Orr mechanism in transition of parallel shear flow

Shear-Flow Transition: the Basin Boundary

The basin of attraction of a stable equilibrium point is investigated for a dynamical system (W97) that has been used to model transition to turbulence in shear flows. The basin boundary contains a linearly unstable equilibrium point Xlb which, in the self-sustaining scenario, plays a role in mediating the transition in that transition orbits cluster around its unstable manifold. However we fin...

An eigenvalue search method using the Orr-Sommerfeld equation for shear flow

A physically-based computational technique was investigated which is intended to estimate an initial guess for complex values of the wavenumber of a disturbance leading to the solution of the fourth-order Orr-Sommerfeld (O-S) equation. The complex wavenumbers, or eigenvalues, were associated with the stability characteristics of a semi-infinite shear flow represented by a hyperbolic-tangent fun...

Yieldlike constitutive transition in shear flow of entangled polymeric fluids.

We describe an unexpected constitutive transition in entangled polymer solutions. At and beyond a critical stress, the initial spatially homogeneous and well-entangled sample transforms from its entangled (coiled) state into a fully disentangled (stretched) state over a period during which the resulting shear rate increases in a spatially inhomogeneous fashion. In the mode of controlled shear r...

A Computational Study of Transition to Turbulence in Shear Flow

Boundary collapse in models of shear-flow transition

We explore two low-dimensional dynamical systems modeling transition to turbulence in shear flows to try to understand the nature of the boundary ∂B of the basin of attraction B of the stable, laminar point at the origin of coordinates. Components of ∂B are found to exist in two types: one (the ’strong’ type) separating B from a complementary set where orbits never relaminarize, and a second (t...