Irregular waves, Department of Mathematics, University of Oslo

Irregular waves

Personal

Name	Title	Telephone	E-mail
John Grue	Professor	+47 228 57228	johng@math.uio.no
Didier Clamond	Post Doctor	+47 228 55853	didier@math.uio.no
Atle Jensen	Research Fellow	+47 228 55841	atlej@math.uio.no
Morten Huseby	Post Doctor	+47 228 55776	mhuseby@math.uio.no

	Background and motivation During the last century, many small and three big accidents due to slide generated waves have occurred in Norway, taking a toll of 170 deaths in addition to huge material damage. At present, 11 areas in Norway are under survillance of NGI due to the significant probability of large, slide-induced, destructive waves. There is geological evidence of several giant under-water slides at Storegga (5000 B.C.) on the Norwegian continental margin. The associated wave may have caused a water elevation of up to 10 meters at the Norwegian coast. Signatures of several similar slide incidents are recently discovered in other parts of the world. Such slides are also of great interest for geologists, due to the massive redistribution of sediments in ocean basins. An actual question is if marginally stable sediments at the continental slopes may be released through off-shore activity in the Norwegian Sea. The consequences, both for oil installations and coastal regions, might be disastrous. In a European perspective, destructive ocean waves have received increasing attention in recent years, e.g., through EU projects. The Mechanics Division has participated in two such projects. There have been several serious European catastrophes throughout history. The most severe incident in the present century took place in Vaiont in Italy, 1963, and caused 2600 casualties. A historic survey of important slide-generated tsnumais is found in Voight (1979). while the Norwegian incidents are compiled by Jørstad (1968). Counting among the seismic events, tsunamis are the no. 5 killer among natural hazards worldwide. In Japan, alone, more than 150 serious accidents have been registered in this century. New investigations The velocity profiles under crest of a total of 62 different steep wave events, in deep water, are measured in laboratory using Particle Image Velocimetry (PIV). The waves take place in the leading unsteady part of a wave train, focusing wave fields and random wave series. Complementary fully nonlinear theoretical/numerical wave computations are performed. The experimental velocities have been put on a nondimensional form in the following way: from the wave record (at a fixed point) the (local) trough-to-trough period, $T_{TT}$ , and the maximal elevation, $\eta_m$ , of an individual large wave event are identified. The local wave slope, $\epsilon$ , and the wavenumber, , are estimated from $\omega^2/(gk)=1+\epsilon^2$ , $k\eta_m=\epsilon+\frac{1}{2}\epsilon^2+\frac{1}{2}\epsilon^3$ , where $\omega=2\pi/T_{TT}$ and denotes the acceleration of gravity. A reference fluid velocity, $\epsilon\sqrt{g/k}$ , is then defined. Waves with a fluid velocity up to 75 % of the estimated wave speed are measured. A corresponding wave slope is . A strong collapse of the nondimensional experimental velocity profiles is found. This is also true with the fully nonlinear computations of transient waves. There is excellent agreement between the present measurements and previously published Laser Doppler Anemometry (LDA) data. A surprising result, obtained by comparison, is that the nondimensional experimental velocities fit with the exponential profile, i.e. e $^{ky}$ , the vertical coordinate, with in the mean water level. A return flow in the wave tank becomes quite visible in some of the random wave experiments. Larger velocities close to the wave crest, and smaller velocities below the mean water line, are then observed. In some of the experiments a weak effect of the finite water depth causes an additional tilt of the velocity profile.

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