,previous studies have mainly focused on steady flow cases,and the scour pattern below submarine pipes induced by high-amplitude transient waves has rarely been investigated.This paper reports the results of 40 experimental runs on transient wave-induced scour below a model pipe in a laboratory flume under a variety of initial conditions.The variables included the bed particle size and gradation,initial water depth,wave height,and slope of the bed layer.Waves were generated by a sudden release of water from a sluice gate,installed in the middle of the flume.A pressure transducer data acquisition system was used to record the wave heights at different time steps.The results indicate that,with a shallower initial depth of flow,the scour depth is relatively large.It was also found that there exists a direct correlation between the induced wave height and the size of the scour hole.It was observed that,in clear water conditions,the size of the scour hole in coarse sediments is smaller,while in live-bed conditions,larger scour holes are created in coarser sediments.It was also observed that at high wave amplitudes,the live-bed conditions are dominant,and consequently the bed elevation is altered.

A FAST ALGORITHM FOR FULL NON-LINEAR TRANSIENT WAVES

The transient surface wave motion is studied by a method which transfers the computational re- gion into a unit circle. In place of the Green's formula of harmonic function the Taylor's series of an analyti- cal function is used. The coefficients of the series are determined by FFT. The numerical filtration is accomplished in the Fourier domain.

Application of transient Rayleigh wave in detection of tunnel lining void area

Transient Rayleigh wave detection is a high-precision nondestructive detection method.At present,it has been widely used in shallow exploration,but rarely used in tunnel lining quality detection.Through the tunnel lining physical model experiment,the layout defects of the double-layer reinforcement lining area were detected and the Rayleigh wave velocity profile and dispersion curve were analyzed after data process-ing,which finally verified the feasibility and accuracy of Rayleigh wave method in detecting the tunnel lining void area.The results show that the method is not affected by the reinforcement inside the lining,the shallow detection is less disturbed and the accuracy is higher,and the data will fluctuate slightly with the deepening of the detection depth.At the same time,this method responds quite accurately to the thickness of the concrete,allowing for the assessment of the tunnel lining’s lack of compactness.This method has high efficiency,good reliability,and simple data processing,and is suitable for nondestructive detection of internal defects of tun-nel lining structure.

Modeling of Propagation and Transformation of Transient Nonlinear Waves on A Current

A novel theoretical approach is applied to predict the propagation and transformation of transient nonlinear waves on a current. The problem was solved by applying an eigenfunction expansion method and the derived semi-analytical solution was employed to study the transformation of wave profile and the evolution of wave spectrum arising from the nonlinear interactions of wave components in a wave train which may lead to the formation of very large waves. The results show that the propagation of wave trains is significantly affected by a current. A relatively small current may substantially affect wave train components and the wave train shape. This is observed for both opposing and following current. The results demonstrate that the application of the nonlinear model has a substantial effect on the shape of a wave spectrum. A train of originally linear and very narrow-banded waves changes its one-peak spectrum to a multi-peak one in a fairly short distance from an initial position. The discrepancies between the wave trains predicted by applying the linear and nonlinear models increase with the increasing wavelength and become significant in shallow water even for waves with low steepness. Laboratory experiments were conducted in a wave flume to verify theoretical results. The free-surface elevations recorded by a system of wave gauges are compared with the results provided by the nonlinear model. Additional verification was achieved by applying a Fourier analysis and comparing wave amplitude spectra obtained from theoretical results with experimental data. A reasonable agreement between theoretical results and experimental data is observed for both amplitudes and phases. The model predicts fairly well multi-peak spectra, including wave spectra with significant nonlinear wave components.

SECOND ORDER TRANSIENT WAVES AROUND A VERTICAL CYLINDER IN A TANK

The free surface problem bound by two cylinders is analysed based on the velocity potential theory. An analytical solution in the take domain is obtained up to the second order in the perturbation expansion. The results are compared with those obtainal from the fully nonlinear theory based on a finite element formulation.It is found that the second order solutiongives a fsr better agreement with the fully nonlinear solution.

ON THE HIGH PRECISION ADAPTIVE OPEN BOUNDARY CONDITIONS FOR TRANSIENT WAVES

The adaptive open boundary conditions (AOBC) designed by Chen and Zou for transient waves overcome the limitation of the existing open boundary conditions (OBC) and can be used for the cases of waves with arbitrary incident angles. In this paper a new family of AOBC has been designed on the basis of the AOBC with first order mentioned above. In comparing with all other OBC with the same order, this new family of AOBC has the highest precision. It can be generalized into 3D problems without difficulty and its forms in different curvilinear coordinate systems can be got very easily. The distinguished advantages above mentioned of the AOBC will be discussed in this paper.

