### Abstract

We present a theory of turbulent elasticity, a property of drift-wave-zonal-flow (DW-ZF) turbulence, which follows from the time delay in the response of DWs to ZF shears. An emergent dimensionless parameter |〈v〉|/Δωk is found to be a measure of the degree of Fickian flux-gradient relation breaking, where |〈v〉| is the ZF shearing rate and Δωk is the turbulence decorrelation rate. For |〈v〉|/Δωk>1, we show that the ZF evolution equation is converted from a diffusion equation, usually assumed, to a telegraph equation, i.e., the turbulent momentum transport changes from a diffusive process to wavelike propagation. This scenario corresponds to a state very close to the marginal instability of the DW-ZF system, e.g., the Dimits shift regime. The frequency of the ZF wave is ΩZF=±γd1/2γmodu1/2, where γd is the ZF friction coefficient and γmodu is the net ZF growth rate for the case of the Fickian flux-gradient relation. This insight provides a natural framework for understanding temporally periodic ZF structures in the Dimits shift regime and in the transition from low confined mode to high confined mode in confined plasmas.

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

Article number | 041101 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 89 |

Issue number | 4 |

DOIs | |

Publication status | Published - Apr 4 2014 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

### Cite this

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*89*(4), [041101]. https://doi.org/10.1103/PhysRevE.89.041101

**Elasticity in drift-wave-zonal-flow turbulence.** / Guo, Z. B.; Diamond, P. H.; Kosuga, Y.; Gürcan, Ö D.

Research output: Contribution to journal › Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 89, no. 4, 041101. https://doi.org/10.1103/PhysRevE.89.041101

}

TY - JOUR

T1 - Elasticity in drift-wave-zonal-flow turbulence

AU - Guo, Z. B.

AU - Diamond, P. H.

AU - Kosuga, Y.

AU - Gürcan, Ö D.

PY - 2014/4/4

Y1 - 2014/4/4

N2 - We present a theory of turbulent elasticity, a property of drift-wave-zonal-flow (DW-ZF) turbulence, which follows from the time delay in the response of DWs to ZF shears. An emergent dimensionless parameter |〈v〉|/Δωk is found to be a measure of the degree of Fickian flux-gradient relation breaking, where |〈v〉| is the ZF shearing rate and Δωk is the turbulence decorrelation rate. For |〈v〉|/Δωk>1, we show that the ZF evolution equation is converted from a diffusion equation, usually assumed, to a telegraph equation, i.e., the turbulent momentum transport changes from a diffusive process to wavelike propagation. This scenario corresponds to a state very close to the marginal instability of the DW-ZF system, e.g., the Dimits shift regime. The frequency of the ZF wave is ΩZF=±γd1/2γmodu1/2, where γd is the ZF friction coefficient and γmodu is the net ZF growth rate for the case of the Fickian flux-gradient relation. This insight provides a natural framework for understanding temporally periodic ZF structures in the Dimits shift regime and in the transition from low confined mode to high confined mode in confined plasmas.

AB - We present a theory of turbulent elasticity, a property of drift-wave-zonal-flow (DW-ZF) turbulence, which follows from the time delay in the response of DWs to ZF shears. An emergent dimensionless parameter |〈v〉|/Δωk is found to be a measure of the degree of Fickian flux-gradient relation breaking, where |〈v〉| is the ZF shearing rate and Δωk is the turbulence decorrelation rate. For |〈v〉|/Δωk>1, we show that the ZF evolution equation is converted from a diffusion equation, usually assumed, to a telegraph equation, i.e., the turbulent momentum transport changes from a diffusive process to wavelike propagation. This scenario corresponds to a state very close to the marginal instability of the DW-ZF system, e.g., the Dimits shift regime. The frequency of the ZF wave is ΩZF=±γd1/2γmodu1/2, where γd is the ZF friction coefficient and γmodu is the net ZF growth rate for the case of the Fickian flux-gradient relation. This insight provides a natural framework for understanding temporally periodic ZF structures in the Dimits shift regime and in the transition from low confined mode to high confined mode in confined plasmas.

UR - http://www.scopus.com/inward/record.url?scp=84899482752&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84899482752&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.89.041101

DO - 10.1103/PhysRevE.89.041101

M3 - Article

AN - SCOPUS:84899482752

VL - 89

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 4

M1 - 041101

ER -