arXiv subjects

Alexandros Alexakis

Publications and source records attributed to Alexandros Alexakis.

At least 55 records · Page 3Linked to original sources

arXiv2017

Condensates in rotating turbulent flows

Using a large number of numerical simulations we examine the steady state of rotating turbulent flows in triple periodic domains, varying the Rossby number $Ro$ (that measures the inverse rotation rate) and the Reynolds number $Re$ (that measures the strength of turbulence). The examined flows are sustained by either a helical or a non-helical Roberts force, that is invariant along the axis of rotation. The forcing acts at a wavenumber $k_f$ such that $k_fL=4$, where $2πL$ is the size of the domain. Different flow behaviours were obtained as the parameters are varied. Above a critical rotation rate the flow becomes quasi two dimensional and transfers energy to the largest scales of the system forming large coherent structures known as condensates. We examine the behaviour of these condensates and their scaling properties close and away from this critical rotation rate. Close to the the critical rotation rate the system transitions super-critically to the condensate state displaying a bimodal behaviour oscillating randomly between an incoherent-turbulent state and a condensate state. Away from the critical rotation rate, it is shown that two distinct mechanisms can saturate the growth of the large scale energy. The first mechanism is due to viscous forces and is similar to the saturation mechanism observed for the inverse cascade in two-dimensional flows. The second mechanism is independent of viscosity and relies on the breaking of the two-dimensionalization condition of the rotating flow. The two mechanisms predict different scaling with respect to the control parameters of the system (Rossby and Reynolds), which are tested with the present results of the numerical simulations. A phase space diagram in the $Re,Ro$ parameter plane is sketched.

physics.flu-dyn↗

arXiv2017

Dynamic anisotropy in MHD turbulence induced by mean magnetic field

In this paper, we study the development of anisotropy in strong MHD turbulence in the presence of a large scale magnetic field B 0 by analyzing the results of direct numerical simulations. Our results show that the developed anisotropy among the different components of the velocity and magnetic field is a direct outcome of the inverse cascade of energy of the perpendicular velocity components u? and a forward cascade of the energy of the parallel component u k . The inverse cascade develops for a strong B0, where the flow exhibits a strong vortical structure by the suppression of fluctuations along the magnetic field. Both the inverse and the forward cascade are examined in detail by investigating the anisotropic energy spectra, the energy fluxes, and the shell to shell energy transfers among different scales.

physics.plasm-ph↗

arXiv2017

The effect of helicity on the correlation time of large scale turbulent flows

Solutions of the forced Navier-Stokes equation have been conjectured to thermalize at scales larger than the forcing scale, similar to an absolute equilibrium obtained for the spectrally-truncated Euler equation. Using direct numeric simulations of Taylor-Green flows and general-periodic helical flows, we present results on the probability density function, energy spectrum, auto-correlation function and correlation time that compare the two systems. In the case of highly helical flows, we derive an analytic expression describing the correlation time for the absolute equilibrium of helical flows that is different from the $E^{-1/2}k^{-1}$-scaling law of weakly helical flows. This model predicts a new helicity-based scaling law for the correlation time as $τ(k)\sim H^{-1/2}k^{-1/2}$. This scaling law is verified in simulations of the truncated Euler equation. In simulations of the Navier-Stokes equations the large scale modes of forced Taylor-Green symmetric flows (with zero total helicity and large separation of scales) follow the same properties as absolute equilibrium including a $τ(k) \sim E^{-1/2}k^{-1}$ scaling for the correlation time. General-periodic helical flows also show similarities between the two systems, however the largest scales of the forced flows deviate from the absolute equilibrium solutions.

physics.flu-dyn↗

arXiv2017

Discontinuous transition from direct to inverse cascade in three-dimensional turbulence

