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Ploughing flows. (English) Zbl 0932.76010

The primary goal is to understand near-bow flows. The actual ship-bow problem is very challenging, especially the computation of the splash that is thrown upward and backward. Fully-submerged bodies are more tractable. However, when a submerged body is very close to the surface, a thin layer of fluid above the body is sort of equivalent to the bow splash. The authors attack this later problem by investigating the following model: the body is a semi-infinite flat plate of width \(H\) which is submerged into a uniform stream of infinitely-deep inviscid incompressible fluid. Far away from the body, the free surface lies at \(y=D\) relatively to the bottom surface of the body. Besides the geometric parameter \(H/D\), another important dimensionless parameter is the Froude number. The authors find analytical solutions in the extreme cases of infinite and zero Froude number. For finite Froude numbers, the problem is investigated numerically. There is a range of Froude numbers within which steady-state flows seem to be impossible.

MSC:

76B20 Ship waves
76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing
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