Three-Wave Forced Hasegawa--Wakatani Model: Reducing Chaos with Zonal Flows
Abstract
We investigate the nonlinear dynamics of resistive drift-wave turbulence with a three-wave truncation of the Hasegawa--Wakatani equations, in which the background density gradient either is fixed or evolves self-consistently, fed by an external particle source P (such as neutral beam injection) and eroded by the turbulent particle flux. Two triads that differ only by a small tilt of the long-wavelength mode are compared, in one this mode is zonal and cannot be driven by the gradient, in the other it is a weakly driven drift wave. Period maps in the plane of the adiabaticity parameter C and the drive show that the zonal triad is almost always regular, whereas the non-zonal triad becomes chaotic. The feedback of the flux on the gradient amplifies this contrast: the fraction of aperiodic states grows considerably in the non-zonal triad and remains negligible in the zonal one. Along a line of constant C at low adiabaticity, the non-zonal triad with a fixed gradient enters chaos through torus breakdown with intermittency and leaves it through an interior crisis and a period-doubling cascade. With the self-consistent gradient, a Neimark--Sacker bifurcation leads to a phase-locked torus that breaks down abruptly, with hysteresis, and chaos then persists up to the largest drive, with the gradient driven intermittently above the threshold of the long-wavelength mode. None of these routes to chaos exists when that mode is zonal.
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BibTeX
@misc{haerter2026threewave,
title = {{Three-Wave Forced Hasegawa--Wakatani Model: Reducing Chaos with Zonal Flows}},
author = {P. Haerter and R. L. Viana and I. L. Caldas},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38792},
eprint = {2610.38792},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38792},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Three-Wave Forced Hasegawa--Wakatani Model: Reducing Chaos with Zonal Flows
AU - P. Haerter
AU - R. L. Viana
AU - I. L. Caldas
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38792
UR - https://arxiv.org/abs/2610.38792
AB - We investigate the nonlinear dynamics of resistive drift-wave turbulence with a three-wave truncation of the Hasegawa--Wakatani equations, in which the background density gradient either is fixed or evolves self-consistently, fed by an external particle source P (such as neutral beam injection) and eroded by the turbulent particle flux. Two triads that differ only by a small tilt of the long-wavelength mode are compared, in one this mode is zonal and cannot be driven by the gradient, in the other it is a weakly driven drift wave. Period maps in the plane of the adiabaticity parameter C and the drive show that the zonal triad is almost always regular, whereas the non-zonal triad becomes chaotic. The feedback of the flux on the gradient amplifies this contrast: the fraction of aperiodic states grows considerably in the non-zonal triad and remains negligible in the zonal one. Along a line of constant C at low adiabaticity, the non-zonal triad with a fixed gradient enters chaos through torus breakdown with intermittency and leaves it through an interior crisis and a period-doubling cascade. With the self-consistent gradient, a Neimark--Sacker bifurcation leads to a phase-locked torus that breaks down abruptly, with hysteresis, and chaos then persists up to the largest drive, with the gradient driven intermittently above the threshold of the long-wavelength mode. None of these routes to chaos exists when that mode is zonal.
ER -