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

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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.