Three-dimensional steep wave impact on a vertical cylinder

In the present study we investigate the 3-D hydrodynamic slamming problem on a vertical cylinder due to the impact of a steep wave that is moving with a steady velocity. The linear theory of the velocity potential is employed by assuming inviscid, incompressible fluid and irrotational flow. As the problem is set in 3-D space, the employment of the Wagner condition is essential. The set of equations we pose, is presented as a mixed boundary value problem for Laplace's equation in 3-D. Apart from the mixed-type of boundary conditions, the problem is complicated by considering that the region of wetted surface of the cylinder is a set whose boundary depends on the vertical coordinate on the cylinder up to the free-surface. We make some simple assumptions at the start but otherwise we proceed analytically. We find closed-form relations for the hydrodynamic variables, namely the time dependent potential, the pressure impulse, the shape of the wave front (from the contact point to beyond the cylinder) and the slamming force

The Radiation Problem of a Submerged Oblate Spheroid in Finite Water Depth Using the Method of the Image Singularities System

This study examines the hydrodynamic parameters of a unique geometry that could be used effectively for wave energy extraction applications. In particular, we are concerned with the oblate spheroidal geometry that provides the advantage of a wider impact area on waves, closer to the free surface where the hydrodynamic pressure is higher. In addition, the problem is formulated and solved analytically via a method that is robust and most importantly very fast. In particular, we develop an analytical formulation for the radiation problem of a fully submerged oblate spheroid in a liquid field of finite water depth. The axisymmetric configuration of the spheroid is considered, i.e., the axis of symmetry is perpendicular to the undisturbed free surface. In order to solve the problem, the method of the image singularities system is employed. This method allows for the expansion of the velocity potential in a series of oblate spheroidal harmonics and the derivation of analytical expressions for the hydrodynamic coefficients for the translational degrees of freedom of the body. Numerical simulations and validations are presented taking into account the slenderness ratio of the spheroid, the immersion below the free surface and the water depth. The validations ensure the correctness and the accuracy of the proposed method. Utilizing the same approach, the whole process is implemented for a disc as well, given that a disc is the limiting case of an oblate spheroid since its semi-minor axis approaches zero

The Radiation Problem of a Submerged Oblate Spheroid in Finite Water Depth Using the Method of the Image Singularities System

This study examines the hydrodynamic parameters of a unique geometry that could be used effectively for wave energy extraction applications. In particular, we are concerned with the oblate spheroidal geometry that provides the advantage of a wider impact area on waves, closer to the free surface where the hydrodynamic pressure is higher. In addition, the problem is formulated and solved analytically via a method that is robust and most importantly very fast. In particular, we develop an analytical formulation for the radiation problem of a fully submerged oblate spheroid in a liquid field of finite water depth. The axisymmetric configuration of the spheroid is considered, i.e., the axis of symmetry is perpendicular to the undisturbed free surface. In order to solve the problem, the method of the image singularities system is employed. This method allows for the expansion of the velocity potential in a series of oblate spheroidal harmonics and the derivation of analytical expressions for the hydrodynamic coefficients for the translational degrees of freedom of the body. Numerical simulations and validations are presented taking into account the slenderness ratio of the spheroid, the immersion below the free surface and the water depth. The validations ensure the correctness and the accuracy of the proposed method. Utilizing the same approach, the whole process is implemented for a disc as well, given that a disc is the limiting case of an oblate spheroid since its semi-minor axis approaches zero

The Method of Image Singularities Employed for Oscillating Oblate Spheroids under a Free Surface

The main objective of this study is to develop a semi-analytical formulation for the radiation problem of a fully immersed spheroid in a liquid field of infinite depth. The term “spheroid” refers herein to the oblate geometry of arbitrary eccentricity and to the axisymmetric case, where the axis of symmetry is normal to the free surface. The proposed numerical approach is based on the method of image singularities, and it enables the accurate and fast calculation of the hydrodynamic coefficients for the translational degrees of freedom of the oblate spheroid. The excellent agreement of the results, with those of other investigators for the limiting case of the sphere and with those obtained using a respected boundary integral equation code, demonstrates the accuracy of the proposed methodology. Finally, extensive calculations are presented, illustrating the direct impact of the immersion depth and the slenderness of the spheroid on the hydrodynamic coefficients

Low-frequency on-site identification of a highly conductive body buried in Earth from a model ellipsoid

International audienceIdentification of a highly conductive orebody buried in Earth using an equivalent, perfectly conducting, triaxial model ellipsoid is investigated. The real data available (three-component magnetic fields collected along a borehole due to a single-frequency current loop at the Earth surface) are simulated via a low frequency, closed-form power series expansion of the electromagnetic fields scattered off an equivalent ellipsoid within a homogeneous, conductive medium, the source itself being idealized as a vertical magnetic dipole nearby. The approach provides formulations amenable to fast yet accurate computations, most of the work being in the construction of the formulations themselves, not in the numerical computations. The inversion scheme is described, which sees the iterative minimization of the least-square discrepancy between the fields due to a given ellipsoid and the data available. Unknowns are semi-axis lengths, angular orientations and coordinates of its centre. Numerical simulations illustrate the approach, before considering experimental single-well log data in a surface-to-borehole configuration at a mining site