Change in the nature and enhancement of Brownian motion in shear flows caused by the non-modal growth of thermal fluctuations

经典布朗运动表示由于在热运动中与周围流体分子碰撞而导致的静态流体中的小被动颗粒的随机运动。非均匀流的存在显著地改变了布朗运动的性质。理解和描述这种变化的本质是至关重要的，因为小的主动/被动粒子在非均匀流体流动中的运动越来越具有实际意义。自然，这导致了显着增加的兴趣，布朗运动的活性粒子在非均匀流动的不同研究社区在最近几年。然而，迄今为止所做的研究并没有涵盖流体流动的微妙之处对布朗运动的影响，对人造微/纳米机器甚至天然颗粒的设计。在这种情况下，深入了解非均匀流体流动对主动/被动布朗粒子运动的影响至关重要。在这个方向上迈出的第一步-研究剪切流中被动粒子的布朗运动（特别是热波动的非模态增长的影响）是该项目的目标。流体动力学稳定性社区在20世纪90年代揭示了非均匀/剪切流的非正常性质。非正态性的本质是：正则/谱数学分析算子的相应本征模是非正交的，在剪切流扰动的线性动力学研究中被证明是非最优的。这种情况引发了这些流动中线性过程的数学方法范式的变化，将焦点从长时间渐近分析转移到短时间行为的研究。结果，在剪切流中线性现象的理解和描述方面取得了突破。有人发现，由于剪切流的非常态诱导的线性现象，导致非常具体的代数/瞬态增长的扰动。在层流剪切流动中，流动的非正态性显著地影响流体分子的热运动，并最终改变静止流体的波动背景-使其各向异性和增强。 具体而言，形成的波动背景的速度场获得的规则性（空间相干性主要是在流向方向），而且，其强度显着超过流体分子的热速度在特定区域的波数空间。自然，这种新的各向异性和增强的流体速度场的波动背景显着影响布朗运动的性质和强度。我们的目标是通过对Langevin方程的重构，揭示和研究平面层流剪切流中被动粒子布朗运动的新特征。

Classical Brownian motion represents the random motion of small passive particles in a quiescent fluid due to collisions with the surrounding fluid molecules in thermal motion. The presence of an inhomogeneous flow significantly changes the character of Brownian motion. It is of fundamental importance to comprehend and describe the essence of this change since the motion of small active/passive particles in inhomogeneous fluid flows acquires more and more practical importance. This, naturally, led to a significant increase in interest to Brownian motion of active particles in inhomogeneous flows from the different research communities in recent years. Nevertheless, the research done to date does not cover the impact of fluid flow subtleties on Brownian motion on design of man-made micro/nanomachines and even of natural particles. In such cases, a thorough understanding of the influence of inhomogeneous fluid flow on the motion of active/passive Brownian particles is critical. To take the first step in this direction – to investigate the Brownian motion of passive particles in shear flows (specifically, the influence of non-modal growth of thermal fluctuations) is the aim of this project.The hydrodynamic stability community revealed the non-normal nature of inhomogeneous/shear flows in the 1990s. The essence of the non-normality is as follows: the corresponding eigenmodes of the operators of canonical/spectral mathematical analysis are non-orthogonal and turned out to be non-optimal in the study of the linear dynamics of perturbations in shear flows. This circumstance initiated the change of paradigm of the mathematical approach of linear processes in these flows, moving focus from the long-time asymptotic analysis to the study of short-time behavior. As a result, a breakthrough in the understanding and description of linear phenomena in shear flows was achieved. It was found that the linear phenomena induced due to the shear flow non-normality, lead to the very specific - algebraic/transient - growth of perturbations. In laminar shear flows, the flow non-normality significantly affects the thermal motion of fluid molecules and eventually modifies the fluctuation background of quiescent fluid -- makes it anisotropic and enhanced. Specifically, the velocity field of the formed fluctuation background acquires regularity (spatial coherence mostly in streamwise direction) and moreover, its strength significantly exceeds the thermal velocity of fluid molecules in specific area of wave number space. Naturally, this new - anisotropic and enhanced - fluctuating background of fluid velocity field significantly affects the nature and intensity of Brownian motion. Our targeted aim is to reveal and study the new character of Brownian motion of passive particles in laminar plane shear flow, by the reconstruction of Langevin equation due to the shear flow non-normality modified fluctuation background.