Propagation of acoustic-gravity waves in inhomogeneous ocean environment based on modal expansions and HP-FEM

A coupled mode model is presented for the propagation of acoustic-gravity waves in layered ocean waveguides. The analysis extends previous work for acoustic waves in inhomogeneous environment. The coupled mode system is derived by means of a variational principle in conjunction with local mode series expansion, obtained by utilizing eigenfunction systems defined in the vertical section. These are obtained through the solution of vertical eigenvalue problems formulated along the waveguide. A crucial factor is the inclusion of additional modes accounting for the effects of spatialy varying boundaries and interfaces. This enhancement provides an implicit summation for the slowly convergent part of the localmode series, rendering the series rapidly convergent, increasing substantialy the efficiency of the method. Particular aspects of the method include high order Lagrange Finite Element Methods for the solution of local vertical eigenvalue problems in the case of multilayered waveguides, and Gauss-type quadrature for the computation of the coupled-mode system coefficients. The above aspects make the present method quite efficient for long range propagation in extended waveguides, such as the ones found in geophysical applications, e.g. ocean basins, as only few modes are needed for the accurate representation of the wave field

Hydroelastic analysis of ice shelves under long wave excitation

Abstract. The transient hydroelastic response of an ice shelf under long wave excitation is analysed by means of the finite element method. The simple model, presented in this work, is used for the simulation of the generated kinematic and stress fields in an ice shelf, when the latter interacts with a tsunami wave. The ice shelf, being of large length compared to its thickness, is modelled as an elastic Euler-Bernoulli beam, constrained at the grounding line. The hydrodynamic field is represented by the linearised shallow water equations. The numerical solution is based on the development of a special hydroelastic finite element for the system of governing of equations. Motivated by the 2011 Sulzberger Ice Shelf (SIS) calving event and its correlation with the Honshu Tsunami, the SIS stable configuration is studied. The extreme values of the bending moment distribution in both space and time are examined. Finally, the location of these extrema is investigated for different values of ice shelf thickness and tsunami wave length

Higher-order fem for nonlinear hydroelastic analysis of a floating elastic strip in shallow-water conditions

The hydroelastic response of a thin, nonlinear, elastic strip floating in shalow-water environment is studied by means of a special higher order finite element scheme. Considering non-negligible stress variation in lateral direction, the nonlinear beam model, developed by Gao, is used for the simulation of large flexural displacement. Full hydroelastic coupling between the floating strip and incident waves is assumed. The derived set of equations is intended to serve as a simplified model for tsunami impact on Very Large Floating Structures (VLFS) or ice floes. The proposed finite element method incorporates Hermite polynomials of fifth degree for the approximation of the beam deflection/upper surface elevation in the hydroelastic coupling region and 5-node Lagrange finite elements for the simulation of the velocity potential in the water region. The resulting second order ordinary differential equation system is converted into a first order one and integrated with respect to time with the Crank-Nicolson method. Two distinct cases of long wave forcing, namely an elevation pulse and an N-wave pulse, are considered. Comparisons against the respective results of the standard, linear Euler-Bernoulli floating beam model are performed and the effect of large displacement in the beam response is studied

Finite element simulation of long wave impact on floating breakwaters with variable stiffness

The hydroelastic response of flexible, floating breakwaters is a subject of interest for coastal engineering applications. In this study, a higher order hydroelastic finite element is applied to the simulation of floating breakwaters of variable stiffness undergoing long wave impact. The main aim is the evaluation of breakwater efficiency in terms of transmitted and reflected wave characteristics. It is established that, for the wave-lengths examined, the maximum amplitude and wave-length of the transmitted pulse are strongly dependent on the breakwater stiffness. Finally it is shown that for case of a periodic stiffness profile the transmitted energy is minimised when the modulation wavelength is comparable to the wavelength of the incoming excitation

Hydroelastic analysis of Very Large Floating Structures in variable bathymetry regions by multi-modal expansions and FEM