Inviscid invariants of flow equations are crucial in determining the direction of the turbulent energy cascade. In this work we investigate a variant of the three dimensional Navier-Stokes equations that shares exactly the same ideal invariants (energy and helicity) and the same symmetries (under rotations, reflexions and scale transforms) as the original equations. It is demonstrated that the examined system displays a change in the direction of the energy cascade when varying the value of a free parameter which controls the relative weights of the triadic interactions between different helical Fourier modes. The transition from a forward to inverse cascade is shown to occur at a critical point in a discontinuous manner with diverging fluctuations close to criticality. Our work thus supports the observation that purely isotropic and three dimensional flow configurations can support inverse energy transfer when interactions are altered and that inside all turbulent flows there is a competition among forward and backward transfer mechanism which might lead to multiple energy-containing turbulent states.

nlin.CD↗

arXiv2017

The onset of turbulent rotating dynamos at the low $Pm$ limit

We demonstrate that the critical magnetic Reynolds number $Rm_c$ for a turbulent non-helical dynamo in the low magnetic Prandtl number $Pm$ limit (i.e. $Pm = Rm/Re \ll 1$) can be significantly reduced if the flow is submitted to global rotation. Even for moderate rotation rates the required energy injection rate can be reduced by a factor more than $10^3$. This strong decrease of the onset is attributed to the reduction of the turbulent fluctuations that makes the flow to have a much larger cut-off length-scale compared to a non-rotating flow of the same Reynolds number. The dynamo thus behaves as if it is driven by laminar behaviour (i.e. high $Pm$ behaviour) even at high values of the Reynolds number (i.e. at low values of $Pm$). Our finding thus points into a new paradigm for the design of new liquid metal dynamo experiments.

physics.flu-dyn↗

arXiv2017

Critical Transitions in Thin Layer Turbulence

We investigate a model of thin layer turbulence that follows the evolution of the two-dimensional motions ${\bf u}_{_{2D}} (x,y)$ along the horizontal directions $(x,y)$ coupled to a single Fourier mode along the vertical direction ($z$) of the form ${\bf u}_q (x, y, z)=[v_x(x,y) \sin(qz), v_y(x,y)\sin(qz), v_z(x,y)\cos(qz)\, ]$, reducing thus the system to two coupled, two-dimensional equations. The reduced dimensionality of the model allows a thorough investigation of the transition from a forward to an inverse cascade of energy as the thickness of the layer $H=π/q$ is varied. Starting from a thick layer and reducing its thickness it is shown that two critical heights are met (i) one for which the forward unidirectional cascade (similar to three-dimensional turbulence) transitions to a bidirectional cascade transferring energy to both small and large scales and (ii) one for which the bidirectional cascade transitions to a unidirectional inverse cascade when the layer becomes very thin (similar to two-dimensional turbulence). The two critical heights are shown to have different properties close to criticality that we are able to analyze with numerical simulations for a wide range of Reynolds numbers and aspect ratios.

physics.flu-dyn↗

arXiv2016

The fate of alpha dynamos at large $Rm$

At the heart of today's solar magnetic field evolution models lies the alpha dynamo description. In this work, we investigate the fate of alpha-dynamos as the magnetic Reynolds number $Rm$ is increased. Using Floquet theory, we are able to precisely quantify mean field effects like the alpha and beta effect (i) by rigorously distinguishing dynamo modes that involve large scale components from the ones that only involve small scales, and by (ii) providing a way to investigate arbitrary large scale separations with minimal computational cost. We apply this framework to helical and non-helical flows as well as to random flows with short correlation time. Our results determine that the alpha-description is valid for $Rm$ smaller than a critical value $Rm_c$ at which small scale dynamo instability starts. When $Rm$ is above $Rm_c$ the dynamo ceases to follow the mean field description and the growth rate of the large scale modes becomes independent of the scale separation while the energy in the large scale modes is inversely proportional to the square of the scale separation. The results in this second regime do not depend on the presence of helicity. Thus alpha-type modeling for solar and stellar models needs to be reevaluated and new directions for mean field modeling are proposed.

