Nick Moore
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SPECIAL MATHEMATICS COLLOQUIUM
Speaker: Nick Moore Abstract Models that combine analytical and numerical techniques can reap the benefits of both, and I will discuss the use of such models in the context of two fluid-structure problems. First, inspired by natural examples such as landform evolution, I will discuss the erosion of solid bodies by flowing fluids. Table-top experiments of soft-clay bodies eroding in flowing water show the formation of sharp corners and facets, contrary to the conventional view of erosion as a smoothing process. We develop a model in which an outer flow couples to a boundary layer flow that shears away solid material. This model allows us to rationalize the experimental measurements and extend our understanding of the process. Ultimately, we find that the body converges to a terminal form characterized by nearly uniform shear stress, which, once developed, shrinks self-similarly in time. Second, I will discuss the motion of bodies through viscoelastic fluids. These fluids store and release elastic energy, leading to characteristically unsteady behavior. As an example, a body settling under gravity experiences an overshoot, in which its descent rate temporarily exceeds terminal velocity. We develop a hybrid analytical/numerical method that accurately captures unsteady behavior such as the velocity overshoot, and, unlike many traditional methods, allows efficient and stable computations when the viscoelastic relaxation timescale is long. I will discuss potential applications of the method to more complicated settings, such as many-body interactions and micro-to-macro viscoelastic models. |