Dimensional reduction is applied to derive a one-dimensional energy functional governing tensile necking localization in a family of initially uniform prismatic solids, including as particular cases rectilinear blocks in plane strain and cylindrical bars undergoing axisymmetric deformations. The energy functional depends on both the axial stretch and its gradient. The coefficient of the gradien...

We examine the bifurcation of a reflected shock in a three-dimensional, square channel through numerical simulations using a distributed memory parallel adaptive mesh refinement, Navier-Stokes solver with multicomponent equation of state and microscopic transport. The three-dimensional, rather than axisymmetric, geometry introduces considerable complexity into the flow structures, particularly ...

We report experimental and numerical results from investigations into the onset of novel localized cellular states in the centrifugally stable regime of Taylor–Couette flow at sufficiently high rates of counter-rotation of the outer cylinder. Quantitative comparison is made between experimental results and those obtained from numerical bifurcation studies of the steady axisymmetric Navier– Stok...

A straight tube with a smooth axisymmetric constriction is an idealised representation of a stenosed artery. We examine the three-dimensional instability of steady flow plus an oscillatory component in a tube with a smooth 75% stenosis using both linear stability analysis and direct numerical simulation. These flows become unstable through a subcritical period-doubling bifurcation involving alt...

Elliptical galaxies are modelled as homeoidally striated Jacobi ellipsoids (Caimmi & Marmo 2005) where the peculiar velocity distribution is anisotropic, or equivalently as their adjoints configurations i.e. classical Jacobi ellipsoids of equal mass and axes, in real or imaginary rotation (Caimmi 2006). Reasons for the coincidence of bifurcation points from axisymmetric to triaxial configuratio...

We study local instabilities of a differentially rotating viscous flow of electrically conducting incompressible fluid subject to an external azimuthal magnetic field. In the presence of the magnetic field, the hydrodynamically stable flow can demonstrate non-axisymmetric azimuthal magnetorotational instability (AMRI) both in the diffusionless case and in the double-diffusive case with viscous ...

This paper examines the manner in which heat release resulting from premixed combustion alters the nature of near-critical, axisymmetric, swirling flow in a straight circular pipe. Attention is confined to dilute premixtures so that exothermicity is weak and a small-disturbance approach applicable. The weak exothermicity is found to have a considerably larger effect on the flow. In the absence ...

Weconsider themanner inwhich time-periodic solutions of an axisymmetric dynamo model can undergo breaking of equatorial symmetry, i.e. loss of pure dipolar or quadrupolar symmetry. By considering the symmetry group underlying the solutions, we show that the fluctuations responsible for the symmetry-breaking can be constrained such that they are in resonance with the former solution. They can th...

We explore experimentally whether axisymmetry breaking can be exploited for the open-loop control of a prototypical hydrodynamic oscillator, namely low-density inertial jet exhibiting global self-excited axisymmetric oscillations. find that when forced transversely or axially at low amplitude, always transitions first from period-1 limit cycle to $\mathbb {T}^2$ quasiperiodicity via Neimark–Sac...