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TECHNICAL PAPERS

A Second Order Lagrangian Model for Irregular Ocean Waves

[+] Author and Article Information
Sébastien Fouques1

Department of Marine Technology, Norwegian University of Science and Technology, No-7491 Trondheim, NorwaySebastien.fouques@marintek.sintef.no

Harald E. Krogstad

Department of Mathematics, Norwegian University of Science and Technology, NO-7491 Trondheim, Norwayharald.krogstad@math.ntnu.no

Dag Myrhaug

Department of Marine Technology, Norwegian University of Science and Technology, NO-7491 Trondheim, Norwaydagmyr@marin.ntnu.no

1

Corresponding author.

J. Offshore Mech. Arct. Eng 128(3), 177-183 (Jun 13, 2005) (7 pages) doi:10.1115/1.2199563 History: Received September 07, 2004; Revised June 13, 2005

Synthetic aperture radar (SAR) imaging of ocean waves involves both the geometry and the kinematics of the sea surface. However, the traditional linear wave theory fails to describe steep waves, which are likely to bring about specular reflection of the radar beam, and it may overestimate the surface fluid velocity that causes the so-called velocity bunching effect. Recently, the interest for a Lagrangian description of ocean gravity waves has increased. Such an approach considers the motion of individual labeled fluid particles and the free surface elevation is derived from the surface particles positions. The first order regular solution to the Lagrangian equations of motion for an inviscid and incompressible fluid is the so-called Gerstner wave. It shows realistic features such as sharper crests and broader troughs as the wave steepness increases. This paper proposes a second order irregular solution to these equations. The general features of the first and second order waves are described, and some statistical properties of various surface parameters such as the orbital velocity, slope, and mean curvature are studied.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Λ(k) and Ψ1(k) for various wave steepnesses

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Figure 2

Excerpt of a Monte Carlo simulation of the 3D first order Lagrangian surface

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Figure 3

Excerpt of a Monte Carlo simulation of 3D first order surface elevation and curvature fields

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Figure 4

PDF estimate of the surface mean curvature

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Figure 5

Excerpt of a Monte Carlo simulation of 2D second order Lagrangian waves. Time interval between two consecutive figures: 0.5S. Solid line: second order Lagrangian solution. Dashed line: first order Lagrangian solution. Dash-dotted line: first order Eulerian solution.

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