Spectral analysis of structure functions and their scaling exponents in forced isotropic turbulence

The pseudospectral method, in conjunction with a new technique for obtaining scaling exponents $\zeta_n$ from the structure functions $S_n(r)$, is presented as an alternative to the extended self-similarity (ESS) method and the use of generalized structure functions. We propose plotting the ratio $|S_n(r)/S_3(r)|$ against the separation $r$ in accordance with a standard technique for analysing experimental data. This method differs from the ESS technique, which plots $S_n(r)$ against $S_3(r)$, with the assumption $S_3(r) \sim r$. Using our method for the particular case of $S_2(r)$ we obtain the new result that the exponent $\zeta_2$ decreases as the Taylor-Reynolds number increases, with $\zeta_2 \to 0.679 \pm 0.013$ as $R_{\lambda} \to \infty$. This supports the idea of finite-viscosity corrections to the K41 prediction for $S_2$, and is the opposite of the result obtained by ESS. The pseudospectral method also permits the forcing to be taken into account exactly through the calculation of the energy input in real space from the work spectrum of the stirring forces.Comment: 31 pages including appendices, 10 figure

Energy transfer and dissipation in forced isotropic turbulence

A model for the Reynolds number dependence of the dimensionless dissipation rate $C_{\varepsilon}$ was derived from the dimensionless K\'{a}rm\'{a}n-Howarth equation, resulting in $C_{\varepsilon}=C_{\varepsilon, \infty} + C/R_L + O(1/R_L^2)$, where $R_L$ is the integral scale Reynolds number. The coefficients $C$ and $C_{\varepsilon,\infty}$ arise from asymptotic expansions of the dimensionless second- and third-order structure functions. This theoretical work was supplemented by direct numerical simulations (DNSs) of forced isotropic turbulence for integral scale Reynolds numbers up to $R_L=5875$ ($R_\lambda=435$), which were used to establish that the decay of dimensionless dissipation with increasing Reynolds number took the form of a power law $R_L^n$ with exponent value $n = -1.000\pm 0.009$, and that this decay of $C_{\varepsilon}$ was actually due to the increase in the Taylor surrogate $U^3/L$. The model equation was fitted to data from the DNS which resulted in the value $C=18.9\pm 1.3$ and in an asymptotic value for $C_\varepsilon$ in the infinite Reynolds number limit of $C_{\varepsilon,\infty} = 0.468 \pm 0.006$.Comment: 26 pages including references and 6 figures. arXiv admin note: text overlap with arXiv:1307.457

Triad interactions and the bidirectional turbulent cascade of magnetic helicity

Using direct numerical simulations we demonstrate that magnetic helicity exhibits a bidirectional turbulent cascade at high but finite magnetic Reynolds numbers. Despite the injection of positive magnetic helicity in the flow, we observe that magnetic helicity of opposite signs is generated between large and small scales. We explain these observations by carrying out an analysis of the magnetohydrodynamic equations reduced to triad interactions using the Fourier helical decomposition. Within this framework, the direct cascade of positive magnetic helicity arises through triad interactions that are associated with small scale dynamo action, while the occurrence of negative magnetic helicity at large scales is explained through triad interactions that are related to stretch-twist-fold dynamics and small scale dynamo action, which compete with the inverse cascade of positive magnetic helicity. Our analytical and numerical results suggest that the direct cascade of magnetic helicity is a finite magnetic Reynolds number $Rm$ effect that will vanish in the limit $Rm \to \infty

Heat transport model for the transition between scaling regimes in quasistatic and full magnetoconvection

In magnetoconvection, the flow is governed by the interplay between gravitational buoyancy and the Lorentz force, with one of these forces dominating in different regimes. In this paper, we develop a model with a single adjustable parameter that accurately captures the smooth transition from a buoyancy-dominated regime to one dominated by the Lorentz force. A perturbative extension of the model accounts for distinct transition features that occur at high Prandtl numbers. We validate the model for magnetoconvection in both the quasistatic regime and at finite magnetic Reynolds numbers using data from direct numerical simulations and existing experimental data sets. The model contains a natural extension to rotating convection and offers a potential generalisation to rotating magnetoconvection

Unifying heat transport model for the transition between buoyancy-dominated and Lorentz-force-dominated regimes in quasistatic magnetoconvection

