# Wave forces on piles: a diffraction theory

01 Dec 1954-
TL;DR: In this paper, a quantitative understanding of the forces developed by wave action against circular piling is presented, where the authors focus on the effect of wave action on circular piling and show that wave action is a powerful force against piling.
Abstract: : Although circular piling is a much-used structural element in shore protection, harbor, and other maritime structures, only recently have significant advances been made toward gaining a quantitative understanding of the forces developed by wave action against piling. The present report deals with this subject.

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TL;DR: In this article, the wave problem is introduced and a derivation of Berkhoff's surface wave theory is outlined, and appropriate boundary conditions are described, for finite and infinite boundaries.
Abstract: The wave problem is introduced and a derivation of Berkhoff's surface wave theory is outlined. Appropriate boundary conditions are described, for finite and infinite boundaries. These equations are then presented in a variational form, which is used as a basis for finite and infinite elements. The elements are used to solve a wide range of unbounded surface wave problems. Comparisons are given with other methods. It is concluded that infinite elements are a competitive method for the solution of such problems.

428 citations

Journal ArticleDOI
TL;DR: In this article, the scattering of surface gravity waves by a circular dock is considered in order to determine the horizontal and vertical forces and torque on the dock, and the solution is shown to have phase independent of depth and so may be obtained from an infinite set of real equations.
Abstract: The scattering of surface gravity waves by a circular dock is considered in order to determine the horizontal and vertical forces and torque on the dock. An incident plane wave is expanded in Bessel functions, and for each mode the problem is formulated in terms of the potential on the cylindrical surface containing the dock and extending to the bottom. The solution is shown to have phase independent of depth and so may be obtained from an infinite set of real equations, which are solved numerically by Galerkin's method. The convergence of the solution is discussed, and some numerical results are presented.This problem has been investigated previously by Miles & Gilbert (1968) by a different method, but their work contained errors.

261 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, the second-order theory explains a significant portion of the nonlinear wave run-up distribution measured at all angles around a large diameter vertical circular cylinder, and the design curves are presented for estimating the maximum secondorder wave runup for a wide range of conditions in terms of the relative depth, relative cylinder size, and wave steepness.
Abstract: Theoretical results for second-order wave run-up around a large diameter vertical circular cylinder are compared to results of 22 laboratory experiments conducted in regular nonlinear waves. In general, the second-order theory explains a significant portion of the nonlinear wave run-up distribution measured at all angles around the cylinder. At the front of the cylinder, for example, measured maximum run-up exceeds linear theory by 44% on average but exceeds the nonlinear theory by only 11% on average. In some cases, both measured run-up and the second-order theory exceed the linear prediction by more than 50%. Similar results are found at the rear of the cylinder where the second-order theory predicts a large increase in wave amplitude for cases where the linear diffraction theory predicts little or no increase. Overall, the nonlinear diffraction theory is found to be valid for the same relative depth and wave steepness conditions applicable to Stokes second-order plane-wave theory. In the last section of the paper, design curves are presented for estimating the maximum second-order wave run-up for a wide range of conditions in terms of the relative depth, relative cylinder size, and wave steepness.

115 citations

Journal ArticleDOI
TL;DR: In this paper, a fully nonlinear domain decomposed solver is proposed for efficient computations of wave loads on surface piercing structures in the time domain, and sensitivity tests of the extent of the inner Navier-Stokes/VOF domain are carried out.
Abstract: A fully nonlinear domain decomposed solver is proposed for efficient computations of wave loads on surface piercing structures in the time domain. A fully nonlinear potential flow solver was combined with a fully nonlinear Navier–Stokes/VOF solver via generalized coupling zones of arbitrary shape. Sensitivity tests of the extent of the inner Navier–Stokes/VOF domain were carried out. Numerical computations of wave loads on surface piercing circular cylinders at intermediate water depths are presented. Four different test cases of increasing complexity were considered; 1) weakly nonlinear regular waves on a sloping bed, 2) phase-focused irregular waves on a flat bed, 3) irregular waves on a sloping bed and 4) multidirectional irregular waves on a sloping bed. For all cases, the free surface elevation and the inline force were successfully compared against experimental measurements.

114 citations