Numerical analysis on random wave-induced porous seabed response

Hydrodynamics of offshore structures with specific focus on wind energy applications

An integrated three-dimensional model for wave-induced seabed response in a porous seabed. I. A sloping seabed

In a natural seabed, the soil properties is complicated, which normally vary with soil depth, change of temperature, and geographic characteristics. Furthermore, anisotropic soil behavior is commonly observed in marine sediments. However, most previous studies have been limited to the case of isotropic seabed with uniform soil characteristics. This chapter consists of three major components: (i) analytical solutions for a seabed with variable permeability; (ii) analytical solution for a cross-isotropic seabed; and (iii) numerical model for a non-homogeneous seabed with cross-anisotropic soil behavior. With the newly analytical solutions and numerical model, effects of variable permeability and cross-isotropic soil behavior on the wave-induced seabed response were examined.

The study of surface gravity wave is very important for the safety of marine vessels and the design of coastal and offshore structures. Gravity-induced sea waves mostly show a nonlinear behaviour, but at a low wave steepness, these waves can be approximated as linear waves and superposition principles can be applied. Various wave phenomena such as standing waves, constructive and destructive interference, wave groups and generation of random waves are based on superposition principle. Random waves are generally modelled using wave spectrum, which is a representation of wave energy in the specified frequency range. Wave spectrum is broken into different wave components which are superposed to produce a random wave. In the present work, volume of fluid method is used for numerical simulation of surface gravity waves. Implicit formulation for volume fraction equation along with the bounded second order in time is used, which allows better temporal accuracy and numerical stability at larger time step size. The surface gravity wave is modelled by providing the wave profiles and velocities at upstream boundary. In the downstream, pressure outlet boundary is used for the specification of the hydrostatic pressure profile. Numerical beach zone is defined adjacent to the pressure outlet boundary to suppress the wave reflections propagating upstream. Random waves are modelled using JONSWAP spectrum. Formation of constructive and destructive interference, standing wave, wave pockets and modelling of random wave is achieved with numerical approach, and wave kinematics are validated against the analytical results.

Conventional investigations of waves–seabed interaction problems have been only concerned with the soil response due to two-dimensional linear progressive waves over a uniform seabed. However, the effects of non-linear waves which have been reported in the literature may be significantly different. In this paper, a finite element model is developed to investigate the non-linear wave-induced seabed response with variable permeability and shear modulus in a three-dimensional domain. The finite element formulations are fully presented in this paper. The numerical model is verified with the previous investigations through the reduced form of the present solution. The numerical results indicate that the influence of non-linear wave components cannot always be ignored without substantial error. Furthermore, the wave-induced seabed response is affected significantly by variable permeability in coarser seabeds and variable shear modulus in finer seabeds. © 1997 by John Wiley & Sons, Ltd.

Limiting conditions for cnoidal and Stokes waves : Laitone E. V., 1962. J. Geophys. Res., 67 (4): 1555–1564

This study investigates the Mach reflection of random waves by numerical simulations and with experimental observations, especially for the difference and similarity between periodic waves and random waves. As the incident angle becomes large, the normalized significant wave height in front of a reflecting wall becomes large. This tendency is the same as the Mach reflection due to the Stokes wave or the cnoidal wave. The wave height distribution in the normal direction to the wall, that is, the width of stem wave is almost the same even if the nonlinearity of incident waves becomes large. This is a different point between the periodic waves and random waves.

In order to provide simple and accurate wave theory in design of offshore structure, an analytical approximation is introduced in this paper. The solution is limited to flat bottom having a constant water depth. Water is considered as inviscid, incompressible and irrotational. The solution satisfies the continuity equation, bottom boundary condition and non-linear kinematic free surface boundary condition exactly. Error for dynamic condition is quite small. The solution is suitable in description of breaking waves. The solution is presented with closed form and dispersion relation is also presented with closed form. In the last century, there have been two main approaches to the nonlinear problems. One of these is perturbation method. Stokes wave and Cnoidal wave are based on the method. The other is numerical method. Dean’s stream function theory is based on the method. In this paper, power series method was considered. The power series method can be applied to certain nonlinear differential equations (initial value problems). The series coefficients are specified by a nonlinear recurrence inherited from the differential equation. Because the non-linear wave problem is a boundary value problem, the power series method cannot be applied to the problem in general. But finite number of coefficients is necessary to describe the wave profile, truncated power series is enough. Therefore the power series method can be applied to the problem. In this case, the series coefficients are specified by a set of equations instead of recurrence. By using the set of equations, the nonlinear wave problem has been solved in this paper.

A comparison of several wave spectra for the random wave diffraction by a semi-infinite breakwater

An Improved Parameterization for Energy Exchange from Wind to Stokes Waves

In the deepwater region, wave and current coexist simultaneously. The presence of currents in the water body alters the form of wave profile and characteristics. This paper presents the experimental study of the dynamic responses of the classic and truss spars subjected to random wave and current. The JONSWAP Spectrum was used to generate the random wave. The responses of the structures due to random wave and current in terms of Response Amplitude Operators (RAO) in surge, heave and pitch were determined and presented. Results showed that the effect of the existence of current together with wave in the water body caused significant increases in the dynamic responses of the structures.

An integrated model of wave-seabed-structure interactions

This paper uses an analytical method to examine the motion of a Tension Leg Fish Cage (TLFC) in regular and random waves. TLFC is a conceptual design of a fish cage based on the Tension Leg Platform (TLP) working principle that is usually used in deep water offshore oil and gas exploration. The idea of providing a safe environment to combine ecotourism and fish farming in a single platform led us to perform an analytical calculation to assess the possibility of using the TLP concept in fish farming. A preliminary conceptual design of TLFC using an HDPE floater with steel cable tendon is presented. The analytical calculation of the response amplitude operator for surge and heave motion is presented using linear airy wave theory with head seas encountering angle. This paper also presents the calculation of TLFC surge and heave motion under random wave loads. The random wave spectra used in this paper are JONSWAP and ISSC spectra. The result shows that the surge and heave motion response of TLFC is relatively small and, therefore, can be analyzed further with more detailed consideration. It is admitted that HDPE is a brittle material that cannot sustain any long period of constant tension. Hence the optimum tendon-floater connection for the structure is subject to further research.

Sorting and Sedimentology Character of Sandy Beach Under Wave Action

The orbital motions in surface gravity waves are of interest for analysing wave records made by accelerometer buoys. In this paper we derive some exact expressions for the first, second and third cumulants of the vertical orbital displacements in a regular Stokes wave of finite amplitude in terms of previously known integral quantities of the wave: the kinetic and potential energies, the phase speed c and the mass-transport velocity U at the free surface. These results generalize a remarkably simple relation found previously between the Lagrangian-mean surface level and the product Uc.Expansions are given in powers of the wave steepness parameter ak which show that the third Lagrangian cumulant is very small – of order (ak)6, indicating a high degree of vertical symmetry in the orbit. This contrasts with the situation in random waves, where the third cumulant is of order (ak)4 only. It is shown that the increased skewness in random waves is due mainly to an O(ak)2 shift in the Lagrangian mean level of individual waves. Such shifts in mean level may be too gradual to be fully detected by some accelerometer buoys. In that case the apparent skewness will be reduced.