2007

This presentation concerns the mathematical formulation of steady surface gravity waves in a Lagrangian description of motion. It will be demonstrated that classical second-order Lagrangian Stokes-like approximations do not represent a steady wave motion in the presence of net mass transport (Stokes drift). A general mathematically correct formulation is then derived. This derivation leads naturally to a Lagrangian Stokes-like perturbation scheme that is uniformly valid for all time, i.e. without secular terms. This scheme is illustrated, both for irrotational waves, with seventh-order and third-order approximations in deep water and finite depth, respectively, and for rotational waves with a third-order approximation of the Gerstner-like wave on finite depth. It is also shown that the Lagrangian approximations are more accurate than their Eulerian counterparts of same order.

Didier Clamond has been a post.-doc. at the Department at Mathematics, UiO. He is now faculty member at the University of Nice, Sophia-Antipolis.

The talk deals with the stability of water waves in a shear flow. A carefully designed numerical solver enables to extend the range of previous calculations, and to obtain results for larger wavelengths (up to 20 cm) and stronger winds (up to a shear-velocity of 1 m/s). The main finding is the appearance of a second unstable mode which quite often turns out to be the dominant one. A comparison between results from the viscous model (Orr-Sommerfeld equations), and those of the inviscid model (Rayleigh equations), for 18cm long waves, reveals some similarity in the structure of the eigenfunctions, but a significant difference in the imaginary part of the eigenvalues (i.e. the growth-rate). It is found that the growth-rate for the viscous model is 10 fold larger than that of the inviscid one.

Michael Stiassnie er professor ved Technion, Israel

M. Stiassnie , A. Regev, and Y. Agnon: The stability and long-time evolution of narrow spectra homogeneous seas subject to inhomogeneous disturbances is studied. Specifically, we study unidirectional spectra, where according to classical homogeneous theory (i.e. the Kinetic equation), no spectral evolution is expected. In the region of instability , recurrent evolution is discovered. This behavior is qualitatively different from recent work on discrete spectra that exhibited irreversible widening of narrow spectra. The inhomogeneous structure of the unstable modes that leads to the recurrent evolution is revealed.

Technip is a world-class player in engineering, technologies and construction services for oil and gas, petrochemical and other industries. With a workforce of > 22,000 people worldwide, and annual revenues of almost 7 billion euros, TECHNIP ranks among the 5 major players in full-service engineering and construction services in the field of hydrocarbons and petrochemicals. Technip Norge is a specialist offshore / subsea construction company with offices in Oslo ( Stabekk ), Stavanger and Haugesund plus a pipeline fabrication yard in Orkanger. Using a fleet of specialist vessels the main areas of activity in Norway are projects for the engineering, procurement, supply and installation of rigid pipelines, flexible risers and subsea structures plus all necessary activities related to this, such as diving, ROV operations, offshore survey, trenching and rock-dumping. The presentation will give a general introduction to the company, our special areas of technical expertise and a brief summary of some of the challanges experienced on one of our recent projects.

Tim Crome is Engineering Manager in Technip Norge AS

Presentasjonen omhandler fokus, hovedsamarbeidspartnere, og om hvordan mekanikk kan bidra til den nye SFFen

Hans Petter Langtangen er utdannet på mekanikk og var ansatt på Matematisk institutt før han flyttet til IFI og etterhvert SIMULA senteret. Langtangen er leder av den nye SFFen