On resonance three-wave interactions and strange attractor
ORAL
Abstract
Nonlinear interactions of waves are important in different media. Specifically, resonant interactions in three- and four-wave clusters play a crucial role in the interaction of waves with disparate scales and in establishing the turbulence spectra in the inertial range of the wave vectors.
The coupling of different triads can result in the onset of a chaotic turbulence regime of wave energy transfer between waves. Previous work [1] suggests such couplings as a possible trigger of Edge Localized Modes in a tokamak.
Most studies on wave-wave interactions consider all individual interacting waves as neutrally stable. However, previous work [2] on a two-dimensional model of the magnetized plasma flow demonstrated that the addition of sink/source terms to the dynamics of individual waves could drastically alter the dynamics of the entire wave ensemble. Specifically, it was shown that changing the strength of the sink/source terms causes a transition from a quiescent quasisteady state regime to a regime with strong intermittent fluctuations of plasma energy and entropy. Therefore, to elucidate the role of sink/source terms in the transition to turbulence, it is instructive to consider their impact on a three-wave resonance interaction.
This talk presents results from a recent publication [3] on resonance three-wave interactions in the presence of linear sink/source terms. It is shown that incorporations of linear sink source terms result in the time dependence of the wave amplitudes, which could exhibit properties of a strange attractor. This finding demonstrates that the transition to turbulent dynamics of the waves could be related not only to the coupling of wave triads but also to the establishing of the strange attractor-like dynamics within individual wave triads.
[1] J. Dominski and A. Diallo Phys. Plasmas 28, 092306 (2021)
[2] S. A. Galkin and S. I. Krasheninnikov, Phys. Plasmas 8, 5091–5095 (2001)
[3] S.I. Krasheninnikov and A.R. Knyazev PoP 29, 010702 (2022)
The coupling of different triads can result in the onset of a chaotic turbulence regime of wave energy transfer between waves. Previous work [1] suggests such couplings as a possible trigger of Edge Localized Modes in a tokamak.
Most studies on wave-wave interactions consider all individual interacting waves as neutrally stable. However, previous work [2] on a two-dimensional model of the magnetized plasma flow demonstrated that the addition of sink/source terms to the dynamics of individual waves could drastically alter the dynamics of the entire wave ensemble. Specifically, it was shown that changing the strength of the sink/source terms causes a transition from a quiescent quasisteady state regime to a regime with strong intermittent fluctuations of plasma energy and entropy. Therefore, to elucidate the role of sink/source terms in the transition to turbulence, it is instructive to consider their impact on a three-wave resonance interaction.
This talk presents results from a recent publication [3] on resonance three-wave interactions in the presence of linear sink/source terms. It is shown that incorporations of linear sink source terms result in the time dependence of the wave amplitudes, which could exhibit properties of a strange attractor. This finding demonstrates that the transition to turbulent dynamics of the waves could be related not only to the coupling of wave triads but also to the establishing of the strange attractor-like dynamics within individual wave triads.
[1] J. Dominski and A. Diallo Phys. Plasmas 28, 092306 (2021)
[2] S. A. Galkin and S. I. Krasheninnikov, Phys. Plasmas 8, 5091–5095 (2001)
[3] S.I. Krasheninnikov and A.R. Knyazev PoP 29, 010702 (2022)
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Presenters
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Alexey R Knyazev
University of California, San Diego
Authors
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Sergei I Krasheninnikov
University of California, San Diego
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Alexey R Knyazev
University of California, San Diego