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首页> 外文期刊>Bulletin of the American Physical Society >APS -70th Annual Meeting of the APS Division of Fluid Dynamics- Event - Surpassing the energy method for nonlinear fluid stability
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APS -70th Annual Meeting of the APS Division of Fluid Dynamics- Event - Surpassing the energy method for nonlinear fluid stability

机译：APS-流体动力学APS部门第70届年会-事件-超越能量方法的非线性流体稳定性

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A basic question in fluid stability is whether a laminar flow is nonlinearly stable to all perturbations. The typical way to verify stability, called the energy method, is to show that the energy of a perturbation must decay monotonically. The energy method is known to be overly conservative in many systems, particularly when turbulence arises subcritically, such as in parallel shear flows. The energy method is a special case of a Lyapunov function method in which the Lyapunov function is the perturbation energy. This talk will present a more general approach in which the Lyapunov functions (1) are not restricted to being quadratic but instead are higher-degree polynomials, and (2) can depend explicitly on the spectrum of the velocity field in the eigenbasis of the energy stability operator. The optimal construction of such Lyapunov functions is complicated but can be done with computer assistance by formulating a polynomial optimization problem, which in turn is formulated as a semidefinite program. This talk will describe the general framework of the method. A companion talk by Federico Fuentes will illustrate its application to planar Couette flow, where we have verified nonlinear stability at larger Reynolds numbers than is possible using the energy method.
机译：流体稳定性的一个基本问题是层流对于所有扰动是否非线性稳定。验证稳定性的典型方法称为能量方法，是表明扰动的能量必须单调衰减。已知能量方法在许多系统中过于保守，特别是在湍流次临界地产生时，例如在平行剪切流中。能量方法是Lyapunov函数方法的特例，其中Lyapunov函数是微扰能量。本演讲将提供一种更通用的方法，其中Lyapunov函数（1）不限于二次函数，而是高次多项式，并且（2）可以明确取决于能量本征基础上速度场的频谱稳定算子。这种Lyapunov函数的最佳构造很复杂，但可以通过公式化多项式优化问题的计算机辅助来完成，该问题又被公式化为半定程序。本演讲将描述该方法的一般框架。费德里科·富恩特斯（Federico Fuentes）的同伴演讲将说明其在平面Couette流中的应用，其中我们已经验证了比能量法更大的雷诺数下的非线性稳定性。

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