We investigate the flow around a circular cylinder vibrating with a prescribed magnitude and frequency at Reynolds number 230. The Navier-stokes equations and the adjoint equations are solved to search for the 3-D nonlinear optimal initial perturbation, which is amplified by the attached shear via the Orr mechanism and then activates wake instabilities. The energy growth and the spanwise distributions of the nonlinear optimal perturbation vary significantly with the initial phase to introduce the perturbation. As the initial perturbation energy increases, linear amplification, nonlinear saturation and nonlinear growth are sequently observed. The last one is owing to the generation of a spanwise homogeneous mode, which modifies the pressure distributions on the cylinder surface and induces an extra lift force. Interestingly, at all the initial phases, this force is opposite to the acceleration of the cylinder, illustrating the potential to reduce the magnitude of vibration.

我们研究了在雷诺数 230 处以规定的幅度和频率振动的圆柱体周围的流动。求解 Navier-stokes 方程和伴随方程以寻找 3-D 非线性最优初始扰动，该扰动被附加剪切放大通过 Orr 机制，然后激活唤醒不稳定性。非线性最优扰动的能量增长和展向分布随着引入扰动的初始阶段而显着变化。随着初始扰动能量的增加，依次观察到线性放大、非线性饱和和非线性增长。最后一个是由于展向均匀模式的产生，它改变了圆柱表面上的压力分布并产生了额外的升力。有趣的是，