Instability in pipe flow.

The long-puzzling, unphysical result that linear stability analyses lead to no transition in pipe flow, even at infinite Reynolds number, is ascribed to the use of stick boundary conditions, because they ignore the amplitude variations associated with the roughness of the wall. Once that length scale is introduced (here, crudely, through a corrugated pipe), linear stability analyses lead to stable vortex formation at low Reynolds number above a finite amplitude of the corrugation and unsteady flow at a higher Reynolds number, where indications are that the vortex dislodges. Remarkably, extrapolation to infinite Reynolds number of both of these transitions leads to a finite and nearly identical value of the amplitude, implying that below this amplitude, the vortex cannot form because the wall is too smooth and, hence, stick boundary results prevail.

Convective Instabilities in Two Liquid Layers.

We perform linear stability calculations for horizontal fluid bilayers, taking into account both buoyancy effects and thermocapillary effects in the presence of a vertical temperature gradient. To help understand the mechanisms driving the instability, we have performed both long-wavelength and short-wavelength analyses. The mechanism for the large wavelength instability is complicated, and the detailed form of the expansion is found to depend on the Crispation and Bond numbers.

Flow Control Through the Use of Topography.

In this work, optimal shaft shapes for flow in the annular space between a rotating shaft with axially-periodic radius and a fixed coaxial outer circular cylinder, are investigated. Axisymmetric steady flows in this geometry are determined by solving the full Navier-Stokes equations in the actual domain. A measure of the flow field, a weighted convex combination of the volume averaged square of the L 2-norm of the velocity and vorticity vectors, is employed.