arXiv subjects

Alexandros Alexakis

Publications and source records attributed to Alexandros Alexakis.

At least 19 recordsLinked to original sources

arXiv2026

Intermittency in Shell Models of Turbulent Cascades: from Single-Branch to Multi-Branch

Intermittency is one of the central features of turbulent transfer: the multi-scale energy cascade is mediated by rare and intense fluctuations. We investigate this phenomenon in a multi-branch shell model, which combines quasi-local triadic nonlinear interactions with a branching structure that mimics the growth of degrees of freedom toward small scales. Comparison with the standard Sabra model shows that branching enhances intermittency, as measured by anomalous scaling exponents of energy-flux structure functions. We further use multiplier statistics and large deviation estimates to characterize the multiplicative nature of the cascade. Our results suggest that reduced descriptions of turbulent intermittency should retain both nonlinear dynamics and geometrical organization. Implications on Navier-Stokes turbulence are discussed.

physics.flu-dyn↗

arXiv2026

Multi-branch Shell Models of Two-Dimensional Turbulence exhibit Dual Energy-Enstrophy Cascades

Classical shell models of turbulence do not display dual cascade - inverse of energy and direct of enstrophy - because they fail to reproduce the right thermal spectra. We propose here a multi-branch shell model, including a geometry hierarchically organized across scales, in order to overcome this limitation. For this model, we demonstrate numerically both the agreement of the thermal spectra with those of two-dimensional fluid equations and the emergence of a statistically stationary dual cascade. This construction also allows us to study local transfers and to investigate both self-similarity and non-Gaussianity.

physics.flu-dyn↗

arXiv2026

Ensemble of Fixed Points in Multi-branch Shell Models of Turbulent Cascades

Stationary solutions of a shell model of turbulence defined on a dyadic tree topology are studied. Each node's amplitude is expressed as the product of amplitude multipliers associated with its ancestors, providing a recursive representation of the cascade process. A geometrical rule governs the tree growth, and we prove the existence of a continuum of fixed points, including the Kolmogorov solution, that sustain a strictly forward energy cascade. Sampling along randomly chosen branches defines a homogeneous Markov chain, enabling a stochastic characterization of extended self-similarity and intermittency through the spectral properties of the associated Feynman-Kac operators. Numerical simulations confirm the theoretical predictions, showing that multi-branch shell models offer a minimal yet physically rich framework for exploring the complexity of nonlinear energy transfer across scales.

physics.flu-dyn↗

arXiv2025

Stability of vortex lattices in rotating flows

Vortex lattices -- highly ordered arrays of vortices -- are known to arise in quantum systems such as type II superconductors and Bose-Einstein condensates. More recently, similar arrangements have been reported in classical rotating fluids. However, the mechanisms governing their formation, stability, and eventual breakdown remain poorly understood. We explore the dynamical stability of vortex lattices in three-dimensional rotating flows. To that end we construct controlled initial conditions consisting of vortex lattices superimposed on turbulent backgrounds. We then characterize their evolution across different Rossby numbers and domain geometries. By introducing an Ekman drag we are able to reach a steady state where vortex lattices persist with near constant amplitude up until spontaneous breakup of the lattice, or an equivalent of ``melting,'' occurs. We examine an ensemble of runs in order to determine the mean lifetime of the lattice as a function of the system parameters. Our results reveal that the stability of the lattices is a memory-less random process whose mean life-time depends sensitively on the system parameters that if finely tuned can lead to very long lived lattice states. These metastable states exhibit statistical properties reminiscent of critical systems and can offer insight into long-lived vortex patterns observed in planetary atmospheres.

physics.flu-dyn↗

arXiv2025

Energy cascades in rotating and stratified turbulence in anisotropic domains

The concept of inverse energy cascades has played a central role in the development of turbulence theory, with applications in two-dimensional and quasi-two-dimensional flows. We examine the presence or absence of inverse energy cascades in rotating stably stratified flows constrained to anisotropic yet fully three-dimensional domains, in a range of parameters that are relevant for planetary atmospheres. In particular, we focus on regimes with aspect ratios, Rossby, and Froude numbers similar to those found in the Earth's and other planets atmospheres. Our results show that, under certain conditions, inverse energy cascades can indeed emerge from the dry fluid dynamics solely, suggesting that this process can play a role in intermediate-scale atmospheric self-organization processes.