A novel frequency domain numerical method for Very Large Floating Structure (VLFS) hydroelasticity is developed. The problem is formulated in the 2D ocean waveguide, featuring a realistic seabed bathymetry and the presence of inhomogeneous, elastic plates of varying thickness and negligible draft. An in vacuo modal expansion for the elastic body deflection, modelled as a structural plate, is employed to decouple the hydrodynamics from structural mechanics. The inhomogeneous plate is considered to undergo cylindrical bending, while depending on the structure slenderness and excitation wavelength the classical thin plate theory and Mindlin's model, accounting for first order shear deformation effects are implemented. A weighted residual approach is employed to cast the formulated problems into a mixed weak form for which dimensionality reduction is sought. This is achieved by an enhanced vertical representation for the wave potential, able to accurately account for abrupt bathymetric changes, following Athanassoulis and Belibassakis (1999). The reduced two-field, weak problem is solved by means of the Finite Element Method (FEM). Finally, a series of comparisons are carried out against published results for a range of configurations

Propagation of acoustic-gravity waves in inhomogeneous ocean environment based on modal expansions and HP-FEM

A coupled mode model is presented for the propagation of acoustic-gravity waves in layered ocean waveguides. The analysis extends previous work for acoustic waves in inhomogeneous environment. The coupled mode system is derived by means of a variational principle in conjunction with local mode series expansion, obtained by utilizing eigenfunction systems defined in the vertical section. These are obtained through the solution of vertical eigenvalue problems formulated along the waveguide. A crucial factor is the inclusion of additional modes accounting for the effects of spatialy varying boundaries and interfaces. This enhancement provides an implicit summation for the slowly convergent part of the localmode series, rendering the series rapidly convergent, increasing substantialy the efficiency of the method. Particular aspects of the method include high order Lagrange Finite Element Methods for the solution of local vertical eigenvalue problems in the case of multilayered waveguides, and Gauss-type quadrature for the computation of the coupled-mode system coefficients. The above aspects make the present method quite efficient for long range propagation in extended waveguides, such as the ones found in geophysical applications, e.g. ocean basins, as only few modes are needed for the accurate representation of the wave field

Higher-order fem for nonlinear hydroelastic analysis of a floating elastic strip in shallow-water conditions

The hydroelastic response of a thin, nonlinear, elastic strip floating in shalow-water environment is studied by means of a special higher order finite element scheme. Considering non-negligible stress variation in lateral direction, the nonlinear beam model, developed by Gao, is used for the simulation of large flexural displacement. Full hydroelastic coupling between the floating strip and incident waves is assumed. The derived set of equations is intended to serve as a simplified model for tsunami impact on Very Large Floating Structures (VLFS) or ice floes. The proposed finite element method incorporates Hermite polynomials of fifth degree for the approximation of the beam deflection/upper surface elevation in the hydroelastic coupling region and 5-node Lagrange finite elements for the simulation of the velocity potential in the water region. The resulting second order ordinary differential equation system is converted into a first order one and integrated with respect to time with the Crank-Nicolson method. Two distinct cases of long wave forcing, namely an elevation pulse and an N-wave pulse, are considered. Comparisons against the respective results of the standard, linear Euler-Bernoulli floating beam model are performed and the effect of large displacement in the beam response is studied

A non-linear BEM-FEM coupled scheme for the performance of flexible flapping-foil thrusters

Recent studies indicate that nature-inspired thrusters based on flexible oscillating foils show enhanced propulsive performance. However, understanding the underlying physics of the fluid-structure interaction (FSI) is essential to improve the eciency of existing devices and pave the way for novel energy-ecient marine thrusters. In the present work, we investigate the eect of chord-wise flexibility on the propulsive performance of flapping-foil thrusters. For this purpose, a numerical method has been developed to simulate the time-dependent structural response of the flexible foil that undergoes prescribed large general motions. The fluid flow model is based on potential theory, whereas the elastic response of the foil is approximated by means of the classical Kirchhoff-Love theory for thin plates under cylindrical bending. The fully coupled FSI problem is treated numerically with a non-linear BEM-FEM scheme. The validity of the proposed scheme is established through comparisons against existing works. The performance of the flapping-foil thrusters over a range of design parameters, including flexural rigidity, Strouhal number, heaving and pitching amplitudes is also studied. The results show a propulsive eciency enhancement of up to 6% for such systems with moderate loss in thrust, compared to rigid foils. Finally, the present model after enhancement could serve as a useful tool in the design, assessment and control of flexible biomimetic flapping-foil thrusters