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# Pulse-train solutions of a spatially-heterogeneous amplitude equation arising in the subcritical instability of narrow-gap spherical Couette flow

### Citation

Blockley, EW and Bassom, AP and Gilbert, AD and Soward, AM, Pulse-train solutions of a spatially-heterogeneous amplitude equation arising in the subcritical instability of narrow-gap spherical Couette flow, Physica D - Nonlinear Phenomena, 228, (1) pp. 1-30. ISSN 0167-2789 (2007) [Refereed Article]

### Copyright Statement

Copyright 2007 Elsevier B.V.

DOI: doi:10.1016/j.physd.2007.01.005

### Abstract

We investigate some complex solutions a(x,t) of the heterogeneous complex-Ginzburg–Landau equation

in which the real driving coefficient λ(x) is either constant or the quadratic . This CGL equation arises in the weakly nonlinear theory of spherical Couette flow between two concentric spheres caused by rotating them both about a common axis with distinct angular velocities in the narrow gap (aspect ratio ε) limit. Roughly square Taylor vortices are confined near the equator, where their amplitude modulation a(x,t) varies with a suitably ‘stretched’ latitude x. The value of Υ_{ε}, which depends on sphere angular velocity ratio, generally tends to zero with ε. Though we report new solutions for Υ

_{ε}≠0, our main focus is the physically more interesting limit Υ

_{ε}=0.

When , uniformly bounded solutions of our CGL equation on −∞

_{n}=(−1)

^{n}π/4, is centred at and oscillates at frequency (2n+1)Ω. The survival of the pulse-train depends upon the nonlinear mutual interaction of close neighbours; self-interaction is inadequate, as the absence of steady solutions shows. For given constant values of λ in excess of some threshold , solutions with pulse-separation were located on a finite range .

Here, we seek new pulse-train solutions, for which the product is spatially periodic on the length

Item Type: | Refereed Article |
---|---|

Keywords: | CGL-equation; Pulse-train; Couette flow; Taylor vortices |

Research Division: | Mathematical Sciences |

Research Group: | Applied Mathematics |

Research Field: | Theoretical and Applied Mechanics |

Objective Division: | Expanding Knowledge |

Objective Group: | Expanding Knowledge |

Objective Field: | Expanding Knowledge in the Mathematical Sciences |

Author: | Bassom, AP (Professor Andrew Bassom) |

ID Code: | 107346 |

Year Published: | 2007 |

Web of Science^{®} Times Cited: | 3 |

Deposited By: | Mathematics and Physics |

Deposited On: | 2016-03-11 |

Last Modified: | 2016-07-06 |

Downloads: | 0 |