physics.flu-dyn↗

arXiv2025

Fluctuations around Turbulence Models

Numerical simulations of turbulent flows at realistic Reynolds numbers generally rely on filtering out small scales from the Navier Stokes equations and modeling their impact through the Reynolds stress tensor ${\tau}_{ij}$. Traditional models approximate ${\tau}_{ij}$ solely as a function of the filtered velocity gradient, leading to deterministic subgrid scale closures. However, small scale fluctuations can locally exhibit instantaneous values whose deviation from the mean can have a significant influence on flow dynamics. In this work, we investigate these effects by employing direct numerical simulations combined with Gaussian filtering to quantify subgrid scale effects and evaluating the local energy flux in both space and time. The mean performance of the canonical Clark model is assessed by conditioning the energy flux distributions on the invariants of the filtered velocity gradient tensor, $Q$ and $R$. The Clark model captures to a good degree the mean energy flux. However, the fluctuations around these mean values for given ($Q,R$) are of the order of the mean displaying fat tailed distributions. To become more precise, we examine the joint distributions of true energy flux and the predictions from both the Clark and the Smagorinsky models. This approach mirrors the strategy adopted in early stochastic subgrid scale models. Clear non Gaussian characteristics emerge from the obtained distributions, particularly through the appearance of heavy tails. The mean, the variance, the skewness and flatness of these distributions are quantified. Our results emphasize that fluctuations are an integral component of the small scale feedback onto large scale dynamics and should be incorporated into subgrid scale modeling through an appropriate stochastic framework.

physics.flu-dyn↗

arXiv2025

Two-dimensional turbulent condensates without bottom drag

The extent to which statistical equilibrium theory is applicable to driven dissipative dynamics remains an important open question in many systems. We use extensive direct numerical simulations of the incompressible two-dimensional (2D) Navier-Stokes equation to examine the steady state of large-scale condensates in 2D turbulence at finite Reynolds number $Re$ in the absence of bottom drag. Large-scale condensates appear above a critical Reynolds number $Re_c\approx 4.19$. Close to this onset, we find a power-law scaling of the energy with $Re-Re_c$, with the energy spectrum at large scales following the absolute equilibrium form proposed by Kraichnan. At larger $Re$, the energy spectrum deviates from this form, displaying a steep power-law range at low wave numbers with exponent $-5$, with most of the energy dissipation occurring within the condensate at large scales. We show that this spectral exponent is consistent with the logarithmic radial vorticity profile of the condensate vortices predicted by quasi-linear theory for a viscously saturated condensate. Our findings shed new light on the classical problem of large-scale turbulent condensation in forced dissipative 2D flows in finite domains, showing that the large scales are close to equilibrium dynamics in weakly turbulent flows but not in the strong condensate regime with $Re\gg1$.

physics.flu-dyn↗

arXiv2024

Large-scale self-organisation in dry turbulent atmospheres

How turbulent convective fluctuations organise to form large-scale structures in planetary atmospheres remains a question that eludes quantitative answers. The assumption that this process is the result of an inverse cascade was suggested half a century ago in two-dimensional fluids, but its applicability to atmospheric and oceanic flows remains heavily debated, hampering our understanding of the energy balance in planetary systems. We show with direct numerical simulations of spatial resolutions of 122882 $\times$ 384 points that rotating and stratified flows can support a bidirectional cascade of energy, in three dimensions, with a ratio of Rossby to Froude numbers comparable to that of the Earth's atmosphere. Our results establish that in dry atmospheres spontaneous order can arise via an inverse cascade to the largest spatial scales.

physics.flu-dyn↗

arXiv2024

Quasi-two-dimensional Turbulence

Many fluid-dynamical systems met in nature are quasi-two-dimensional: they are constrained to evolve in approximately two dimensions with little or no variation along the third direction. This has a drastic effect in the flow evolution because the properties of three dimensional turbulence are fundamentally different from those of two dimensional turbulence. In three-dimensions energy is transferred on average towards small scales, while in two dimensions energy is transferred towards large scales. Quasi-two-dimensional flows thus stand in a crossroad, with two-dimensional motions attempting to self-organize and generate large scales while three dimensional perturbations cause disorder, disrupting any large scale organization. Where is energy transferred in such systems? It has been realized recently that in fact the two behaviors can coexist with a simultaneous transfer of energy both to large and to small scales. How the cascade properties change as the variations along the third direction are suppressed has lead to discovery of different regimes or phases of turbulence of unexpected richness in behavior. Here, recent discoveries on such systems are reviewed. It is described how the transition from three-dimensional to two-dimensional flows takes place, the different phases of turbulence met and the nature of the transitions from one phase to the other. Finally, the implications these new discoveries have on different physical systems are discussed.

