论文标题
波湍流：毛细管波的情况（审查）
Wave turbulence: the case of capillary waves (a review)
论文作者
论文摘要
毛细血管波可能是最简单的例子，以引入波湍流。自Zakharov和Filonenko（1967）发表的第一篇论文以来，毛细血管波湍流一直是许多研究的主题，但是动力学方程的讲义推导仍然缺乏。本文的目的是在没有重力和深水的近似情况下提出这种推导。我们使用Eulerian方法和在平衡升高周围的泰勒膨胀，以获得动力学方程的速度潜力。在三波相互作用中使用方向极性会导致该方程式的紧凑形式，该形式与以前的工作完全兼容。确切的溶液是通过应用于波数的所谓Zakharov转换来得出的，并讨论了这些溶液的性质。还审查了近几十年来完成的实验和数值工作。
Capillary waves are perhaps the simplest example to consider for an introduction to wave turbulence. Since the first paper by Zakharov and Filonenko (1967), capillary wave turbulence has been the subject of many studies but a didactic derivation of the kinetic equation is still lacking. It is the objective of this paper to present such a derivation in absence of gravity and in the approximation of deep water. We use the Eulerian method and a Taylor expansion around the equilibrium elevation for the velocity potential to derive the kinetic equation. The use of directional polarities for three-wave interactions leads to a compact form for this equation which is fully compatible with previous work. The exact solutions are derived with the so-called Zakharov transformation applied to wavenumbers and the nature of these solutions is discussed. Experimental and numerical works done in recent decades are also reviewed.
