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Parametric instability of the interface between two fluids
The flat interface between two fluids in a vertically vibrating vessel may be parametrically excited, leading to the generation of standing waves. The equations constituting the stability problem forExpand
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Bifurcation Analysis for Timesteppers
A collection of methods is presented to adapt a pre-existing timestepping code to perform various bifurcation-theoretic tasks. It is shown that the implicit linear step of a time-stepping code canExpand
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Krylov methods for the incompressible Navier-Stokes equations
Methods are presented for time evolution, steady-state solving and linear stability analysis for the incompressible Navier-Stokes equations at low to moderate Reynolds numbers. The methods use KrylovExpand
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Order within chaos : towards a deterministic approach to turbulence
Free Oscillator - Damped Oscillator Forced Oscillator - Parametric Oscillator The Fourier Transform Poincare Sections Three Examples of Dynamical Systems To Chaos: Temporal Chaos in DissipativeExpand
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Asymmetry and Hopf bifurcation in spherical Couette flow
Spherical Couette flow is studied with a view to elucidating the transitions between various axisymmetric steady‐state flow configurations. A stable, equatorially asymmetric state discovered byExpand
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Mean flow of turbulent-laminar patterns in plane Couette flow
A turbulent–laminar banded pattern in plane Couette flow is studied numerically. This pattern is statistically steady, is oriented obliquely to the streamwise direction, and has a very largeExpand
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Computational study of turbulent laminar patterns in couette flow.
Turbulent-laminar patterns near transition are simulated in plane Couette flow using an extension of the minimal-flow-unit methodology. Computational domains are of minimal size in two directions butExpand
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Numerical Bifurcation Methods and their Application to Fluid Dynamics: Analysis beyond Simulation
We provide an overview of current techniques and typical applications of numerical bifurcation analysis in fluid dynamical problems. Many of these problems are characterized by high-dimensionalExpand
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The 1[ratio ]2 mode interaction in exactly counter-rotating von Kármán swirling flow
The flow produced in an enclosed cylinder of height-to-radius ratio of two by the counter-rotation of the top and bottom disks is numerically investigated. When the Reynolds number based on cylinderExpand
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Survey of instability thresholds of flow between exactly counter-rotating disks
The three-dimensional linear instability of axisymmetric flow between exactly counter-rotating disks is studied numerically. The dynamics are governed by two parameters, the Reynolds number Re basedExpand
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