Waves and wave resistance of thin bodies moving at low speed: the free-surface nonlinear effect
Waves and wave resistance of thin bodies moving at low speed: the free-surface nonlinear effect
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低速运动的薄体的波和波阻：自由表面非线性效应
DOI：
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发表时间：
1975
影响因子：
3.7
通讯作者：
G. Dagan
中科院分区：
文献类型：
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作者：
G. Dagan
自由表面重力流通过沉体或浮体的线性化理论是基于长细参数e中速度势的微扰展开，且弗劳德数F保持固定。结果表明，当F→0时，自由波振幅和相关波阻趋于零，但在此极限下，线性化解不是均匀的：当F→0时，二阶项与一阶项之比变得无界，且ε固定。这种非均匀性（在以前的工作中称为“第二弗劳德数悖论”）与自由曲面条件的非线性有关。结合ε和F，导出了二维流动薄体膨胀均匀性的判据。这些准则取决于前缘（和尾缘）的形状：随着形状变得更细，线性化解对更小的f有效。借助坐标应变方法，导出了流过沉体的二维流动的均匀一阶近似。这种张力导致车身轮廓的大多数奇异点（光滑形状的前缘和后缘）的明显位移，因此导致有效弗劳德数的明显变化。
The linearized theory of free-surface gravity flow past submerged or floating bodies is based on a perturbation expansion of the velocity potential in the slenderness parameter e with the Froude number F kept fixed. It is shown that, although the free-wave amplitude and the associated wave resistance tend to zero as F → 0, the linearized solution is not uniform in this limit: the ratio between the second- and first-order terms becomes unbounded as F → 0 with ε fixed. This non-uniformity (called ‘the second Froude number paradox’ in previous work) is related to the nonlinearity of the free-surface condition. Criteria for uniformity of the thin-body expansion, combining ε and F, are derived for two-dimensional flows. These criteria depend on the shape of the leading (and trailing) edge: as the shape becomes finer the linearized solution becomes valid for smaller F. Uniform first-order approximations for two-dimensional flow past submerged bodies are derived with the aid of the method of co-ordinate straining. The straining leads to an apparent displacement of the most singular points of the body contour (the leading and trailing edges for a smooth shape) and, therefore, to an apparent change in the effective Froude number.