Howard A. Stone
Division of Engineering and Applied Sciences
Harvard University
Some new results related to two contributions of G.I. Taylor: (i) swimming micro-organisms and (ii) hydrodynamic dispersion
What can a fluid dynamicist communicate to an audience in a Control and Dynamical Systems Seminar? Two themes suggest themselves owing to the generic structure of the mathematical/physical problems. The first concerns the manner in which small swimmers may deform themselves in order to achieve motion in a viscous fluid (low Reynolds number hydrodynamics). Here we investigate the possible utility of swimming using traveling waves tangent to the surface of a spherically shaped micro-organism. Second, convective-diffusion equations are familiar and have many common applications. Frequently, the average description of these problems leads again to a convective-diffusion equation in which the velocity gradients contribute to a constant effective dispersion coefficient. We outline two model problems that require spatially dependent dispersivities.