开尔文船舶波型的视角是多少？
What is the apparent angle of a Kelvin ship wave pattern?
摘要：
虽然包含开尔文船舶波型的半角通常被接受为19.47度，但最近对足够快速移动的船舶的观测和计算表明，视尾流角随着船舶速度而减小。对这种角度减小的一种解释依赖于这样的假设，即船不能产生比其船体长度大得多的波长。另一种解释是，在实践中观察到的波型是由最高峰的位置定义的;对于由足够快速移动的物体产生的尾流，这些最高峰不再位于最外面的发散波上，从而导致更小的视角。本文着重研究了自由表面绕流单个淹没点源和绕流一对淹没点源的问题。在这些问题的线性版本中，我们测量由最高峰形成的表观尾流角，并观察到以下三个制度：一个小弗劳德数模式，其中发散波不可见;标准波模式，其中最大峰发生在最外面的发散波;和第三个制度，其中最高峰形成一个V形的角度远小于开尔文角。对于非线性流动，我们证明了非线性的影响，增加了明显的尾流角，使一些高度非线性的解决方案有明显的尾流角大于开尔文角。对于较大的弗劳德数，对表观尾流角的影响可能更加显著，强非线性可能会将波型从第三状态转移到第二状态。我们希望我们的非线性结果将转化为其他更复杂的流动配置，如流动由于一个稳定移动的封闭体，如潜艇。
英文摘要：
While the half-angle which encloses a Kelvin ship wave pattern is commonly accepted to be 19.47 degrees, recent observations and calculations for sufficiently fast-moving ships suggest that the apparent wake angle decreases with ship speed. One explanation for this decrease in angle relies on the assumption that a ship cannot generate wavelengths much greater than its hull length. An alternative interpretation is that the wave pattern that is observed in practice is defined by the location of the highest peaks; for wakes created by sufficiently fast-moving objects, these highest peaks no longer lie on the outermost divergent waves, resulting in a smaller apparent angle. In this paper, we focus on the problems of free surface flow past a single submerged point source and past a submerged source doublet. In the linear version of these problems, we measure the apparent wake angle formed by the highest peaks, and observe the following three regimes: a small Froude number pattern, in which the divergent waves are not visible; standard wave patterns for which the maximum peaks occur on the outermost divergent waves; and a third regime in which the highest peaks form a V-shape with an angle much less than the Kelvin angle. For nonlinear flows, we demonstrate that nonlinearity has the effect of increasing the apparent wake angle so that some highly nonlinear solutions have apparent wake angles that are greater than Kelvin's angle. For large Froude numbers, the effect on apparent wake angle can be more dramatic, with the possibility of strong nonlinearity shifting the wave pattern from the third regime to the second. We expect our nonlinear results will translate to other more complicated flow configurations, such as flow due to a steadily moving closed body such as a submarine.
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