Author

# Lars Skjelbreia

Bio: Lars Skjelbreia is an academic researcher. The author has contributed to research in topics: Dispersion (water waves) & Trigonometric series. The author has an hindex of 1, co-authored 2 publications receiving 171 citations.

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29 Jan 2011

TL;DR: In this article, the results of the fifth order theory and values of the various coefficients as a function of the parameter d/L were presented for gravity waves of greater steepness.

Abstract: In dealing with problems connected with gravity waves, scientists and engineers frequently find it necessary to make lengthy theoretical calculations involving such wave characteristics as wave height, wave length, period, and water depth. Several approximate theoretical expressions have been derived relating the above parameters. Airy, for instance, contributed a very valuable and complete theory for waves traveling over a horizontal bottom in any depth of water. Due to the simplicity of the Airy theory, it is frequently used by engineers. This theory, however, was developed for waves of very small heights and is inaccurate for waves of finite height. Stokes presented a similar solution for waves of finite height by use of trigonometric series. Using five terms in the series, this solution will extend the range covered by the Airy theory to waves of greater steepness. No attempt has been made in this paper to specify the range where the theory is applicable. The coefficients in these series are very complicated and for a numerical problem, the calculations become very tedious. Because of this difficulty, this theory would be very little used by engineers unless the value of the coefficient is presented in tabular form. The purpose of this paper is to present the results of the fifth order theory and values of the various coefficients as a function of the parameter d/L.

185 citations

01 Nov 1960

1 citations

##### Cited by

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TL;DR: In this paper, the authors considered some aspects of water impact and green water loading by numerically investigating a dambreak problem and water entry problems, based on the Navier-Stokes equations that describe the flow of a viscous fluid.

618 citations

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TL;DR: In this article, an alternative Stokes theory for steady waves in water of constant depth is presented where the expansion parameter is the wave steepness itself, and the first step in application requires the solution of one nonlinear equation, rather than two or three simultaneously as has been previously necessary.

Abstract: An alternative Stokes theory for steady waves in water of constant depth is presented where the expansion parameter is the wave steepness itself. The first step in application requires the solution of one nonlinear equation, rather than two or three simultaneously as has been previously necessary. In addition to the usually specified design parameters of wave height, period and water depth, it is also necessary to specify the current or mass flux to apply any steady wave theory. The reason being that the waves almost always travel on some finite current and the apparent wave period is actually a Dopplershifted period. Most previous theories have ignored this, and their application has been indefinite, if not wrong, at first order. A numerical method for testing theoretical results is proposed, which shows that two existing theories are wrong at fifth order, while the present theory and that of Chappelear are correct. Comparisons with experiments and accurate numerical results show that the present theory ...

488 citations

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TL;DR: In this article, the authors introduce OpenFOAM® as a tool to consider for coastal engineering applications as it solves 3D domains and considers two-phase flow, and demonstrate that active wave absorption is found to enhance stability by decreasing the energy of the system and correcting the increasing water level on long simulations.

482 citations

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TL;DR: In this article, a finite Fourier series is used to give a set of nonlinear equations which can be solved using Newton's method for the numerical solution of steadily progressing periodic waves on irrotational flow over a horizontal bed.

Abstract: A method for the numerical solution of steadily progressing periodic waves on irrotational flow over a horizontal bed is presented. No analytical approximations are made. A finite Fourier series, similar to Dean's stream function series, is used to give a set of nonlinear equations which can be solved using Newton's method. Application to laboratory and field situations is emphasized throughout. When compared with known results for wave speed, results from the method agree closely. Results for fluid velocities are compared with experiment and agreement found to be good, unlike results from analytical theories for high waves.The problem of shoaling waves can conveniently be studied using the present method because of its validity for all wavelengths except the solitary wave limit, using the conventional first-order approximation that on a sloping bottom the waves at any depth act as if the bed were horizontal. Wave period, energy flux and mass flux are conserved. Comparisons with experimental results show good agreement.

424 citations

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TL;DR: In this article, landslide generated impulse waves were investigated in a two-dimensional physical laboratory model based on the generalized Froude similarity, and four wave types were determined: weakly nonlinear oscillatory wave, nonlinear transition wave, solitary-like wave and dissipative transient bore.

Abstract: Landslide generated impulse waves were investigated in a two-dimensional physical laboratory model based on the generalized Froude similarity. The recorded wave profiles were extremely unsteady and nonlinear. Four wave types were determined: weakly nonlinear oscillatory wave, non-linear transition wave, solitary-like wave and dissipative transient bore. Most of the generated impulse waves were located in the intermediate water depth wave regime. Nevertheless the propagation velocity of the leading wave crest closely followed the theoretical approximations for a solitary wave. Between 4 and 50% of the kinetic slide impact energy propagated outward in the impulse wave train. The applicability ranges of the classical nonlinear wave theories to landslide generated impulse waves were determined. The main wave characteristics were related to the landslide parameters driving the entire wave generation process. The slide Froude number was identified as the dominant parameter. The physical model results were compared to the giant rockslide generated impulse wave which struck the shores of the Lituya Bay, Alaska, in 1958.

298 citations