Propagation characteristics of transient waves in low-strain integrity testing on cast-in-situ concrete thin-wall pipe piles

The three-dimensional effects of pile head and the applicability of plane-section assumption are main problems in low-strain dynamic tests on cast-in-situ concrete thin-wall pipe piles.The velocity and displacement responses were calculated by a theoretical formula deduced by the authors.The frequency and influencing factor of high-frequency interference were analyzed.A numerical method was established to calculate the peak value and arrival time of incoming waves on top of the piles.The regularity along circumferential and the influence of radius or impulse width were studied.The applicability of plane-section assumption was investigated by comparison of velocity responses at different points in the sections at different depths.The waveform of velocity response at different points forked after the first peak,indicating that the propagation of stress waves did not well meet the plane-section assumption.

Efficient Generation of Freak Waves in Laboratory

In the present study, Kriebel＇ s method is improved to generate freak waves in laboratory. The improved method superposes a random wave train with two transient wave trains to simulate freak wave events in a wave tank. The freak waves are more nonlinear than what generated with Kriebel＇ s method of the same energy. It can ＇also generate freak waves to satisfy all the qualifications of the adopted definition with less energy than Kriebel＇ s and can hardly influence the significant wave height.

Violent Transient Sloshing-Wave Interaction with a Baffle in a Three-Dimensional Numerical Tank

A finite difference model for solving Navier Stokes viscous liquid sloshing-wave interaction with baffles in a tank. equations with turbulence taken into accotmt is used to investigate The volume-of-fluid and virtual boundary force methods are employed to simulate free surface flow interaction with structures. A liquid sloshing experimental apparatus was established to evaluate the accuracy of the proposed model, as well as to study nonlinear sloshing in a prismatic tank with the baffles. Damping effects of sloshing in a rectangular tank with bottom-mounted vertical baffles and vertical baffles touching the free surface are studied numerically and experimentally. Good agreement is obtained between the present numerical results and experimental data. The numerical results match well with the current experimental data for strong nonlinear sloshing with large free surface slopes. The reduction in sloshing-wave elevation and impact pressure induced by the bottom-mounted vertical baffle and the vertical baffle touching the free surface is estimated by varying the external excitation frequency and the location and height of the vertical baffle under horizontal excitation.

Transient response of a concrete tunnel in an elastic rock with imperfect contact

The two-dimensional transient response of an imperfect bonded circular lined pipeline lying in an elastic infinite medium is investigated.Imperfect boundary conditions between the surrounding elastic rock and the tunnel are modelled with a two-linear-spring design.The novelty of the manuscript consists in studying at the same time transient regimes and imperfect bonded interfaces for simulating the dynamic response of a tunnel embedded in an elastic infinite rock.Wave propagation fields in tunnel and rock are expressed in terms of infinite Bessel and Hankel series.To solve the transient problem,the Laplace transform and the associated Durbin’s algorithm are performed.To exhibit the dynamic responses,influences of various parameters such as the quality of the interface conditions and the thickness of the lining are presented.The dynamic hoop stresses and the solid displacements of both the tunnel and the rock are also proposed.

An artificial neural network based deep collocation method for the solution of transient linear and nonlinear partial differential equations

A combined deep machine learning(DML)and collocation based approach to solve the partial differential equations using artificial neural networks is proposed.The developed method is applied to solve problems governed by the Sine–Gordon equation(SGE),the scalar wave equation and elasto-dynamics.Two methods are studied:one is a space-time formulation and the other is a semi-discrete method based on an implicit Runge–Kutta(RK)time integration.The methodology is implemented using the Tensorflow framework and it is tested on several numerical examples.Based on the results,the relative normalized error was observed to be less than 5%in all cases.

