Alvaro Meseguer

Linearized pipe flow to Reynolds number 10 7

A Fourier-Chebyshev Petro-Galerkin spectral method is described for high-accuracy computation of linearized dynamics for flow in an infinite circular pipe. Our code is unusual in being based on solenoidal velocity variables and in being written in MATLAB. Systematic studies are presented of the dependence of eigenvalues, transient growth factors, and other quantities on the axial and azimuthal wave numbers and the Reynolds number R for R ranging from 102 to the idealized (physically unrealizable) value 107. Implications for transition to turbulence are considered in the light of recent theoretical results of S.J. Chapman.

Streak breakdown instability in pipe Poiseuille flow

This work is devoted to the study of the stability of Hagen–Poiseuille flow or pipe flow. The analysis is focused on the streak breakdown process by which two-dimensional streamwise-independent finite amplitude perturbations transiently modulate the basic flow leading to a profile that contains saddle points and is linearly unstable with respect to very small streamwise-dependent perturbations. This mechanism is one possible route of transition to turbulence in subcritical shear flows. The exploration is carried out for initial disturbances of different finite amplitudes and axial and azimuthal periodicity. This study covers a wide range of Reynolds numbers and the double threshold curve obtained for transition is consistent with experimental observations.

Energy transient growth in the Taylor–Couette problem

This work is devoted to the study of transient growth of perturbations in the Taylor-Couette problem due to nonnormal mechanisms. The study is carried out for a particular small gap case and is mostly focused on the linearly stable regime of counter-rotation. The exploration covers a wide range of inner and outer angular speeds as well as axial and azimuthal modes. Clear evidence of transient growth is found as long as the counter-rotation is increased. The numerical results are in agreement with former analyses based on energy methods. Similarities with transient growth mechanisms in plane Couette flow and in Hagen-Poiseuille flow are found. This is reflected in the modulation of the basic circular Couette flow by the presence of azimuthal streaks as a result of the nonmodal growth of initial axisymmetric perturbations. This study might shed some light on the subcritical transition to turbulence which is found experimentally in Taylor-Couette flow when the cylinders rotate in opposite directions. This work was supported by UK Engineering and Physical Sciences Research Council Grant GR/M30890.

Stability control and catastrophic transition in a forced Taylor-Couette system

Harmonic axial motion of the inner cylinder in the Taylor–Couette system can efficiently shift the onset of instability to larger inner cylinder rotation rates. However, once instability has set in, a rapid sequence of symmetry-breaking bifurcations results in complex spatio-temporal dynamics even for very low post-critical values of the rotation rate. Using spectral computations, we present a detailed study of this sudden transition, shedding light on the nature of the complex flows observed in recent laboratory experiments. In particular, it is shown that these bifurcations are responsible for some of the experimentally observed frequencies which had been attributed to background noise. Movies are available with the online version of the paper.

Pipe flow transition threshold following localized impulsive perturbations

A numerical study of the destabilizing effects of localized impulsive perturbations in pressure-driven Hagen-Poiseuille or pipe flow is presented. The numerics intend to ellucidate the intrinsic mechanisms of subcritical transition to turbulence in pipe flow by reproducing very recent experimental explorations carried out by Hof, Juel, and Mullin [Phys. Rev. Lett. 91, 244502 (2003)], concluding that the minimum amplitude of a perturbation required to cause transition scales as the inverse of the Reynolds number, i.e., O(Re−1). The numerical model simulates the experimental disturbance generator based on impulsive injection of fluid through six slits azimuthally equispaced on a perimeter around the pipe. This is accomplished by introducing a local time-dependent impulsive volume force term in the Navier-Stokes equations for the perturbation velocity field, fulfilling incompressibility constraints. A comprehensive exploration of the critical amplitudes that trigger transition as a function of the injection ...

