Hydrodynamic Bifurcation Research Articles

Hydrodynamic bifurcation in electro-osmotically driven periodic flows

In this paper we report a novel inertial instability that occurs in electro-osmotically driven channel flows. We assume that the charge motion under the influence of an externally applied electric field is confined to a small vicinity of the channel walls that, effectively, drives a bulk flow through a prescribed slip velocity at the boundaries. Here, we study spatially-periodic wall velocity modulations in a two-dimensional straight channel numerically. At low slip velocities, the bulk flow consists of a set of vortices along each wall that are left-right symmetric, while at sufficiently high slip velocities, this flow loses its stability though a supercritical bifurcation. Surprisingly, the new flow state that bifurcates from a left-right symmetric base flow has a rather strong mean component along the channel, which is similar to pressure-driven velocity profiles. The instability sets in at rather small Reynolds numbers of about 20-30, and we discuss its potential applications in microfluidic devices.

Angles in normal placental chorionic surface vessel networks follow hydrodynamic bifurcation rules

Angles in normal placental chorionic surface vessel networks follow hydrodynamic bifurcation rules

Emergence of upstream swimming via a hydrodynamic transition.

We demonstrate that upstream swimming of sperm emerges via an orientation disorder-order transition. The order parameter, the average orientation of the sperm head against the flow, follows a 0.5 power law with the deviation from the critical flow shear rate (γ-γ_{c}). This transition is successfully explained by a hydrodynamic bifurcation theory, which extends the sperm upstream swimming to a broad class of near surface microswimmers that possess front-back asymmetry and circular motion.

Cyclic nonlinear dynamo action in a finite Taylor Couette flow

We present calculations of dynamo action in a finite Taylor-Couette configuration. The first hydrodynamic bifurcation is an imperfect pitchfork bifurcation giving rise to Taylor vortices. This flow is used in kinematic dynamo computations showing a Hopf bifurcation towards a localized magnetic structure of typical length twice as long as the velocity typical length. Using Taylor vortices and the magnetic eigenvector obtained from the kinematic regime, the nonlinear dynamo shows a striking cyclic behaviour where the symmetries with respect to the median plane play a major role.

The rational Krylov algorithm for nonsymmetric eigenvalue problems. III: Complex shifts for real matrices

A new algorithm for the computation of eigenvalues of a nonsymmetric matrix pencil is described. It is a generalization of the shifted and inverted Lanczos (or Arnoldi) algorithm, in which several shifts are used in one run. It computes an orthogonal basis and a small Hessenberg pencil. The eigensolution of the Hessenberg pencil, gives Ritz approximations to the solution of the original pencil. It is shown how complex shifts can be used to compute a real block Hessenberg pencil to a real matrix pair. Two applicationx, one coming from an aircraft stability problem and the other from a hydrodynamic bifurcation, have been tested and results are reported.