physics.flu-dyn↗

arXiv2016

Helically Decomposed Turbulence

A decomposition of the energy and helicity fluxes in a turbulent hydrodynamic flow is proposed. The decomposition is based on the projection of the flow to a helical basis that allows to investigate separately the role of interactions among modes of different helicity. The proposed formalism is then applied in large scale numerical simulations of a non-helical and a helical flow, where the decomposed fluxes are explicitly calculated. It is shown that the total energy flux can be split in to three fluxes that independently remain constant in the inertial range. One of these fluxes that corresponds to the interactions of fields with the same helicity is negative implying the presence of an inverse cascade that is `hidden' inside the forward cascade. Similar to the energy flux the helicity flux is also shown that it can be decomposed to two fluxes that remain constant in the inertial range. Implications of these results as well possible new directions for investigations are discussed.

physics.flu-dyn↗

arXiv2016

Large-scale instabilities of helical flows

Large-scale hydrodynamic instabilities of periodic helical flows are investigated using $3$D Floquet numerical computations. A minimal three-modes analytical model that reproduce and explains some of the full Floquet results is derived. The growth-rate $σ$ of the most unstable modes (at small scale, low Reynolds number $Re$ and small wavenumber $q$) is found to scale differently in the presence or absence of anisotropic kinetic alpha (\AKA{}) effect. When an $AKA$ effect is present the scaling $σ\propto q\; Re\,$ predicted by the $AKA$ effect theory [U. Frisch, Z. S. She, and P. L. Sulem, Physica D: Nonlinear Phenomena 28, 382 (1987)] is recovered for $Re\ll 1$ as expected (with most of the energy of the unstable mode concentrated in the large scales). However, as $Re$ increases, the growth-rate is found to saturate and most of the energy is found at small scales. In the absence of \AKA{} effect, it is found that flows can still have large-scale instabilities, but with a negative eddy-viscosity scaling $σ\propto ν(b Re^2-1) q^2$. The instability appears only above a critical value of the Reynolds number $Re^{c}$. For values of $Re$ above a second critical value $Re^{c}_{S}$ beyond which small-scale instabilities are present, the growth-rate becomes independent of $q$ and the energy of the perturbation at large scales decreases with scale separation. A simple two-modes model is derived that well describes the behaviors of energy concentration and growth-rates of various unstable flows. In the non-linear regime (at moderate values of $Re$) and in the presence of scale separation, the forcing scale and the largest scales of the system are found to be the most dominant energetically.

physics.flu-dyn↗

arXiv2016

Fluctuations of electrical conductivity: a new source for astrophysical magnetic fields

We consider the generation of magnetic field by the flow of a fluid for which the electrical conductivity is nonuniform. A new amplification mechanism is found which leads to dynamo action for flows much simpler than those considered so far. In particular, the fluctuations of the electrical conductivity provide a way to bypass anti-dynamo theorems. For astrophysical objects, we show through three-dimensional global numerical simulations that the temperature-driven fluctuations of the electrical conductivity can amplify an otherwise decaying large scale equatorial dipolar field. This effect could play a role for the generation of the unusually tilted magnetic field of the iced giants Neptune and Uranus.

physics.flu-dyn↗

arXiv2015

Optimal lengthscale for a turbulent dynamo

We demonstrate that there is an optimal forcing length scale for low Prandtl number dynamo flows, that can significantly reduce the required energy injection rate. The investigation is based on simulations of the induction equation in a periodic box of size $2πL$. The flows considered are turbulent ABC flows forced at different forcing wavenumbers $k_f$ simulated using a subgrid turbulent model. The critical magnetic Reynolds number $Rm_c^T$ decreases as the forcing wavenumber $k_f$ increases from the smallest allowed $k_{min}=1/L$. At large $k_f$ on the other hand, $Rm_c^T$ increases with the forcing wavenumber as $Rm_c^T \propto \sqrt{ k_f}$ in agreement with mean-field scaling prediction. At $k_f L\simeq 4$ an optimal wavenumber is reached where $Rm_c^T$ obtains its minimum value. At this optimal wavenumber $Rm_c^T$ is smaller by more than a factor of ten than the case forced in $k_f=1$. This leads to a reduction of the energy injection rate by three orders of magnitude when compared to the case that the system is forced in the largest scales and thus provides a new strategy for the design of a fully turbulent experimental dynamo.