In magnetoconvection, the flow of an electromagnetically conductive fluid is driven by a combination of buoyancy forces, which create the fluid motion due to thermal expansion and contraction, and Lorentz forces, which distort the convective flow structure in the presence of a magnetic field. The differences in the global flow structures in the buoyancy-dominated and Lorentz-force-dominated regimes lead to different heat transport properties in these regimes, reflected in distinct dimensionless scaling relations of the global heat flux (Nusselt number Nu) versus the strength of buoyancy (Rayleigh number Ra) and electromagnetic forces (Hartmann number Ha). Here, we propose a theoretical model for the transition between these two regimes for the case of a static vertical magnetic field applied across a convective fluid layer confined between two isothermal, a lower warmer and an upper colder, horizontal surfaces. The model suggests that the scaling exponents γ in the buoyancy-dominated regime, Nu∼Raγ, and ξ in the Lorentz-force-dominated regime, Nu∼(Ha−2Ra)ξ, are related as ξ=γ/(1−2γ), and the onset of the transition scales with Ha−1/γRa. These theoretical results are supported by our direct numerical simulations for 10≤Ha≤2000, Prandtl number Pr=0.025 and Ra up to 109 and data from the literature

Phase Transition to Large Scale Coherent Structures in Two-Dimensional Active Matter Turbulence

The collective motion of microswimmers in suspensions induce patterns of vortices on scales that are much larger than the characteristic size of a microswimmer, attaining a state called bacterial turbulence. Hydrodynamic turbulence acts on even larger scales and is dominated by inertial transport of energy. Using an established modification of the Navier-Stokes equation that accounts for the small scale forcing of hydrodynamic flow by microswimmers, we study the properties of a dense supensions of microswimmers in two dimensions, where the conservation of enstrophy can drive an inverse cascade through which energy is accumulated on the largest scales. We find that the dynamical and statistical properties of the flow show a sharp transition to the formation of vortices at the largest length scale. The results show that 2d bacterial and hydrodynamic turbulence are separated by a subcritical phase transition.Comment: postprint versio

A-priori study of the subgrid energy transfers for small-scale dynamo in kinematic and saturation regimes

The statistical properties of the subgrid energy transfers of homogeneous small-scale dynamo are investigated during the kinematic, nonlinear and statistically saturated stages. We carry out an a priori analysis of data obtained from an ensemble of direct numerical simulations on $512^3$ grid points and at unity magnetic Prandtl number. In order to provide guidance for subgrid-scale (SGS) modelling of different types of energy transfer that occur in magnetohydrodynamic dynamos, we consider the SGS stress tensors originating from inertial dynamics, Lorentz force and the magnetic induction separately. We find that all SGS energy transfers display some degree of intermittency as quantified by the scale-dependence of their respective probability density functions. Concerning the inertial dynamics, a depletion of intermittency occurs in presence of a saturated dynamo.Comment: postprint versio

From two-dimensional to three-dimensional turbulence through two-dimensional three-component flows

The relevance of two-dimensional three-components (2D3C) flows goes well beyond their occurrence in nature, and a deeper understanding of their dynamics might be also helpful in order to shed further light on the dynamics of pure two-dimenional (2D) or three-dimensional (3D) flows and vice versa. The purpose of the present paper is to make a step in this direction through a combination of numerical and analytical work. The analytical part is mainly concerned with the behavior of 2D3C flows in isolation and the connection between the geometry of the nonlinear interactions and the resulting energy transfer directions. Special emphasis is given to the role of helicity. We show that a generic 2D3C flow can be described by two stream functions corresponding to the two helical sectors of the velocity field. The projection onto one helical sector (homochiral flow) leads to a full 3D constraint and to the inviscid conservation of the total (three dimensional) enstrophy and hence to an inverse cascade of the kinetic energy of the third component also. The coupling between several 2D3C flows is studied through a set of suitably designed direct numerical simulations (DNS), where we also explore the transition between 2D and fully 3D turbulence. In particular, we find that the coupling of three 2D3C flows on mutually orthogonal planes subject to small-scale forcing leads to stationary 3D out-of-equilibrium dynamics at the energy containing scales. The transition between 2D and 3D turbulence is then explored through adding a percentage of fully 3D Fourier modes in the volume.Comment: postprint versio

Condensate formation and multiscale dynamics in two-dimensional active suspensions

The collective effects of microswimmers in active suspensions result in active turbulence, a spatiotemporally chaotic dynamics at mesoscale, which is characterized by the presence of vortices and jets at scales much larger than the characteristic size of the individual active constituents. To describe this dynamics, Navier-Stokes-based one-fluid models driven by small-scale forces have been proposed. Here, we provide a justification of such models for the case of dense suspensions in two dimensions (2d). We subsequently carry out an in-depth numerical study of the properties of one-fluid models as a function of the active driving in view of possible transition scenarios from active turbulence to large-scale pattern, referred to as condensate, formation induced by the classical inverse energy cascade in Newtonian 2d turbulence. Using a one-fluid model it was recently shown (Linkmann et al., Phys. Rev. Lett. (in press)) that two-dimensional active suspensions support two non-equilibrium steady states, one with a condensate and one without, which are separated by a subcritical transition. Here, we report further details on this transition such as hysteresis and discuss a low-dimensional model that describes the main features of the transition through nonlocal-in-scale coupling between the small-scale driving and the condensate