Department of Applied Mathematics, University of Washington, Seattle, Washington 98195-3925, USA.
Department of Mechanical Engineering, University of Washington, Seattle, Washington 98195-2420, USA.
Phys Rev E. 2016 Mar;93(3):033108. doi: 10.1103/PhysRevE.93.033108. Epub 2016 Mar 9.
In this work we investigate the dynamics of inertial particles using finite-time Lyapunov exponents (FTLE). In particular, we characterize the attractor and repeller structures underlying preferential concentration of inertial particles in terms of FTLE fields of the underlying carrier fluid. Inertial particles that are heavier than the ambient fluid (aerosols) attract onto ridges of the negative-time fluid FTLE. This negative-time FTLE ridge becomes a repeller for particles that are lighter than the carrier fluid (bubbles). We also examine the inertial FTLE (iFTLE) determined by the trajectories of inertial particles evolved using the Maxey-Riley equations with nonzero Stokes number and density ratio. Finally, we explore the low-pass filtering effect of Stokes number. These ideas are demonstrated on two-dimensional numerical simulations of the unsteady double-gyre flow.
在这项工作中，我们使用有限时间李雅普诺夫指数（FTLE）研究惯性粒子的动力学。特别地，我们根据基础载体流体的 FTLE 场来描述惯性粒子优先集中的吸引子和排斥子结构。比环境流体（气溶胶）重的惯性粒子吸引到负时间流体 FTLE 的脊上。对于比载体流体（气泡）轻的粒子，这个负时间 FTLE 脊成为一个排斥子。我们还检查了由使用带有非零斯托克斯数和密度比的麦克斯韦-赖利方程演化的惯性粒子轨迹确定的惯性 FTLE（iFTLE）。最后，我们探索了斯托克斯数的低通滤波效应。这些想法在非定常双涡旋流的二维数值模拟中得到了验证。
