Bruce Rodenborn

Harmonic generation by reflecting internal waves

The generation of internal gravity waves by tidal flow over topography is an important oceanic process that redistributes tidal energy in the ocean. Internal waves reflect from boundaries, creating harmonics and mixing. We use laboratory experiments and two-dimensional numerical simulations of the Navier–Stokes equations to determine the value of the topographic slope that gives the most intense generation of second harmonic waves in the reflection process. The results from our experiments and simulations agree well but differ markedly from theoretical predictions by S. A. Thorpe [“On the reflection of a train of finite amplitude waves from a uniform slope,” J. Fluid Mech. 178, 279 (1987)] and A. Tabaei et al. [“Nonlinear effects in reflecting and colliding internal wave beams,” J. Fluid Mech. 526, 217 (2005)], except for nearly inviscid, weakly nonlinear flow. However, even for weakly nonlinear flow (where the Dauxois–Young amplitude parameter value is only 0.01), we find that the ratio of the reflected ...

Propulsive matrix of a helical flagellum

We study the propulsion matrix of bacterial flagella numerically using slender body theory and the regularized Stokeslet method in a biologically relevant parameter regime. All three independent elements of the matrix are measured by computing propulsive force and torque generated by a rotating flagellum, and the drag force on a translating flagellum. Numerical results are compared with the predictions of resistive force theory, which is often used to interpret micro-organism propulsion. Neglecting hydrodynamic interactions between different parts of a flagellum in resistive force theory leads to both qualitative and quantitative discrepancies between the theoretical prediction of resistive force theory and the numerical results. We improve the original theory by empirically incorporating the effects of hydrodynamic interactions and propose new expressions for propulsive matrix elements that are accurate over the parameter regime explored.