Abstract

1: Controlling vortex shedding using spanwise-varying passive or active actuation (namely three-dimensional control) has recently been reported as a very efficient method for regulating two-dimensional bluff-body wakes. However, the mechanism of how the designed controller regulates vortex shedding is not clearly understood. To understand this mechanism, we study a linear stability analysis of two-dimensional wakes, the base flow of which is modified with a given spanwise waviness. Floquet theory for determining absolute instability in spatially periodic flows is first introduced, and we show that the spanwise wavy base-flow modification stabilizes the absolute instability of two-dimensional parallel wakes. The physical mechanism of the stabilization is explained in terms of vortex dynamics. Finally, the sensitivity of absolute instability to spanwise wavy base-flow modification is investigated, showing that absolute instability of two-dimensional wakes is much less sensitive to spanwise wavy base-flow modification than to two-dimensional modification.

2: Hydrodynamic focusing of cells is a robust feature in downflowing suspensions of swimming gyrotatic microorganisms. In the early experiments with a downward pipe flow, Kessler (1986, J. Fluid Mech, 173:191-205) observed that the focused beam-like structure of cells in the region of most rapid downflow exhibits regular-spaced axisymmetric blips, but the mechanism by which the blips are formed has not been well understood yet. For this purpose, we perform a linear stability analysis of a downflowing suspension of randomly swimming gyrotactic cells in a two-dimensional vertical channel. For relatively small flow rates, the focused beam in the channel exhibits a varicose instability strikingly similar to the blips in the pipe flow, and this becomes gradually damped out as the flow rate increases. It is found that the varicose instability essentially originates from the interaction of cell-concentration fluctuations with the horizontal gradient of the cell-orientation vector field, which does not appear in uniform suspensions. A comparison is finally made with recent experimental results by Croze & Bees (2013, In preparation), showing qualitatively good agreement.