# Wave Forces on an Elliptic Cylinder

01 Mar 1985-Journal of Waterway Port Coastal and Ocean Engineering-asce (American Society of Civil Engineers)-Vol. 111, Iss: 2, pp 433-449

TL;DR: In this paper, two approximate methods are presented for the calculation of the wave induced forces and moments on a vertical, surface-piercing cylinder of elliptic cross section, which provide a substantial reduction in computational effort when Compared with the exact solution which involves the numerical evaluation of Mathieu functions.

Abstract: Two approximate methods are presented for the calculation of the wave induced forces and moments on a vertical, surface‐piercing cylinder of elliptic cross section. Both methods provide a substantial reduction in computational effort when Compared with the exact solution which involves the numerical evaluation of Mathieu functions. One method involves the expansion of the exact expressions for the forces and moments for small values of the elliptic eccentricity parameter. The second method is based on Green's theorem and gives rise to an integral equation for the fluid velocity potential on the cylinder surface. Numerical results are presented for a range of relevant parameters and show excellent agreement with the computed values of the exact solution.

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TL;DR: In this article, the authors derived a relation for the fluid motion through thin porous structures in addition to the conventional governing equation and boundary conditions for small-amplitude waves in ideal fluids.

Abstract: Diffraction of water waves by porous breakwaters is studied based on the linear potential wave theory. The formulation of the problem includes a newly derived relation for the fluid motion through thin porous structures in addition to the conventional governing equation and boundary conditions for small-amplitude waves in ideal fluids. The porous boundary condition, indirectly verified by collected experimental data, is obtained by assuming that the flow within the porous medium is governed by a convection-neglected and porous-effect-modeled Euler equation. A vertically two-dimensional problem with long-crested waves propagating in the normal direction of an infinite porous wall is first solved and the solution is compared with available experimental data. The wave diffraction by a semiinfinite porous wall is then studied by the boundary-layer method, in which the outer approximation is formulated by virtue of the reduced two-dimensional solution. It is demonstrated that neglect of the inertial effect of the porous medium leads to an overestimate of the functional performance of a porous breakwater.

280 citations

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TL;DR: In this article, a finite element model for the solution of Helmholtz problems at higher frequencies is described, which offers the possibility of computing many wavelengths in a single finite element.

Abstract: This paper describes a finite element model for the solution of Helmholtz problems at higher frequencies that offers the possibility of computing many wavelengths in a single finite element. The approach is based on partition of unity isoparametric elements. At each finite element node the potential is expanded in a discrete series of planar waves, each propagating at a specified angle. These angles can be uniformly distributed or may be carefully chosen. They can also be the same for all nodes of the studied mesh or may vary from one node to another. The implemented approach is used to solve a few practical problems such as the diffraction of plane waves by cylinders and spheres. The wave number is increased and the mesh remains unchanged until a single finite element contains many wavelengths in each spatial direction and therefore the dimension of the whole problem is greatly reduced. Issues related to the integration and the conditioning are also discussed.

131 citations

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TL;DR: In this paper, two new explicit empirical formulas were proposed to determine the original intensity factors on Neumann and Dirichlet boundary in the singular boundary method (SBM) solution of 2D and 3D potential and Helmholtz problems.

Abstract: This short communication proposes two new explicit empirical formulas to determine the original intensity factors on Neumann and Dirichlet boundary in the singular boundary method (SBM) solution of 2D and 3D potential and Helmholtz problems. Without numerical integration and subtracting and adding-back technique, the original intensity factors can be obtained directly by implementing the proposed explicit empirical formulas. The numerical investigations show that the SBM with these new explicit empirical formulas can provide the accurate solutions of several benchmark examples in comparison with the analytical, Boundary element method (BEM) and Regularized meshless method (RMM) solutions. In most cases, the present SBM with empirical formulas yields the similar numerical accuracy as the BEM and the SBM in which the original intensity factors are evaluated by the other time-consuming approaches. It is worthy of noting that the empirical formula costs far less CPU and storage requirements at the same number of boundary nodes and performs more stably than the inverse interpolation technique in the SBM.

55 citations

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TL;DR: In this paper, a semi-analytical solution methodology for the linear hydrodynamic diffraction induced by arrays of elliptical cylinders subjected to incident waves is presented, where the solution of the Laplace equation in elliptic coordinates for both the incident and the diffracted waves is formulated analytically in terms of the even and odd periodic and radial Mathieu functions.