physics.flu-dyn↗

arXiv2015

Transition from 2D HD to 2D MHD turbulence

We investigate the critical transition from an inverse cascade of energy to a forward energy cascade in a two-dimensional magneto-hydrodynamic flow as the ratio of magnetic to mechanical forcing amplitude is varied. It is found that the critical transition is the result of two competing processes. The first process is due to hydrodynamic interactions, cascades the energy to the large scales. The second process couples small scale magnetic fields to large scale flows transferring the energy back to the small scales via a non-local mechanism. At marginality the two cascades are both present and cancel each other. The phase space diagram of the transition is sketched.

physics.flu-dyn↗

arXiv2015

Statistical equilibria of large scales in dissipative hydrodynamic turbulence

We present a numerical study of the statistical properties of three-dimensional dissipative turbulent flows at scales larger than the forcing scale. Our results indicate that the large scale flow can be described to a large degree by the truncated Euler equations with the predictions of the zero flux solutions given by absolute equilibrium theory, both for helical and non-helical flows. Thus, the functional shape of the large scale spectra can be predicted provided that scales sufficiently larger than the forcing length scale but also sufficiently smaller than the box size are examined. Deviations from the predictions of absolute equilibrium are discussed.

physics.flu-dyn↗

arXiv2014

Rotating Taylor-Green Flow

The steady state of a forced Taylor-Green flow is investigated in a rotating frame of reference. The investigation involves the results of 184 numerical simulations for different Reynolds number $\mathrm{Re}_{_{F}}$ and Rossby number $\mathrm{Ro}_{_F}$. The large number of examined runs allows a systematic study that enables the mapping of the different behaviors observed to the parameter space ($\mathrm{Re}_{_{F}},\mathrm{Ro}_{_{F}}$), and the examination of different limiting procedures for approaching the large $\mathrm{Re}_{_{F}}$ small $\mathrm{Ro}_{_F}$ limit. Four distinctly different states were identified: {\it laminar, intermittent bursts, quasi-2D condensates, and weakly rotating turbulence}. These four different states are separated by power-law boundaries $\mathrm{Ro}_{_F} \propto \mathrm{Re}_{_{F}}^{-γ}$ in the small $\mathrm{Ro}_{_F}$ limit. In this limit, the predictions of asymptotic expansions can be directly compared to the results of the direct numerical simulations. While the first order expansion is in good agreement with the results of the linear stability theory, it fails to reproduce the dynamical behavior of the quasi-2D part of the flow in the nonlinear regime, indicating that higher order terms in the expansion need to be taken in to account. The large number of simulations allows also to investigate the scaling that relates the amplitude of the fluctuations with the energy dissipation rate and the control parameters of the system for the different states of the flow. Different scaling was observed for different states of the flow, that are discussed in detail. The present results clearly demonstrate that the limits small Rossby and large Reynolds do not commute and it is important to specify the order in which they are taken.

