标题： 柯尔莫哥洛夫尺度连接线性水动力学稳定性和湍流 显示英文标题

标题： Kolmogorov scaling bridges linear hydrodynamic stability and turbulence

摘要： 在动能如何分布在众多惯性（中间）尺度上的方式是湍流的一个基本特征。 根据Kolmogorov的1941理论，基于量纲分析，该范围内的能量谱函数形式是-5/3谱。 实验证据已积累以支持这一规律。 到目前为止，这一规律被认为是非线性相互作用特有的湍流动力学的一个独特部分。 我们在这里展示，这种图景也存在于三维稳定扰动波在中间波数范围内的线性动力学中。 通过这些波的瞬态寿命的大量计算，在典型的剪切流中，我们可以观察到当它们离开瞬态阶段并进入最终指数衰减时所保留的能量显示出非常接近-5/3谱的谱。 观测时间也显示出类似的标度。 这种标度仅依赖于波数，即它对波相对于基本流的倾斜度、初始条件的形状对称性和雷诺数不敏感。 显示英文摘要

摘要： The way in which kinetic energy is distributed over the multiplicity of inertial (intermediate) scales is a fundamental feature of turbulence. According to Kolmogorov's 1941 theory, on the basis of a dimensional analysis, the form of the energy spectrum function in this range is the -5/3 spectrum. Experimental evidence has accumulated to support this law. Until now, this law has been considered a distinctive part of the nonlinear interaction specific to the turbulence dynamics. We show here that this picture is also present in the linear dynamics of three-dimensional stable perturbation waves in the intermediate wavenumber range. Through extensive computation of the transient life of these waves, in typical shear flows, we can observe that the residual energy they have when they leave the transient phase and enter into the final exponential decay shows a spectrum that is very close to the -5/3 spectrum. The observation times also show a similar scaling. The scaling depends on the wavenumber only, i.e. it is not sensitive to the inclination of the waves to the basic flow, the shape-symmetry of the initial condition and the Reynolds number.