涡环稳定性一直是学者们普遍关心的话题，涡环作为流动中普遍存在的一种现象，不但广泛存在于自然界，且与人类活动息息相关。本项目拟从瞬态稳定性分析出发结合三维直接数值模拟、水动力学实验，研究涡环在有限扰动下的失稳与转捩等物理机制，并与仿生水母射流涡环的三维结构相结合，寻找其中的内在关联。具体研究包括两部分：一是自由射流涡环在最优扰动下的瞬态稳定性研究，重点关注在有限扰动下涡环的周向失稳、断裂，重连等机制；第二部分是水母推进中的三维流场结构的研究，重点对比不同形态及运动方式水母的涡环周向失稳特性，例如对比扁平水母与细长水母、柔性缘膜与刚性缘膜、连续缘膜与分段缘膜等，并总结几何、运动特征对水母涡环周向失稳的影响规律，以及周向失稳对水母推进性能的影响，为进一步优化仿生水母的设计提供理论支撑。本项目拟提出的涡环周向失稳的控制方法，也可一定程度上帮助解释目前工程上应用的射流混合增强、降噪等装置的物理机制。

Vortex rings are canonical structures in fluid mechanics, due to their broad appearance in the natural world, ranging from volcanic eruptions to the propulsion of jellyfish and other aquatic creatures. They also have wide engineering applications, for example, in underwater drilling, combustion, and artificial olfaction. Consideration of instability and turbulent transition of vortex rings is an active area of research, not least because vortex rings, due to the inherent symmetry of their characteristic state, allow the controlled investigation of the relative importance of vorticity distribution, intensity, and flow curvature in the onset of instability. . In this proposed project, by using stability analysis methods, three-dimensional direct numerical simulations, and hydrodynamic experiments, we aim to understand the underlying physical mechanisms of the instabilities and laminar-turbulence transition of vortex rings, particularly with finite-amplitude perturbations. We note that the perturbations are introduced by either the optimal perturbation field, which is calculated by transient growth analysis, or in the experiments, by placing a small-scale obstacle on the route of vortex ring travelling. Moreover, as the most significant innovation of this project, we will discover the relevance of transient instabilities of vortex rings to the biomimetic jet propulsion such as that of a jellyfish. The main content includes two parts: first, the study of development of perturbations on free jet vortex rings via transient growth analysis, direction numerical simulations, and hydrodynamic experiments. We focus on the symmetry breaking process characterized by the onset of azimuthal wavy structures, breakup, generation and reconnection of the vortex rings. Second, we will attempt to correlate the vortex ring instabilities with the three-dimensional flow structures in the wake of a jellyfish, and concentrate on the comparison between the jellyfishes with different morphologies and kinetic parameters in the transient instability behaviors. For example, we will compare the prolate and the oblate jellyfishes, flexible and rigid bell margins, continuous and segmented bell margins. We will study how the morphology and kinetics affect the instability of vortex rings produced by jellyfish, as well as the consequent influence on the propulsion performance. . The output of this project will help us understand the three-dimensional flow structures in the wake of a biomimetic jellyfish and improve the performance of current robotic jellyfish. Moreover, it can also help understand the underlying physical mechanisms of the control strategies for mixing enhancement and noise reduction in coaxial jets.