physics.flu-dyn↗

arXiv2014

On the edge of an inverse cascade

We demonstrate that systems with a parameter-controlled inverse cascade can exhibit critical behavior for which at the critical value of the control parameter the inverse cascade stops. In the vicinity of such a critical point standard phenomenological estimates for the energy balance will fail since the energy flux towards large length scales becomes zero. We demonstrate these concepts using the computationally tractable model of two-dimensional magneto-hydrodynamics in a periodic box. In the absence of any external magnetic forcing the system reduces to hydrodynamic fluid turbulence with an inverse energy cascade. In the presence of strong magnetic forcing the system behaves as 2D magneto-hydrodynamic turbulence with forward energy cascade. As the amplitude of the magnetic forcing is varied a critical value is met for which the energy flux towards the large scales becomes zero. Close to this point the energy flux scales as a power law with the departure from the critical point and the normalized amplitude of the fluctuations diverges. Similar behavior is observed for the flux of the square vector potential for which no inverse flux is observed for weak magnetic forcing, while a finite inverse flux is observed for magnetic forcing above the critical point. We conjecture that this behavior is generic for systems of variable inverse cascade.

physics.flu-dyn↗

arXiv2014

Self-organisation and non-linear dynamics in driven magnetohydrodynamic turbulent flows

Magnetohydrodynamic turbulent flows driven by random mechanical and electromagnetic external forces of zero helicities are investigated by means of direct numerical simulations. It is shown that despite the absence of helicities in the forcing, the system is attracted to self-organized helical states that exhibit laminar behaviour despite the large value of the Reynolds numbers examined. We demonstrate that the correlation time of the external forces is controlling the time spent on these states, i.e. for short correlation times the system remains in the turbulent state while as the correlation time is increased the system spends more and more time in the self-organised states. As a result, time averaged statistics can significantly be affected by the time spent on these states. These results have important theoretical implications for the understanding of the suppression of non-linearities in plasma fusion devises as well as in astrophysical observations.

physics.plasm-ph↗

arXiv2014

The role of dissipation in flexural wave turbulence: from experimental spectrum to Kolmogorov-Zakharov spectrum

The Weak Turbulence Theory has been applied to waves in thin elastic plates obeying the Föppl-Von Kármán dynamical equations. Subsequent experiments have shown a strong discrepancy between the theoretical predictions and the measurements. Both the dynamical equations and the Weak Turbulence Theory treatment require some restrictive hypotheses. Here a direct numerical simulation of the Föppl-Von Kármán equations is performed and reproduces qualitatively and quantitatively the experimental results when the experimentally measured damping rate of waves $γ_\mathbf{k}= a + bk^2$ is used. This confirms that the Föppl-Von Kármán equations are a valid theoretical framework to describe our experiments. When we progressively tune the dissipation so that to localize it at the smallest scales, we observe a gradual transition between the experimental spectrum and the Kolmogorov-Zakharov prediction. Thus it is shown dissipation has a major influence on the scaling properties stationary solutions of weakly non linear wave turbulence.

nlin.CD↗

arXiv2013

The signature of initial conditions on magnetohydrodynamic turbulence

We demonstrate that special correlations in the initial conditions of freely evolving, homogeneous magnetohydrodynamic (MHD) turbulence can lead to the formation of enormous current sheets. These coherent structures are observed at the peak of the energy dissipation rate and are the carriers of long-range correlations despite all the non-linear interactions during the formation of turbulence. Even though the largest scale separation has been achieved at this point, these structures are coherent with a size that spans our computational domain dominating the scaling of the energy spectrum, which follows a $E \propto k^{-2}$ power law. As Reynolds number increases curling of the current sheets, due to Kelvin-Helmhotlz type instabilities and reconnection, modifies the scaling of the energy spectrum from $k^{-2}$ towards $k^{-5/3}$. This transition occurs at the highest Reynolds numbers of direct numerical simulations with resolutions up to $2048^3$ grid points. Finite Reynolds number behaviour is observed due to the initial correlations without reaching a finite asymptote for the energy dissipation rate and with an unexpected scaling between the Taylor and the integral scale Reynolds numbers, i.e. $Re_λ\propto Re^{2/3}$. Our results, therefore, demonstrate that even state-of-the-art numerical simulations of the highest resolution can be influenced by the choice of initial conditions and consequently they are inadequate to deduce unequivocally the fate of universality in MHD turbulence.

physics.flu-dyn↗