physics.flu-dyn↗

arXiv2024

Magnetic reconnection, plasmoids and numerical resolution

Explaining fast magnetic reconnection in electrically conducting plasmas has been a theoretical challenge in plasma physics since its first description by Eugene N. Parker. In the recent years the observed reconnection rate has been shown by numerical simulations to be explained by the plasmoid instability that appears in highly conductive plasmas. In this work we show that the plasmoid instability is very sensitive to the numerical resolution used. It is shown that well resolved runs display no plasmoid instability even at Lundquist number as large as $5\cdot10^5$ achieved at resolutions of $32\,768^2$ grid points. On the contrary in simulations that are under-resolved below a threshold, the plasmoid instability manifests itself with the formation of larger plasmoids the larger the under-resolving is. The present results thus question the description of the plasmoid instability as a mechanism for fast magnetic reconnection.

physics.plasm-ph↗

arXiv2023

Fluctuation Relations at Large Scales in Three-Dimensional Hydrodynamic Turbulence

It has long been conjectured that, in three dimensional turbulence, velocity modes at scales larger than the forcing scale follow equilibrium dynamics. Recent numerical and experimental evidence show that such modes share the same mean energy and therefore support this claim, but equilibrium dynamics does not reduce to equipartition of energy. In this work, a large set of direct numerical simulations is carried out to investigate if fluctuation-dissipation relations and the fluctuation theorem also apply at these scales. These two results link out-of-equilibrium properties of a forced system with its behavior at equilibrium. Both relations are verified quantitatively by the results of our simulations, further supporting that large scale modes display equilibrium dynamics. They provide new tools to characterize both the mean value and the fluctuations of the injected energy by a large scale force acting on turbulence driven by small scale random noise.

physics.flu-dyn↗

arXiv2023

Exact intermittent solutions in a turbulence multi branch shell model

Reproducing complex phenomena with simple models marks our understanding of the phenomena themselves and this is what Jack Herring's work demonstrated multiple times. In that spirit, this work studies a turbulence shell model consisting of a hierarchy of structures of different scales $\ell_n$ such that each structure transfers its energy to two substructures of scale $\ell_{n+1} = \ell_n /λ$. For this model we construct exact inertial range solutions that display intermittency ie absence of self-similarity. Using a large ensemble of these solutions we investigate how the probability distributions of the velocity modes change with scale. It is demonstrated that while velocity amplitudes are not scale invariant their ratios are. Furthermore using large deviation theory we show how the probability distributions of the velocity modes can be re-scaled to collapse in a scale independent form. Finally, we discuss the implications the present results have for real turbulent flows.

physics.flu-dyn↗

arXiv2023

How far does turbulence spread?

How locally injected turbulence, spreads in space is investigated with direct numerical simulations. We consider a turbulent flow in a long channel generated by a forcing that is localised in space. The forcing is such that it does not inject any mean momentum in the flow. We show that at long times a statistically stationary state is reached where the turbulent energy density in space fluctuates around a mean profile that peaks at the forcing location and decreases fast away from it. We measure this profile as a function of the distance from the forcing region for different values of the Reynolds number. It is shown, that as the Reynolds number is increased, it converges to a Reynolds-independent profile implying that turbulence spreads due to self-advection and not molecular diffusion. In this limit therefore, turbulence plays the simultaneous role of cascading the energy to smaller scales and transporting it to larger distances. The two effects are shown to be of the same order of magnitude. Thus a new turbulent state is reached where turbulent transport and turbulent cascade are equally important and control its properties.

physics.flu-dyn↗

arXiv2022

Local fluxes in MHD Turbulence

Using highly resolved direct numerical simulations we examine the statistical properties of the local energy flux rate $Π_\ell(x)$ towards small scales for three isotropic turbulent magnetohydrodynamic flows, which differ in strength and structure of the magnetic field. We analyse the cascade process both in the kinetic and magnetic energy, disentangling the different flux contributions to the overall energy dynamics. The results show that the probability distribution of the local energy flux develops long tails related to extreme events, similar to the hydrodynamic case. The different terms of the energy flux display different properties and show sensitivity on the type of the flow examined. We further examine the joint pdf between the local energy flux and the gradients of the involved fields. The results point out a correlation with the magnetic field gradients, showing however a dispersion much stronger than what is observed in hydrodynamic flows. Finally, it is also shown that the local energy flux shows some dependence on the local amplitude of the magnetic field. The present results have implications for subgrid scale models that we discuss.

