arXiv subjects

Pierre L. Guillon

Publications and source records attributed to Pierre L. Guillon.

3 recordsLinked to original sources

arXiv2026

Anisotropic truncation for turbulent transport and zonal flows in the Hasegawa-Wakatani system

Reduced models based on an anisotropic truncation of the Fourier space, retaining only a few poloidal wave-numbers while keeping the full radial resolution, are developed and first applied to the Hasegawa-Wakatani system. The impact of the truncation is studied first by considering the fixed-gradient formulation, and by comparing to direct numerical simulations (DNS). The turbulent particle flux, and the transition from quasi-two dimensional turbulence to the zonal flow (ZF) dominated state, are used as the main criteria for validation. It is found that at least 4 poloidal modes, distributed around the most unstable mode, are needed to observe a sharp transition, and that about 10 modes are needed to reproduce each transport regime. Then, similar reduced models are developed in a flux-driven formulation and compared to the DNS, focusing on two cases far from the nonlinear threshold of the transition from turbulence to zonal dominated states of the fixed gradient formulation. In that case, using 10 modes allows to match the probability distribution function of the particle flux of the DNS approximately. Considering the role played by different poloidal scales in the turbulent cascade, it is observed that in the turbulent state, an inverse energy cascade in radial wave-numbers takes place at large poloidal scales, while a forward enstrophy cascade in radial wave-numbers is observed to occur at smaller poloidal scales. Moreover, when they form, ZFs feed on poloidal scales that are around and slightly smaller than the injection scale, while giving their energy to the larger poloidal scales. In that case, there is an anisotropic inverse energy transfer, akin to inverse cascade, from the energy injection to the large poloidal scales through ZFs, while the forward enstrophy cascade seems to stay isotropic.

physics.plasm-ph↗

arXiv2025

Flux-driven turbulent transport using penalisation in the Hasegawa-Wakatani system

First numerical results from the newly-developed pseudo-spectral code P-FLARE (Penalised FLux-driven Algorithm for REduced models) are presented. This flux-driven turbulence/transport code uses a pseudo-spectral formulation with the penalisation method in order to impose radial boundary conditions. Its concise, flexible structure allows implementing various quasi-two dimensional reduced fluid models in flux-driven formulation. Here, results from simulations of the modified Hasegawa-Wakatani system are discussed, where particle transport and zonal flow formation, together with profile relaxation, are studied. It is shown that coupled spreading/profile relaxation that one obtains for this system is consistent with a simple one dimensional model of coupled spreading/transport equations. Then, the effect of a particle source is investigated, which results in the observation of sandpile-like critical behaviour. The model displays profile stiffness for certain parameters, with very different input fluxes resulting in very similar mean density gradients. This is due to different zonal flow levels around the critical value for the control parameter (i.e. the ratio of the adiabaticity parameter to the mean gradient) and the existence for this system of a hysteresis loop for the transition from 2D turbulence to a zonal flow dominated state.

physics.plasm-ph↗

arXiv2025

Phase Transition From Turbulence To Zonal Flows In The Hasegawa-Wakatani System

The transition between two-dimensional hydrodynamic turbulence and quasi-one-dimensional zonostrophic turbulence is examined in the modified Hasegawa-Wakatani system, which is considered as a minimal model of $β$-plane-like drift-wave turbulence with an intrinsic instability. Extensive parameter scans were performed across a wide range of values for the adiabaticity parameter $C$ describing the strength of coupling between the two equations. A sharp transition from 2D isotropic turbulence to a quasi-1D system, dominated by zonal flows, is observed using the fraction of the kinetic energy of the zonal modes as the order parameter, at $C\approx0.1$. It is shown that this transition exhibits a hysteresis loop around the transition point, where the adiabaticity parameter plays the role of the control parameter of its non-linear self-organisation. It was also observed that the radial particle flux scales with the adiabaticity parameter following two different power law dependencies in the two regimes. A simple quasi-linear saturation rule which accounts for the presence of zonal flows is proposed, and is shown to agree very well with the observed nonlinear fluxes. Motivated by the phenomenon of quasi-one dimensionalisation of the system at high $C$, a number of reduction schemes based on a limited number of modes were investigated and the results were compared to direct numerical simulations. In particular, it was observed that a minimal reduced model consisting of $2$ poloidal and $2$ radial modes was able to replicate the phase transition behaviour, while any further reduction failed to capture it.

physics.plasm-ph↗