We introduce fluctuating hydrodynamics approaches on surfaces for capturing the drift-diffusion dynamics of particles and microstructures immersed within curved fluid interfaces of spherical shape. We take into account the interfacial hydrodynamic coupling, traction coupling with the surrounding bulk fluid, and thermal fluctuations. For fluid-structure interactions, we introduce Immersed Boundary Methods (IBM) and related Stochastic Eulerian-Lagrangian Methods (SELM) for curved surfaces. We use these approaches to investigate the statistics of surface fluctuating hydrodynamics and microstructures. For velocity autocorrelations, we find characteristic power-law scalings $\tau^{-1}$, $\tau^{-2}$, and plateaus can emerge. This depends on the physical regime associated with the geometry, surface viscosity, and bulk viscosity. This differs from the characteristic $\tau^{-3/2}$ scaling for bulk three dimensional fluids. We develop theory explaining these observed power-laws associated with time-scales for dissipation within the fluid interface and coupling to the surrounding fluid. We then use our introduced methods to investigate a few example systems and roles of hydrodynamic coupling and thermal fluctuations including for the kinetics of passive particles and active microswimmers in curved fluid interfaces.

翻译：本文引入了曲面上的波动流体动力学方法，用于捕捉浸没在球形弯曲流体界面中的粒子与微结构漂移-扩散动力学。我们考虑了界面水动力学耦合、与周围体相流体的牵引耦合以及热涨落效应。针对流固相互作用，我们提出了适用于曲面的浸入边界方法(IBM)及相关随机欧拉-拉格朗日方法(SELM)。利用这些方法，我们研究了曲面波动流体动力学与微结构的统计特性。在速度自相关函数中，我们发现了特征幂律标度$\tau^{-1}$、$\tau^{-2}$及平台区，其出现取决于与几何形状、表面黏度和体相黏度相关的物理区段。这与三维体相流体的特征$\tau^{-3/2}$标度截然不同。我们建立了理论框架，从流体界面内耗散时间尺度及与周围流体耦合的角度解释了这些观测到的幂律行为。最后，我们运用所提出的方法研究了若干实例系统，包括被动粒子与活性微泳者在弯曲流体界面中的动力学行为，以及水动力学耦合与热涨落所起的作用。