This work studies the dynamics of linear non-modal waves in viscoelastic pipe flows of FENE-P fluids using transient growth and resolvent analyses. We particularly focus on the time evolution of the amplification of the disturbance energy (using the 4th-order Runge–Kutta method) and discuss the dynamical traits of the Orr and the critical-layer mechanisms in the conformation tensor field when the transient energy increases. The helical mode undergoes a larger energy growth than the axisymmetric mode. The effects of various flow parameters have been investigated on the growth rate and energy amplification of the non-modal waves and the optimal flow structures. It is found that when the elastic effect is stronger, the amplitude of the optimal conformation tensor in the pipe centre region becomes greater from a non-modal perspective.

这项工作使用瞬态增长和解析分析来研究 FENE-P 流体粘弹性管流中线性非模态波的动力学。我们特别关注扰动能量放大的时间演化（使用四阶 Runge-Kutta 方法），并讨论了当瞬态能量增加时 Orr 的动力学特征和构象张量场中的临界层机制。螺旋模式比轴对称模式经历更大的能量增长。研究了各种流动参数对非模态波的增长速率和能量放大以及最佳流动结构的影响。从非模态的角度发现，当弹性效应越强时，管道中心区域最优构象张量的幅值越大。