Institut Jean le Rond D'Alembert, UMR 7190, Université Pierre et Marie Curie, Paris, France.
Phys Rev Lett. 2011 Mar 11;106(10):104502. doi: 10.1103/PhysRevLett.106.104502.
We show that the Kelvin-Helmholtz instability excited by a localized perturbation yields a self-similar wave. The instability of the mixing layer was first conceived by Helmholtz as the inevitable growth of any localized irregularity into a spiral, but the search and uncovering of the resulting self-similar evolution was hindered by the technical success of Kelvin's wavelike perturbation theory. The identification of a self-similar solution is useful since its specific structure is witness of a subtle nonlinear equilibrium among the forces involved. By simulating numerically the Navier-Stokes equations, we analyze the properties of the wave: growth rate, propagation speed and the dependency of its shape upon the density ratio of the two phases of the mixing layer.
我们证明，局域扰动激发的开尔文-亥姆霍兹不稳定性产生自相似波。混合层的不稳定性最初是由亥姆霍兹设想的，即任何局域不规则性必然会增长为螺旋形，但由于开尔文波动扰动理论的技术成功，这种自相似演化的搜索和揭示受到了阻碍。自相似解的识别是有用的，因为它的特定结构是所涉及的力之间微妙的非线性平衡的见证。通过数值模拟纳维-斯托克斯方程，我们分析了波的性质：增长率、传播速度以及其形状对混合层两相密度比的依赖性。
