arXiv subjects

Özgür D. Gürcan

Publications and source records attributed to Özgür D. Gürcan.

10 recordsLinked to original sources

arXiv2026

The role of different nonlinearities and potential vorticity conservation in two-dimensional fluid ITG models

The nature of turbulent energy cascade of simple two-dimensional fluid models of ion temperature gradient driven turbulence is studied in detail. Notably, it is observed that a minimal two-field model of toroidal ITG, behaves qualitatively differently with or without the diamagnetic nonlinearity. In its absence, the zonal flows always dominate and the system never reaches a high-transport state. In contrast, when this term is included, zonal flows dominate only near marginality, while away from it, an inverse cascade with high levels of transport is observed, requiring large-scale dissipation (hypoviscosity) to saturate and hyperviscosity to regularize small scale instability associated with this nonlinear term. However introducing such a term, together with the existence of the curvature term, breaks potential vorticity conservation, which is one of the key symmetries of drift-wave turbulence. This can be remedied by considering a more complete model that retains higher-order terms in the pressure equation. This form of the model, with four nonlinearities, conserves potential vorticity and behaves similarly to the original model, requiring hyperviscosity to saturate since the added nonlinearity generates small scale instability also for the pressure equation. To characterize the roles of potential vorticity conservation and higher-order terms in the pressure equation, the behavior of both the standard ITG system, and the potential vorticity conserving system, is studied by analyzing their spectra, turbulent cascades, and sensitivity to viscosity. Finally, the direction of turbulent cascade due to the different nonlinearities (i.e. the diamagnetic nonlinearity in particular) is investigated by examining their contributions to the spectral energy transfer and by considering the triadic instability assumption for each of these nonlinearities separately.

physics.plasm-ph↗

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↗

arXiv2026

Nonlinear phase synchronization and the role of spacing in shell models

A shell model can be considered as a chain of triads, where each triad can be interpreted as a nonlinear oscillator that can be mapped to a spinning top. Investigating the relation between phase dynamics and intermittency in a such a chain of nonlinear oscillators, it is found that synchronization is linked to increased energy transfer. In particular, the results provide evidence that the observed systematic increase of intermittency, as the shell spacing is decreased, is associated with strong phase alignment among consecutive triadic phases, facilitating the energy cascade. It is shown that while the overall level of synchronization can be quantified using a Kuramoto order parameter for the global phase coherence in the inertial range, a local, weighted Kuramoto parameter can be used for the detection of burst-like events propagating across shells in the inertial range. This novel analysis reveals how partially phase-locked states are associated with the passage of extreme events of energy flux. Applying this method to helical shell models, reveals that for a particular class of helical interactions, a reduction in phase coherence correlates with suppression of intermittency. When inverse cascade scenarios are considered using two different shell models including a non local helical shell model, and a local standard shell model with a modified conservation law, it was shown that a particular phase organization is needed in order to sustain the inverse energy cascade. It was also observed that the PDFs of the triadic phases were peaked in accordance with the basic considerations of the form of the flux, which suggests that a triadic phase of π/2 and -π/2 maximizes the forward and the inverse energy cascades respectively.

nlin.CD↗

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

Shell Models on Recurrent Sequences: Fibonacci, Padovan and Other Series

A new class of shell models is proposed, where the shell variables are defined on a recurrent sequence of integer wave-numbers such as the Fibonacci or the Padovan series, or their variations including a sequence made of square roots of Fibonacci numbers rounded to the nearest integer. Considering the simplest model, which involves only local interactions, the interaction coefficients can be generalized in such a way that the inviscid invariants, such as energy and helicity, can be conserved even though there is no exact self-similarity. It is shown that these models basically have identical features with standard shell models, and produce the same power law spectra, similar spectral fluxes and analogous deviation from self-similar scaling of the structure functions implying comparable levels of turbulent intermittency. Such a formulation potentially opens up the possibility of using shell models, or their generalizations along with discretized regular grids, such as those found in direct numerical simulations, either as diagnostic tools, or subgrid models. It also allows to develop models where the wave-number shells can be interpreted as sparsely decimated sets of wave-numbers over an initially regular grid. In addition to conventional shell models with local interactions that result in forward cascade, a particular helical shell model with long range interactions is considered on a similarly recurrent sequence of wave numbers, corresponding to the Fibonacci series, and found to result in the usual inverse cascade.

