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Abstract
En 中文
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 similar or equal to 1. The phenomenon is new and the waves were 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, with periods of 30-60 s, 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 similar or equal to 1 document symmetries of the waves at positive or negative 1 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 similar or equal to 1, while the growth in U is only very weak for Delta h/h << 1 ( the asymptotics). Calculations show good agreement with observations.
Keywords:
geophysical and geological flows
topographic effects
waves/free-surface flows
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