Inviscid Simulations of Interacting Flags and Falling Sheets

We present a fluid dynamics video showing simulations of flexible bodies flapping and falling in an inviscid fluid. Vortex sheets are shed from the trailing edges of the bodies according to the Kutta condition. For interacting flags, a sampling of synchronous and asynchronous states are shown. For falling flexible sheets, the basic behavior is a repeated series of accelerations to a critical speed at which the sheet buckles, and rapidly decelerates, shedding large vortices. Examples of persistent circling, quasi-periodic flapping, and more complex trajectories are shown.Comment: APS DFD Gallery of Fluid Motion 200

Transition to branching flows in optimal planar convection

We study steady flows that are optimal for heat transfer in a two-dimensional periodic domain. The flows maximize heat transfer under the constraints of incompressibility and a given energy budget (i.e. mean viscous power dissipation). Using an unconstrained optimization approach, we compute optima starting from 30--50 random initializations across several decades of Pe, the energy budget parameter. At Pe between 10$^{4.5}$ and 10$^{4.75}$, convective rolls with U-shaped branching near the walls emerge. They exceed the heat transfer of the simple convective roll optimum at Pe between 10$^{5}$ and 10$^{5.25}$. At larger Pe, multiple layers of branching occur in the optima, and become increasingly elongated and asymmetrical. Compared to the simple convective roll, the branching flows have lower maximum speeds and thinner boundary layers, but nearly the same maximum power density.Comment: 18 pages, 10 figure