Extensional channel flow revisited: a dynamical systems perspective.

Extensional self-similar flows in a channel are explored numerically for arbitrary stretching-shrinking rates of the confining parallel walls. The present analysis embraces time integrations, and continuations of steady and periodic solutions unfolded in the parameter space. Previous studies focused on the analysis of branches of steady solutions for particular stretching-shrinking rates, although recent studies focused also on the dynamical aspects of the problems.

Subcritical equilibria in Taylor-Couette flow.

Nonlinear equilibrium states characterized by strongly localized vortex pairs are calculated in the linearly stable parameter region of counterrotating Taylor-Couette flow. These subcritical states are rotating waves whose region of existence is consistent with the critical threshold for relaminarization observed in experiments. For sufficiently rapid outer cylinder rotation the solutions extend beyond the static inner cylinder case to corotation, thus exceeding, for the first time, the boundary defined by the inviscid Rayleigh's stability criterion.

Instability mechanisms and transition scenarios of spiral turbulence in Taylor-Couette flow.

Alternating laminar and turbulent helical bands appearing in shear flows between counterrotating cylinders are accurately computed and the near-wall instability phenomena responsible for their generation identified. The computations show that this intermittent regime can only exist within large domains and that its spiral coherence is not dictated by endwall boundary conditions. A supercritical transition route, consisting of a progressive helical alignment of localized turbulent spots, is carefully studied.

Transition in localized pipe flow turbulence.

Direct numerical simulation of transitional pipe flow is carried out in a long computational domain in order to characterize the dynamics within the saddle region of phase space that separates laminar flow from turbulent intermittency. For Reynolds numbers ranging from Re=1800 to 2800, a shoot and bisection method is used to compute critical trajectories. The chaotic saddle or edge state approached by these trajectories is studied in detail.

Families of subcritical spirals in highly counter-rotating Taylor-Couette flow.

A comprehensive numerical exploration of secondary finite-amplitude solutions in small-gap Taylor-Couette flow for high counter-rotating Reynolds numbers is provided, using Newton-Krylov methods embedded within arclength continuation schemes. Two different families of rotating waves have been identified: short axial wavelength subcritical spirals ascribed to centrifugal mechanisms and large axial scale supercritical spirals and ribbons associated with shear dynamics in the outer linearly stable radial region. This study is a first step taken in order to provide the inner structure of the skeleton of equilibria that may be responsible for the intermittent regime usually termed as spiral turbulence that has been reported by many experimentalists in the past.

Critical threshold in pipe flow transition.

This study provides a numerical characterization of the basin of attraction of the laminar Hagen-Poiseuille flow by measuring the minimal amplitude of a perturbation required to trigger transition. For pressure-driven pipe flow, the analysis presented here covers autonomous and impulsive scenarios where either the flow is perturbed with an initial disturbance with a well-defined norm or perturbed by means of local impulsive forcing that mimics injections through the pipe wall. In both the cases, the exploration is carried out for a wide range of Reynolds numbers by means of a computational method that numerically resolves the transitional dynamics.

Complex dynamical states in binary mixture convection with weak negative Soret coupling.

Binary convection in large-aspect-ratio annular containers heated from below is studied numerically for a water-ethanol mixture. High-resolution numerical tools based on spectral methods are used to solve the hydrodynamic equations in the two-dimensional approximation. The weakly nonlinear states arising very close to the onset of convection, the strongly nonlinear bursts of amplitude that precede the small-amplitude states, and the dispersive chaotic states encountered further above onset in experiments for mixtures with a weak negative Soret coupling are analyzed in detail in extended domains of aspect ratio 80.