Nonlinear Random Motion Analysis of Coupled Heave-Pitch Motions of a Spar Platform Considering lst-Order and 2nd-Order Wave Loads

In this study, the coupled heave-pitch motion equations of a spar platform were established by considering lst-order and 2nd-order random wave loads and the effects of time-varying displacement volume and transient wave elevation. We generated random wave loads based on frequency-domain wave load transfer functions and the Joint North Sea Wave Project （JONSWAP） wave spectrum, designed program codes to solve the motion equations, and then simulated the coupled heave-pitch motion responses of the platform in the time domain. We then calculated and compared the motion responses in different sea conditions and separately investigated the effects of 2nd-order random wave loads and transient wave elevation. The results show that the coupled heave-pitch motion responses of the platform are primarily dominated by wave height and the characteristic wave period, the latter of which has a greater impact. 2nd-order mean wave loads mainly affect the average heave value. The platform＇s pitch increases after the 2nd-order low frequency wave loads are taken into account. The platform＇s heave is underestimated if the transient wave elevation term in the motion equations is neglected.

Hydroelastic Behaviour and Analysis of Marine Structures

Hydroelasticity of marine structures with and without forward speed is studied directly using time dependent Boundary Integral Equation Method with Neumann-Kelvin linearisation where the potential is considered as the impulsive velocity potential.The exciting and radiation hydrodynamic parameters are predicted in time with transient wave Green function whilst the structural analysis is solved with Euler-Bernoulli beam method at which modeshapes are defined analytically.The modal analysis is used to approximate the hydroelastic behaviour of the floating systems through fully coupling of the structural and hydrodynamic analyses.As it is expected,it is found with numerical experience that the effects of the rigid body modes are greater than elastic modes in the case of stiff structures.The predicted numerical results of the present in-house computational tool ITU-WAVE are compared with experimental results for validation purposes and show the acceptable agreements.

SECOND-ORDER TRANSIENT STANDING WAVES IN A RECTANGULAR TANK

Analytical solution are derived based on the Fourier series for the three dimensional transient free surface problem in a rectangular tank. The analysis is based on the Stokes Perturbation and the second order result is obtained.

Possible linkage between winter extreme low temperature events over China and synoptic-scale transient wave activity

Based on NECP/NCAR reanalysis data and daily temperature data of 743 stations in China, possible causes of winter extreme low temperature events are explored from the perspective of the synoptic-scale transient wave (STW) activity. Results suggest that there is a close linkage between STW activity and extreme low temperature events. Firstly, case studies are carried out on the years with the most and least frequent extreme low temperature events. In the winter of 1967, two strong and stable STW trains were maintained over the Eurasian continent, and the strong westerly jet provided a good channel for the propagation of STW. Located in the downstream area of those two STW trains, China was significantly influenced by them and experienced frequent extreme low temperature events. Further analysis suggest that the intensity of the upstream transient wave and the areas where the transient waves reached are completely consistent with the intensity of extreme low temperature and the areas where frequent extreme low temperature event happened, respectively. In contrast, Westerly jet in 2006 was weaker and the path of transient wave propagation was shorter and weaker, resulting in the low frequency of extreme temperature. Secondly, in their long term variations, westerly jet is also consistent with the extreme low temperature frequency. The transient wave path changed before and after the 1980s. Further investigation suggests that transient wave intensities in key areas exhibit in-phase changes with the frequency of extreme low temperature events in the periods of 1959-1979 and 1986-2006. Meanwhile, the main features of transient wave activities in high-frequent years and low-frequent years of extreme low temperature events are similar to those of 1967 and 2006, respectively. Results indicate that winter extreme low temperature events in China have a very close relationship with the transient wave activity, implying the propagation and activity of STW are important factors affecting the winter extreme low temperature events in China. This study can also provide a new clue for better understanding the mechanisms of the extreme temperature events.

The nonlinear evolution of rogue waves generated by means of wave focusing technique

Generating the rogue waves in offshore engineering is investigated,first of all,to forecast its occurrence to protect the offshore structure from being attacked,to study the mechanism and hydrodynamic properties of rouge wave experimentally as well as the rouge/structure interaction for the structure design.To achieve these purposes demands an accurate wave generation and calculation.In this paper,we establish a spatial domain model of fourth order nonlinear Schrdinger(NLS) equation for describing deep-water wave trains in the moving coordinate system.In order to generate rogue waves in the experimental tank efficiently,we take care that the transient water wave(TWW) determines precisely the concentration of time/place.First we simulate the three-dimensional wave using TWW in the numerical tank and modeling the deepwater basin with a double-side multi-segmented wave-maker in Shanghai Jiao Tong University(SJTU) under the linear superposing theory.To discuss its nonlinearity for guiding the experiment,we set the TWW as the initial condition of the NLS equation.The differences between the linear and nonlinear simulations are presented.Meanwhile,the characteristics of the transient water wave,including water particle velocity and wave slope,are investigated,which are important factors in safeguarding the offshore structures.