nlin.CD↗

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↗

arXiv2024

Internally Driven $β$-plane Plasma Turbulence Using the Hasegawa-Wakatani System

General problem of plasma turbulence can be formulated as advection of potential vorticity (PV), which handles flow self-organization, coupled to a number of other fields, whose gradients provide free energy sources. Therefore, focusing on PV evolution separates the underlying linear instability from the flow self-organization, and clarifies key spatial scales in terms of balances between various time scales. Considering the Hasegawa-Wakatani model as a minimal, nontrivial model of plasma turbulence where the energy is injected internally by a linear instability, we find that the critical wavenumber $k_{c}=C/κ$ where $C$ is the adiabaticity parameter and $κ$ is the normalized density gradient separates the adiabatic (or highly zonostrophic) behavior for large scales from the hydrodynamic behavior at small scales. In the adiabatic range the non-zonal part of the wave-number spectrum goes from $E(k)\proptoγ_{k}U^{-1}k^{-2}$ around the peak to $E(k) \propto ω_{k}^{2} k^{-3}$ in the "inertial" range, where $γ_{k}$ and $ω_{k}$ are the linear growth and frequency and $U$ is the rms zonal velocity. This proposed spectrum fits very well for the large $k_{c}$ case, where the bulk of the spectrum is in the adiabatic range. In contrast for small $k_{c}$, we get the usual forward enstrophy cascade with $E(k)\proptoε_{W}^{2/3}k^{-3}$, where $ε_{W}$ is the enstrophy dissipation. In contrast for $k_{c}\approx 1$, the system transitions to hydrodynamic forward enstrophy cascade right after the injection range, with zonal flows at large scales and forward enstrophy cascade at small scales. It is argued that the ratio $R_β\equiv k_β/k_{\text{peak}}\approx k_{c}/k_{\text{peak}}$ where $k_{\text{peak}}$ is the peak wave-number can be defined as the zonostrophy parameter.

physics.plasm-ph↗

arXiv2020

Dynamical Complex Network Models of the Turbulent Cascade

Cascade models based on dynamical complex networks are proposed as models of turbulent energy cascade. Taking a simple shell model as the initial regular lattice with only nearest neighbor interactions, small world network models are constructed by adding or replacing some of the existing local interactions by nonlocal ones. The models are then evolved over time, both by solving for the shell variable for velocity using an arbitrary network generalization of the shell model evolution and by rewiring the network each time from the original lattice in regular time intervals. This results in a more intermittent time evolution with larger variations of the wave-number spectrum. It also results in an actual increase in intermittency as computed from the fitted exponents of structure functions as computed from these models. It appears that the intermittency increases as the ratio of random nonlocal connections to local nearest neighbor connections increases.

physics.flu-dyn↗

arXiv2019

A Differential Approximation Model For Passive Scalar Turbulence

Two dimensional passive scalar turbulence is studied by means of a k-space diffusion model based on a third order differential approximation. This simple description of local nonlinear interactions in Fourier space is shown to present a general expression, in line with previous seminal works, and appears to be suitable for various 2D turbulence problems. Steady state solutions for the spectral energy density of the flow is shown to recover the Kraichnan-Kolmogorov phenomenology of the dual cascade, while various passive scalar spectra, such as Batchelor or Obukhov-Corssin spectra are recovered as steady state solutions of the spectral energy density of the passive scalar. These analytical results are then corroborated by numerical solutions of the time evolving problem with energy and passive scalar injection and dissipation on a logarithmic wavenumber space grid over a large range of scales. The particular power law spectra that is obtained is found to depend mainly on the location of the kinetic and passive scalar energy injections.

physics.flu-dyn↗

arXiv2017

Stable and unstable roots of ion temperature gradient driven mode using curvature modified plasma dispersion functions

Basic, local kinetic theory of ion temperature gradient driven (ITG) mode, with adiabatic electrons is reconsidered. Standard unstable, purely oscillating as well as damped solutions of the local dispersion relation are obtained using a bracketing technique that uses the argument principle. This method requires computing the plasma dielectric function and its derivatives, which are implemented here using modified plasma dispersion functions with curvature and their derivatives, and allows bracketing/following the zeros of the plasma dielectric function which corresponds to different roots of the ITG dispersion relation. We provide an open source implementation of the derivatives of modified plasma dispersion functions with curvature, which are used in this formulation. Studying the local ITG dispersion, we find that near the threshold of instability the unstable branch is rather asymmetric with oscillating solutions towards lower wave numbers (i.e. drift waves), and damped solutions toward higher wave numbers. This suggests a process akin to inverse cascade by coupling to the oscillating branch towards lower wave numbers may play a role in the nonlinear evolution of the ITG, near the instability threshold. Also, using the algorithm, the linear wave diffusion is estimated for the marginally stable ITG mode.

physics.plasm-ph↗