Mathematical Sciences Seminar
Wednesday, 11/28 at 3:30pm in RI-222

Speaker: Dr. Nick Moore, Applied Math Lab, Courant Institute, NYU

Title: Reduced-order modeling of fluid-structure interactions

Abstract:
Reduced-order models can lend unique insight into physical phenomena by stripping away all but the most essential principles.  I will discuss the use of reduced models in the context of two fluid-structure problems.  First, I will discuss motion in viscoelastic fluids.  These fluids store and release elastic energy, leading to motion that is characteristically unsteady.  A canonical example is the gravitational settling of body, in which terminal velocity is exceeded on a transient timescale.  We have recently developed a "weak-coupling" method that gives semi-analytical solutions to this classical problem and other more complicated problems.  I will discuss a biologically-inspired extension in which the body is propelled by an oscillating force, intended to mimic a swimming stroke.  Secondly, I will discuss the erosion of bodies by fluid flow.  Inspired by natural examples such as the formation of landforms, our study focuses on the mutual interaction between changing shape and flow.  Table-top experiments of soft-clay in flowing water reveal the formation of sharp corners and facets, contrary to the common notion that erosion tends to smooth bodies.  We appeal to a reduced flow-model that combines an outer flow with a boundary layer flow in order to rationalize these observations and make new predictions.