主讲人：Prof. John Grue, Department of Mathematics, University of Oslo, Norway
学术报告1：Ship generated mini-tsunamis
学术报告2：Particle paths and drift velocity in water waves at finite depth
Very long waves are generated when a ship moves across an appreciable depth change Delta h comparable to the average and relatively shallow water depth h at the location, with Delta h/h simeq 1. The phenomenon is new and the waves are recently observed in the Oslofjord in Norway. The 0.5-1 km long waves, extending across the 2-3 km wide fjord, are observed as run-ups and run-downs along the shore, of periods of 30-60 seconds, where a wave height up to 1.4 m has been measured. The waves travelling with the shallow water speed, found ahead of the ships moving at subcritical depth Froude number, behave like a mini-tsunami. A qualitative explanation of the linear generation mechanism is provided by an asymptotic analysis, valid for Delta h/h<<1 and long waves, expressing the generation in terms of a pressure impulse at the depth change. Complementary fully dispersive calculations for Delta h/h simeq 1 document symmetries of the waves at positive or negative Delta h. The wave height grows with the ship speed U according to U^n with n in the range 3-4, for Delta h/h simeq 1, while the growth in U is only very weak for Delta h/h<<1 (the asymptotics). Calculations show good agreement with observations.
REFERENCE: J. Grue (2017) Ship generated mini-tsunamis, J. Fluid Mech. 816, 142-166.
The Lagrangian paths, horizontal Lagrangian drift velocity, U_L, and the Lagrangian excess period, T_L-T_0, where T_L is the Lagrangian period and T_0 the Eulerian linear period, are obtained by particle tracking velocimetry (PTV) in non-breaking periodic laboratory waves at a finite water depth of h=0.2 m, wave height of H=0.49h and wavenumber of k=0.785/h. Both U_L and T_L-T_0 are functions of the average vertical position of the paths, Y, where -1<Y/h<0. The functional relationships U_L(Y) and T_L-T_0=f(Y) are very similar. Comparisons to calculations by the inviscid strongly nonlinear Fenton method and the second-order theory show that the streaming velocities in the boundary layers below the wave surface and above the fluid bottom contribute to a strongly enhanced forward drift velocity and excess period. The experimental drift velocity shear becomes more than twice that obtained by the Fenton method which again is approximately twice that of the second-order theory close to the surface. There is no mass flux of the periodic experimental waves and no pressure gradient. The results from a total number of 80 000 experimental particle paths in the different phases and vertical positions of the waves show a strong collapse. The particle paths are closed at the two vertical positions where U_L=0.
REFERENCE: J. Grue and J. Kolaas (2017) Experimental particle paths and drift velocity in steep
waves at finite water depth. J. Fluid Mech. 810 R1-1-10.
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