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. For , the present work provides critical amplitudes that decay as Re−3/2 and Re−1 for the autonomous and impulsive scenarios, respectively. For Re=2875, accurate threshold amplitudes are found for constant mass-flux pipe by means of a shooting method that provides critical trajectories that never relaminarize or trigger transition. These transient states are used as initial guesses in a damped Newton–Krylov method formulated to find periodic travelling wave solutions that either travel downstream or exhibit a helicoidal advection.

The role of streamwise perturbations in pipe flow transition

The phenomenon of subcritical transition in Hagen-Poiseuille or pipe flow is explored for a wide range of Reynolds numbers within the interval Re∊[2.5×103,1.26×104] by means of a computational method that numerically resolves the transitional dynamics with nearly 3.5×104 degrees of freedom on a medium aspect-ratio domain of length 32π∕5. The aim of this exploration is to provide a theoretical characterization of the basin of attraction of the basic regime by measuring the minimal amplitude of an initial global perturbation leading to transition. The analysis is based on a particular theoretical scenario that considers streamwise-independent finite amplitude initial vortical perturbations that trigger global transition via optimal inflectional instabilities of streamwise-dependent modes with selected axial wave numbers. Disturbances consisting of 1, 2, and 3 pairs of vortices are investigated. Special attention is given to relaminarization phenomena that is frequently observed for low Reynolds numbers. Lon...

Double Hopf bifurcation in corotating spiral Poiseuille flow

Nonlinear dynamics of the spiral Poiseuille problem for moderate axial through flow is investigated numerically within the corotating regime for medium gap geometry. The neighborhood of a double Hopf bifurcation point of the linear stability boundary, where spiral waves of opposite axial phase propagation compete, is explored by accurately solving time-dependent Navier-Stokes equations with a solenoidal spectral method. The mode interaction generates a quasiperiodic stable regime of interpenetrating spirals, which coexists with stable limit cycles associated with the aforementioned spiral waves of opposite helicoidal orientation. The spatiotemporal properties of the computed solutions are explained and discussed in terms of equivariant bifurcation and normal form theories. Similar flows have also been observed experimentally in the past within the corotating region.

Bifurcations with imperfect SO(2) symmetry and pinning of rotating waves

Rotating waves are periodic solutions in SO(2) equivariant dynamical systems. Their precession frequency changes with parameters and it may change sign, passing through zero. When this happens, the dynamical system is very sensitive to imperfections that break the SO(2) symmetry and the waves may become trapped by the imperfections, resulting in steady solutions that exist in a finite region in parameter space. This is the so-called pinning phenomenon. In this study, we analyse the breaking of the SO(2) symmetry in a dynamical system close to a Hopf bifurcation whose frequency changes sign along a curve in parameter space. The problem is very complex, as it involves the complete unfolding of high codimension. A detailed analysis of different types of imperfections indicates that a pinning region surrounded by infinite-period bifurcation curves appears in all cases. Complex bifurcational processes, strongly dependent on the specifics of the symmetry breaking, appear very close to the intersection of the Hopf bifurcation and the pinning region. Scaling laws of the pinning region width and partial breaking of SO(2) to Zm are also considered. Previous as well as new experimental and numerical studies of pinned rotating waves are reviewed in the light of the new theoretical results.

On the stability of medium gap corotating spiral Poiseuille flow

New features of the linear stability of the spiral Poiseuille flow for a wide range of inner and outer independent rotation speeds of the cylinders and imposed axial pressure gradient are investigated. The analysis is focused on the corotating situation and for a particular radius ratio η=0.5. Unexpected changes in the angle of the bifurcated spiral regimes are found for moderate values of the axial speed as the outer rotation is increased. In particular, tricritical points are detected, where modes associated with azimuthal wave numbers of opposite signs coexist at criticality. The present study is extended to high values of the axial speed of the flow and, to the authors’ knowledge, the complete critical surface in the three-dimensional parameter space is obtained for the first time, providing new results on the behavior of the Tollmien-Schlichting instability. Increasing the rotation rate of the outer cylinder, the Tollmien-Schlichting instability is no longer dominant, resulting in a dramatic decrease...