The nonlinear behaviour of a constant vorticity layer at a wall
The nonlinear behaviour of a constant vorticity layer at a wall
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壁面上恒定涡度层的非线性行为
DOI：
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发表时间：
1981
影响因子：
3.7
通讯作者：
D. Pullin
中科院分区：
文献类型：
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作者：
D. Pullin
所谓的“水袋”方法是用来研究一个二维无粘层的行为恒定涡量ω和平均厚度δ相邻的壁有滑移。导出了一个非线性初始值方程，该方程描述了将层内旋转流体与无旋转自由流体分离的材料界面的运动，该界面受到流向循环扰动到其未扰动形状的情况。该方程的线性化解表明，波长λ的正弦扰动在无限远处以相对于流体的速度ωλ[1−exp(−4πδ/λ)]/4π的中性稳定开尔文-亥姆霍兹波的一种模式传播。在一定波长范围内和有限扰动幅度下的全非线性方程的数值解显示出不同的行为。当振幅足够大时，界面谷演变成无旋转流体的长楔状物，它们被“夹带”到层中，并被旋转流体的裂片或凸起与自由流分开。这种单模非线性界面畸变可以在很宽的波长范围内产生，没有基于δ的优先标度的迹象。本文认为，该界面行为与近年来在恒压湍流边界层外部的烟气流动可视化研究中观察到的湍流和非湍流流体界面的流动特征有明显的相似之处。计算得到的旋转流体叶状速度与等效线性化波速相差不大，与现有的少数湍流-非湍流界面上的凸起速度测量值基本吻合，叶状速度场与实验中观察到的一般流型在定性上基本一致。然而，在缺乏优选尺度或尺度范围的情况下，得出的结论是，目前的结果不能被解释为支持在层的外层存在大规模相干运动的假设。
The so-called ‘water-bag’ method is used to study the behaviour of a two-dimensional inviscid layer of constant vorticity ω and of mean thickness δ adjacent to a wall with slip at the wall. A nonlinear initial-value equation is derived which describes the motion of the material interface separating the rotational fluid within the layer from the irrotational free stream, for the case where this interface is subject to streamwise cyclic disturbances to its undisturbed shape. A linearized solution to this equation shows that a sinusoidal disturbance of wavelength λ propagates as one mode of a neutrally stable Kelvin-Helmholtz wave with velocity ωλ[1 − exp (−4πδ/λ)]/4π relative to the fluid at infinity. Numerical solutions of the full nonlinear equation for a range of wavelengths and finite disturbance amplitudes indicate different behaviour. For sufficiently large amplitude the interface valleys evolve into long re-entrant wedges of irrotational fluid which are ‘entrained’ into the layer and which are separated from the free stream by lobes or bulges of rotational fluid. This single-mode nonlinear interfacial distortion could be generated over a broad wavelength range with no indication of preferential scaling based on δ. It is suggested that the interface behaviour bears distinct resemblance to flow features observed at the interface between turbulent and non-turbulent fluid in recent smoke-in-air flow-visualization studies of the outer part of a constant pressure turbulent boundary layer. The calculated rotational fluid lobe velocities, which are not very different from the equivalent linearized wave velocities, are found to be in reasonable agreement with the few existing measurements of the velocity of bulges at the turbulent–nonturbulent fluid interface, while the computed velocity field in the lobe is in qualitative agreement with the general flow pattern observed in experiments. In the absence of a preferred scale or range of scales for the development of the interfacial distortion, however, it is concluded that the present results cannot be interpreted as supporting the hypothesis of the presence of largescale coherent motions in the outer part of the layer.