Stochastic Reductions for Inertial Fluid-Structure Interactions Subject to Thermal Fluctuations

We investigate the dynamics of elastic microstructures that interact with a fluid flow when subject to thermal fluctuations. We perform analysis to obtain systematically simplified descriptions of the mechanics in the limiting regimes when (i) the coupling forces that transfer momentum between the fluid and microstructures is strong, (ii) the mass of the microstructures is small relative to the displaced mass of the fluid, and (iii) the response to stresses results in hydrodynamics that relax rapidly to a quasi-steady-state relative to the motions of the microstructure. We derive effective equations using a singular perturbation analysis of the Backward Kolmogorov equations of the stochastic process. Our continuum mechanics description is based on the Stochastic Eulerian Lagrangian Method (SELM) which provides a framework for approximation of the fluid-structure interactions when subject to thermal fluctuations. We perform a dimension analysis of the SELM equations to identify key non-dimensional groups and to characterize precisely each of the limiting physical regimes. The reduced equations offer insights into the physical accuracy of SELM descriptions in comparison with classical results. The reduced equations also elimintate rapid time-scales from the dynamics and provide possible approaches for the development of more efficient computational methods for simulations of fluid-structure interactions when subject to thermal fluctuations.