43 citations

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TL;DR: In this paper, the authors derived analytical solutions of hydrodynamic pressure and force on an elliptical hollow cylinder by assigning reasonable boundary conditions and by solving the Mathieu's differential equation in elliptical coordinate system.

43 citations

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TL;DR: In this paper, the authors present a review of numerical methods for diffraction and radiation of water wave s by natural boundarie s or man-made structure s i s of con siderable im portance in ocean engineering.

Abstract: The subject of diffraction and radiation of water wave s by natural boundarie s or man-made structure s i s of con siderable im portance in ocean engineering. A s a re sult of the ra pid growth of ocean e xploration and tran sportation, detailed knowledge of wave effect s i s now a virtual nece ssity for the safe de sign of co stly pro ject s such a s tanker s and their mooring s, off shore terminal s and drilling rig s, etc. Predicting the re spon se s to po ssible incident waves i s essential for the safe and economical o peration of exi sting and new harbor s. Effect s of t sunami s along a coa st line mu st be under stood in order to devi se mea sure s for protecting live s and pro pertie s. In di scu ssing wave effect s it i s im portant to di stingui sh between small and large bodie s (of ty pical dimen sion a) in com pari son with the characteri stic wave length (2n/k) and the wave am plitude (A). For small ka and large A/a [�0( 1)], vortex shedding and flow se paration are dominant, but diffraction i s in significant, i.e. while the body i s affected by the wave field near by, it doe s not materially alter the wave field at large. For small A/a and ka � 0(1 ), se paration become s in signi ficant while diffraction become s crucial. It i s to the latter category that thi s review i s addre ssed. In the conte xt of linearized theory, some analytical solution s are available for sim ple geometrie s by em ploying either re sult s that are known in cla ssical phy sic s (a circular vertical cylinder, a semi-in finite long breakwater, etc) or other exact technique s ( e.g., Dean 1945, Ur sell 1947, 1948, John 1948, Hein s 1948, Lewin 196 3, Mei 1966). A sym ptot ic theorie s for short or long wave s have al so been deve lo ped. Thi s review cover s numerical methods f or arbitrary geometrie s and frequencie s for which exten sive u se of the com puter i s nece ssary. It i s further re stricted to sim ple harmonic wave s. The more general ca se s of tran sient or random wave s can in princi ple be obtained by Fou rier integral s from the single-frequency re spon se calculated for all frequencie s (0 < W < CfJ). Direct calculation of tran sient problem s u sing tran sient Green function s ha s ju st begun ( see Shaw 197 5, Harten 197 5).

174 citations

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62 citations

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TL;DR: In this paper, the authors deal with the interaction of a train of regular surface waves with a large submerged oil storage tank resting on the ocean floor, in water of finite depth.

Abstract: In the design of submerged oil storage vessels where the structure generally has limited net negative buoyancy, the wave forces are of considerable importance in the design. This paper deals with the interaction of a train of regular surface waves with a large submerged oil storage tank resting on the ocean floor, in water of finite depth. Linear wave theory is used to describe the incident wave and viscous effects are neglected on the basis that the size of the submerged object is large compared to the height of the incident wave. The problem is formulated in the form of a potential flow problem and to solve this problem, point wave sources are distributed over the immersed surface. The strengths of these sources are then adjusted to satisfy the no-flow condition at the surface of the object. Results from a computer program based on these theoretical concepts are compared with experimental results from wave channel testing.

53 citations

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TL;DR: In this article, the mathematical solution to the diffraction problem is obtained on the basis of the linearized long-wave approximation for a shiplike body with beam-to-length ratio approximately equal to 0.2.

Abstract: Exciting forces and moments due to plane incident waves on a stationary platform are studied in the report. The platform is a vertical cylinder with a finite draft and elliptical cross section. The mathematical solution to the diffraction problem is obtained on the basis of the linearized long-wave approximation. Numerical results via Mathieu functions are presented for a shiplike body with beam-to-length ratio approximately equal to 0.2. Various draft-to-depth ratios and angles of incidence are considered. Results have been checked with the limiting case of a circular cylinder for the long-wavelength range. Aside from its own practical interest, the present theory provides a basis for comparison with other approximate theories of slender-body type and serves as a prelude to the corresponding calculations for arbitrary wavelengths. (Author)

38 citations