### Abstract

Original language | English |
---|---|

Article number | 122307 |

Number of pages | 15 |

Journal | Physics of Plasmas |

Volume | 24 |

DOIs | |

Publication status | Published - 14 Dec 2017 |

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### Bibliographical note

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing.The following article appeared in Pringle, C, McMillan, B & Teaca, B 2017, 'A nonlinear approach to transition in subcritical plasmas with sheared flow' Physics of Plasmas, vol 24, 122307 and may be found at https://dx.doi.org/10.1063/1.4999848

### Cite this

*Physics of Plasmas*,

*24*, [122307]. https://doi.org/10.1063/1.4999848

**A nonlinear approach to transition in subcritical plasmas with sheared flow.** / Pringle, Chris; McMillan, Ben; Teaca, Bogdan.

Research output: Contribution to journal › Article

*Physics of Plasmas*, vol. 24, 122307. https://doi.org/10.1063/1.4999848

}

TY - JOUR

T1 - A nonlinear approach to transition in subcritical plasmas with sheared flow

AU - Pringle, Chris

AU - McMillan, Ben

AU - Teaca, Bogdan

N1 - This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in Pringle, C, McMillan, B & Teaca, B 2017, 'A nonlinear approach to transition in subcritical plasmas with sheared flow' Physics of Plasmas, vol 24, 122307 and may be found at https://dx.doi.org/10.1063/1.4999848

PY - 2017/12/14

Y1 - 2017/12/14

N2 - In many plasma systems, introducing a small background shear flow is enough to stabilize the system linearly. The nonlinear dynamics are much less sensitive to sheared flows than the average linear growthrates, and very small amplitude perturbations can lead to sustained turbulence. We explore the general problem of characterizing how and when the transition from near-laminar states to sustained turbulence occurs; a model of the interchange instability being used as a concrete example. These questions are fundamentally nonlinear, and the answers must go beyond the linear transient amplification of small perturbations. Two methods that account for nonlinear interactions are therefore explored here. The first method explored is edge tracking, which identifies the boundary between the basins of attraction of the laminar and turbulent states. Here, the edge is found to be structured around an exact, localized, traveling wave solution; a solution that is qualitatively similar to avalanche-like bursts seen in the turbulent regime. The second method is an application of nonlinear, non-modal stability theory which allows us to identify the smallest disturbances which can trigger turbulence (the minimal seed for the problem) and hence to quantify how stable the laminar regime is. The results obtained from these fully nonlinear methods provides confidence in the derivation of a semi-analytic approximation for the minimal seed.

AB - In many plasma systems, introducing a small background shear flow is enough to stabilize the system linearly. The nonlinear dynamics are much less sensitive to sheared flows than the average linear growthrates, and very small amplitude perturbations can lead to sustained turbulence. We explore the general problem of characterizing how and when the transition from near-laminar states to sustained turbulence occurs; a model of the interchange instability being used as a concrete example. These questions are fundamentally nonlinear, and the answers must go beyond the linear transient amplification of small perturbations. Two methods that account for nonlinear interactions are therefore explored here. The first method explored is edge tracking, which identifies the boundary between the basins of attraction of the laminar and turbulent states. Here, the edge is found to be structured around an exact, localized, traveling wave solution; a solution that is qualitatively similar to avalanche-like bursts seen in the turbulent regime. The second method is an application of nonlinear, non-modal stability theory which allows us to identify the smallest disturbances which can trigger turbulence (the minimal seed for the problem) and hence to quantify how stable the laminar regime is. The results obtained from these fully nonlinear methods provides confidence in the derivation of a semi-analytic approximation for the minimal seed.

U2 - 10.1063/1.4999848

DO - 10.1063/1.4999848

M3 - Article

VL - 24

JO - Physics of Plasmas

JF - Physics of Plasmas

SN - 1070-664X

M1 - 122307

ER -