Colloquium: In the Blink of An Eye

In the Blink of An Eye:
Dynamics of the Rapid Creation and Collapse of Dry Spot Regions in Fluid Layers

Dr. Dylan Odessa, Wake Forest University

Thursday, September 21 – 11:00AM
Location: 016 Manchester Hall

When the free surface of a fluid under gravity creates a dry spot by intersecting a confining bottom boundary, the evolution of the fluid system and the subsequent collapse of the dry spot pose many fundamental questions, from both mathematical and physical viewpoints. Models of the dynamics of this phenomenon can be valuable in isolating relevant mechanisms governing the collapse. This talk will present results from applying such simplified models to the above setup, and show their effectiveness, and limitations, by comparing model predictions with results from experimental data from dry spot collapse. In particular, we present a novel way to overcome the experimental challenge of creating a dry-spot cavity without generating significant initial velocity in the bulk of the fluid. We then will expand the simplified parabola-shape analysis of a dry spot and expand it to include higher order even polynomials in both one and two spatial dimensions. We refine techniques for evolving the solution through careful analysis of hyperbolic features such as characteristics. The solutions we examine develop a shock in the derivative at finite time that leads to the filling of an otherwise persistent dry spot.