Phase and amplitude evolution in the network of triadic interactions of the Hasegawa-Wakatani system
Artikel i vetenskaplig tidskrift, 2022

Hasegawa-Wakatani system, commonly used as a toy model of dissipative drift waves in fusion
devices is revisited with considerations of phase and amplitude dynamics of its triadic interactions.
It is observed that a single resonant triad can saturate via three way phase locking where the phase
differences between dominant modes converge to constant values as individual phases increase in
time. This allows the system to have approximately constant amplitude solutions. Non-resonant
triads show similar behavior only when one of its legs is a zonal wave number. However when an
additional triad, which is a reflection of the original one with respect to the y axis is included, the
behavior of the resulting triad pair is shown to be more complex. In particular, it is found that
triads involving small radial wave numbers (large scale zonal flows) end up transferring their energy
to the subdominant mode which keeps growing exponentially, while those involving larger radial
wave numbers (small scale zonal flows) tend to find steady chaotic or limit cycle states (or decay
to zero). In order to study the dynamics in a connected network of triads, a network formulation
is considered including a pump mode, and a number of zonal and non-zonal subdominant modes as
a dynamical system. It was observed that the zonal modes become clearly dominant only when a
large number of triads are connected. When the zonal flow becomes dominant as a ’collective mean
field’, individual interactions between modes become less important, which is consistent with the
inhomogeneous wave-kinetic picture. Finally, the results of direct numerical simulation is discussed
for the same parameters and various forms of the order parameter are computed. It is observed
that nonlinear phase dynamics results in a flattening of the large scale phase velocity as a function
of scale in direct numerical simulations.

Triadic interactions


Phase evolution


Özgür Gürcan

Johan Anderson

Chalmers, Rymd-, geo- och miljövetenskap

Sara Moradi

Nukleär teknik

A. Biancalani

P. Morel

Physics of Plasmas

1070-664X (ISSN) 1089-7674 (eISSN)

Vol. 29 5


Grundläggande vetenskaper


Atom- och molekylfysik och optik

Fusion, plasma och rymdfysik

Den kondenserade materiens fysik



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