ANALYSIS AND EXPERIMENT ON TRANSIENT DYNAMIC RESPONSE IN FINITE MINDLIN PLATE

The transient wave propagation in the finite rectangular Mindlin plate is investi- gated by the analytical and experimental methods. The generalized ray method （GRM） which has been successfully applied to study the transient responses of beams, planar trusses, space frames and infinite layered media is extended to investigate the transient wave propagation and early short time transient response in finite Mindlin plate. Combining the wave solution, the shock source and the boundary conditions, the ray groups transmitted in the finite rectangular plate can be determined. Numerical simulations and experiments are performed and compared with each other. The results show that the transient wave propagation and early short time transient responses in the finite plate can be studied using the GRM. The early short time transient acceler- ations are very large for the finite plate subjected to the unit impulse, while the early short time transient displacements are very small. The early short time transient accelerations under the unit impulse are much larger than those under the unit step impulse. The thickness and material characteristics have remarkable effects on the early short time transient responses.

Propagation of Strong Wave Package Center and Latitudinal Movement of Western Pacific Subtropical High

On the basis of studying wave package propagation, this paper investigated the relationship between high frequency wave package propagation and transient waves＇ evolvement or the subtropical high＇s latitudinal movement. The results showed that during winter the lifetime of wave package was longer and usually persisted for 7-10 days with a propagating speed of 2-10 m s-l. Usually they propagated southeastward at the beginning, then turned to northeast. During summer the lifetime and intensity of wave package became shorter and weaker. It availed development （attenuation） of troughs when the strong wave package center was intensified （weakened） which overlapped with trough. If strong wave package center kept overlapping with ridge, the ridge would abate later in a few days. Obvious jumping northward （retreating southward） processes of Western Pacific subtropical high （WPSH） were （not） usually related to strong wave package centers located at South China Sea area （South Asia area and Temperate Zone） for 5 days or longer. After two seasonal jumping processes, there were persisting strong wave package centers for 5 days or longer. WPSH retreating processes were also related to activities of strong wave package centers over South Asian area and temperate area as well as the strong wave package centers of typhoon, and all these centers persisted for 5 days or longer.

Diagnostic Study of Global Energy Cycle of the GRAPES Global Model in the Mixed Space-Time Domain

Some important diagnostic characteristics for a model’s physical background are reflected in the model’s energy transport, conversion, and cycle. Diagnosing the atmospheric energy cycle is a suitable way towards understanding and improving numerical models. In this study, formulations of the “Mixed Space-Time Domain”energy cycle are calculated and the roles of stationary and transient waves within the atmospheric energy cycle of the Global-Regional Assimilation and Prediction System （GRAPES） model are diagnosed and compared with the NCEP analysis data for July 2011. Contributions of the zonal-mean components of the energy cycle are investigated to explain the performance of numerical models. The results show that the GRAPES model has the capability to reproduce the main features of the global energy cycle as compared with the NCEP analysis. Zonal available potential energy （AZ） is converted into stationary eddy available potential energy （ASE） and transient eddy available potential energy （ATE）, and ASE and ATE have similar values. The nonlinear conversion between the two eddy energy terms is directed from the stationary to the transient. AZ becomes larger with increased forecast lead time, reflecting an enhancement of the meridional temperature gradient, which strengthens the zonal baroclinic processes and makes the conversion from AZ to eddy potential energy larger, especially for CAT （conversion from AZ to ATE）. The zonal kinetic energy （KZ） has a similar value to the sum of the stationary and transient eddy kinetic energy. Barotropic conversions are directed from eddy to zonal kinetic energy. The zonal conversion from AZ to KZ in GRAPES is around 1.5 times larger than in the NCEP analysis. The contributions of zonal energy cycle components show that transient eddy kinetic energy （KTE） is associated with the Southern Hemisphere subtropical jet and the conversion from KZ to KTE reduces in the upper tropopause near 30？S. The nonlinear barotropic conversion between stationary and transient kinetic energy terms （CKTE） is reduced predominantly by the weaker KTE.

THE INITIAL FLOW STATE OF A BROKEN DAM

This paper utilizes the main feature of the flow at the initial stage of a broken dam which obeys similarity rule and will reduce the mathematical difficulties involved. We get the finite acceleration and velocity at the corner fluid point which had been calculated as infinity by former researcher with wrong method.