Finite-time barriers to front propagation in two-dimensional fluid flows.
Finite-time barriers to front propagation in two-dimensional fluid flows.
复制标题
二维流体流动中前沿传播的有限时间障碍。
作者：
J. Mahoney;K. Mitchell
最近的理论和实验研究证明了某些不变流形（称为燃烧不变流形（BIM））的作用，作为流动流体中传播的反应前沿的单向动力障碍。这些屏障在二维流体流动中形成一维曲线。在先前的研究中，流体速度场被要求是与时间无关的或时间周期的。在本研究中，我们开发了一种仅基于有限时间间隔内的流体速度数据来识别突出的单向障碍的方法，该数据可能具有任意的时间依赖性。我们将这种屏障称为燃烧拉格朗日相干结构（bLCS），类似于被动平流中常用的拉格朗日相干结构（LCS）。我们的方法基于采用 Farazmand 等人引入的稳态“拉格朗日剪切”曲线的 LCS 变分公式。 [Physica D 278-279, 44 (2014)] 在被动平流的背景下。我们通过证明 bLCS 紧密跟踪 BIM 来获得与时间无关的、具有反向“风”的双涡流通道流，从而对我们的技术进行数值验证。
Recent theoretical and experimental investigations have demonstrated the role of certain invariant manifolds, termed burning invariant manifolds (BIMs), as one-way dynamical barriers to reaction fronts propagating within a flowing fluid. These barriers form one-dimensional curves in a two-dimensional fluid flow. In prior studies, the fluid velocity field was required to be either time-independent or time-periodic. In the present study, we develop an approach to identify prominent one-way barriers based only on fluid velocity data over a finite time interval, which may have arbitrary time-dependence. We call such a barrier a burning Lagrangian coherent structure (bLCS) in analogy to Lagrangian coherent structures (LCSs) commonly used in passive advection. Our approach is based on the variational formulation of LCSs using curves of stationary "Lagrangian shear," introduced by Farazmand et al. [Physica D 278-279, 44 (2014)] in the context of passive advection. We numerically validate our technique by demonstrating that the bLCS closely tracks the BIM for a time-independent, double-vortex channel flow with an opposing "wind."