physics.flu-dyn↗

arXiv2022

Saturation of turbulent helical dynamos

The presence of large scale magnetic fields in nature is often attributed to the inverse cascade of magnetic helicity driven by turbulent helical dynamos. In this work we show that in turbulent helical dynamos, the inverse flux of magnetic helicity towards the large scales $Π_{\mathcal{H}}$ is bounded by $|Π_{\mathcal{H}}|\le c εk_η^{-1}$, where $ε$ is the energy injection rate, $k_η$ is the Kolmogorov magnetic dissipation wavenumber and $c$ an order one constant. Assuming the classical isotropic turbulence scaling, the inverse flux of magnetic helicity $Π_{\mathcal{H}}$ decreases at least as a $-3/4$ power-law with the magnetic Reynolds number $Rm$ : $|Π_{\mathcal{H}} | \le c ε\ell_f Rm^{-3/4}\max[Pm,1]^{1/4}$, where $Pm$ the magnetic Prandtl number and $\ell_f$ the forcing lengthscale. We demonstrate this scaling with $Rm$ using direct numerical simulations of turbulent dynamos forced at intermediate scales. The results further indicate that nonlinear saturation is achieved by a balance between the inverse cascade and dissipation at domain size scales $L$ for which the saturation value of the magnetic energy is bounded by ${\mathcal{E}}_\text{m}\leq c L (ε\ell_f)^{2/3} Rm^{1/4}\max[1,Pm]^{1/4}$. Numerical simulations also demonstrate this bound.

physics.flu-dyn↗

arXiv2022

Inducing intermittency in the inverse cascade of two dimensional turbulence by a fractal forcing

We demonstrate that like in the forward cascade of three dimensional turbulence that displays intermittency (lack of self-similarity) due to the concentration of energy dissipation in a small set of fractal dimension less than three, the inverse cascade of two-dimensional turbulence can also display lack of self-similarity and intermittency if the energy injection is constrained in a fractal set of dimension less than two. A series of numerical simulations of two dimensional turbulence are examined, using different forcing functions of the same forcing length-scale but different fractal dimension $D$ that varies from the classical $D=2$ case to the point vortex case $D=0$. It is shown that as the fractal dimension of the forcing is decreased from $D=2$, the self-similarity is lost and intermittency appears, with the scaling of the different structure functions $\langle |δu_\|^p| \rangle\propto r^{ζ_p}$ differs from the dimensional analysis prediction $ζ_p=p/3$. The present model thus provides a unique example that intermittency is controlled and can thus shed light and provide test beds for multi-fractal models of turbulence.

physics.flu-dyn↗

arXiv2022

Bistability of the large-scale dynamics in quasi-two-dimensional turbulence

In many geophysical and astrophysical flows, suppression of fluctuations along one direction of the flow drives a quasi-2D upscale flux of kinetic energy, leading to the formation of strong vortex condensates at the largest scales. Recent studies have shown that the transition towards this condensate state is hysteretic, giving rise to a limited bistable range in which both the condensate state as well as the regular 3D state can exist at the same parameter values. In this work, we use direct numerical simulations of thin-layer flow to investigate whether this bistable range survives as the domain size and turbulence intensity are increased. By studying the time scales at which rare transitions occur from one state into the other, we find that the bistable range grows as the box size and/or Reynolds number Re are increased, showing that the bistability is neither a finite-size nor a finite-Re effect. We furthermore predict a crossover from a bimodal regime at low box size, low Re to a regime of pure hysteresis at high box size, high Re, in which any transition from one state to the other is prohibited at any finite time scale.

physics.flu-dyn↗

arXiv2021

Energy cascades in rapidly rotating and stratified turbulence within elongated domains

We study forced, rapildy rotating and stably stratified turbulence in an elongated domain using an asymptotic expansion at simultaneously low Rossby number $Ro\ll1$ and large domain height compared to the energy injection scale, $h=H/\ell_{in}\gg1$. The resulting equations depend on the parameter $λ=(h Ro )^{-1}$ and the Froude number $Fr$. An extensive set of direct numerical simulations (DNS) is performed to explore the parameter space $(λ,Fr)$. We show that a forward energy cascade occurs in one region of this space, and a split energy cascade outside it. At weak stratification (large $Fr$), an inverse cascade is observed for sufficiently large $λ$. At strong stratification (small $Fr$) the flow becomes approximately hydrostatic and an inverse cascade is always observed. For both weak and strong stratification, we present theoretical arguments supporting the observed energy cascade phenomenology. Our results shed light on an asymptotic region in the phase diagram of rotating and stratified turbulence, which is difficult to attain by brute-force DNS.

physics.flu-dyn↗