It is known that rapidly rotating turbulent flows are characterized by the emergence of simultaneous upscale and downscale energy transfer. Indeed, both numerics and experiments show the formation of large-scale anisotropic vortices together with the development of small-scale dissipative structures. However the organization of interactions leading to this complex dynamics remains unclear. Two different mechanisms are known to be able to transfer energy upscale in a turbulent flow. The first is characterized by two-dimensional interactions among triads lying on the twodimensional, three-component (2D3C)/slow manifold, namely on the Fourier plane perpendicular to the rotation axis. The second mechanism is three-dimensional and consists of interactions between triads with the same sign of helicity (homochiral). Here, we present a detailed numerical study of rotating flows using a suite of high Reynolds number direct numerical simulations (DNS) within different parameter regimes to analyze both upscale and downscale cascade ranges. We find that the upscale cascade at wave numbers close to the forcing scale is generated by increasingly dominant homochiral interactions which couple the three-dimensional bulk and the 2D3C plane. This coupling produces an accumulation of energy in the 2D3C plane, which then transfers energy to smaller wave numbers thanks to the two-dimensional mechanism. In the forward cascade range, we find that the energy transfer is dominated by heterochiral triads and is dominated primarily by interaction within the fast manifold where kz = 0. We further analyze the energy transfer in different regions in the real-space domain. In particular, we distinguish high-strain from high-vorticity regions and we uncover that while the mean transfer is produced inside regions of strain, the rare but extreme events of energy transfer occur primarily inside the large-scale column vortices. PACS numbers: * postprint version of the manuscript published in Phys. Rev. Fluids 3, 034802, (2018) † Electronic address: michele.buzzicotti@roma2.infn.it ‡ Electronic address: hussein@rochester.edu § Electronic address: biferale@roma2.infn.it ¶ Electronic address: linkmann@roma2.infn.it arXiv:1711.07054v2 [physics.flu-dyn]

A model for the Reynolds number dependence of the dimensionless dissipation rate C ε was derived from the dimensionless Kármán-Howarth equation, resulting in, where R L is the integral scale Reynolds number. The coefficients C and C ε,∞ 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 λ = 435), which were used to establish that the decay of dimensionless dissipation with increasing Reynolds number took the form of a power law R n L with exponent value n = −1.000 ± 0.009, and that this decay of C ε 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 ± 1.3 and in an asymptotic value for C ε in the infinite Reynolds number limit of C ε,∞ = 0.468 ± 0.006.

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. PACS numbers: 47.52.+j; 05.40.JcThin layers of bacteria in their planctonic phase form vortical structures that are reminiscent of vortices in turbulent flows [1][2][3]. This state has been called "bacterial turbulence" [1] because of the shape and form of the patterns, and has been seen in many swimming microorganisms [1-3] and in active nematics [4][5][6]. Bacterial turbulence usually appears on scales much smaller than those of hydrodynamic turbulence, with its inertial range dynamics and the characteristic energy cascades [7]. A measure of this separation is the Reynolds number, which is of order 10 −4 − 10 −6 for an isolated swimmer in a fluid at rest [8] and typically several tens of thousands in hydrodynamic turbulence. Recent studies of the rheology of bacterial suspensions have indicated, however, that the active motion of pusher-type bacteria can lower considerably the effective viscosity of the suspension [9][10][11][12][13][14], to the point where it approaches zero, reaching an active-matter induced "superfluid" phase where the energy input from active processes compensates viscous dissipation [15,16]. In such a situation the collective action of microswimmers can produce a dynamics that may reach the transition to the inertial range in fluid flow, as evidenced by the breaking of helical symmetry in 3d [17]. In two dimensions, a possible connection to hydrodynamic turbulence is particularly intriguing because the energy cascade proceeds from small to large scales and can result in an accumulation of energy at the largest scales admitted by the domain, thereby forming a so-called condensate [18][19][20]. If bacterial turbulence can couple to hydrodynamic turbulence, then the inverse cascade in 2d provides a mechanism by which even larger scales can be driven. We here discuss the conditions under which such a coupling between bacterial and hydrodynamic turbulence can occur.It has recently been shown that the pattern-formation process associated with bacterial turbulence can be captured by minimal models where activity in encoded in suitable forcing terms in the dynamical equations [17,21].Most previo...

Spectral transfer processes in homogeneous magnetohydrodynamic (MHD) turbulence are investigated analytically by decomposition of the velocity and magnetic fields in Fourier space into helical modes. Steady solutions of the dynamical system which governs the evolution of the helical modes are determined, and a stability analysis of these solutions is carried out. The interpretation of the analysis is that unstable solutions lead to energy transfer between the interacting modes while stable solutions do not. From this, a dependence of possible interscale energy and helicity transfers on the helicities of the interacting modes is derived. As expected from the inverse cascade of magnetic helicity in 3-D MHD turbulence, mode interactions with like helicities lead to transfer of energy and magnetic helicity to smaller wavenumbers. However, some interactions of modes with unlike helicities also contribute to an inverse energy transfer. As such, an inverse energy cascade for non-helical magnetic fields is shown to be possible. Furthermore, it is found that high values of the cross-helicity may have an asymmetric effect on forward and reverse transfer of energy, where forward transfer is more quenched in regions of high cross-helicity than reverse transfer. This conforms with recent observations of solar wind turbulence. For specific helical interactions the relation to dynamo action is established. The present analysis provides new theoretical insights into physical processes where inverse cascade and dynamo action are involved, such as the evolution of cosmological and astrophysical magnetic fields and laboratory plasmas.

The effects of different filtering strategies on the statistical properties of the resolvedto-subfilter scale (SFS) energy transfer are analysed in forced homogeneous and isotropic turbulence. We carry out a priori analyses of the statistical characteristics of SFS energy transfer by filtering data obtained from direct numerical simulations with up to 2048 3 grid points as a function of the filter cut-off scale. In order to quantify the dependence of extreme events and anomalous scaling on the filter, we compare a sharp Fourier Galerkin projector, a Gaussian filter and a novel class of Galerkin projectors with non-sharp spectral filter profiles. Of interest is the importance of Galilean invariance and we confirm that local SFS energy transfer displays intermittency scaling in both skewness and flatness as a function of the cut-off scale. Furthermore, we quantify the robustness of scaling as a function of the filtering type.

We present a numerical and analytical study of incompressible homogeneous conducting fluids using a helical Fourier representation. We analytically study both small-and large-scale dynamo properties, as well as the inverse cascade of magnetic helicity, in the most general minimal subset of interacting velocity and magnetic fields on a closed Fourier triad. We mainly focus on the dependency of magnetic field growth as a function of the distribution of kinetic and magnetic helicities among the three interacting wavenumbers. By combining direct numerical simulations of the full magnetohydrodynamics equations with the helical Fourier decomposition we numerically confirm that in the kinematic dynamo regime the system develops a large-scale magnetic helicity with opposite sign compared to the small-scale kinetic helicity, a sort of triad-by-triad α-effect in Fourier space. Concerning the small-scale perturbations, we predict theoretically and confirm numerically that the largest instability is achieved for the magnetic component with the same helicity of the flow, in agreement with the Stretch-Twist-Fold mechanism. Vice versa, in presence of a Lorentz feedback on the velocity, we find that the inverse cascade of magnetic helicity is mostly local if magnetic and kinetic helicities have opposite sign, while it is more nonlocal and more intense if they have the same sign, as predicted by the analytical approach. Our analytical and numerical results further demonstrate the potential of the helical Fourier decomposition to elucidate the entangled dynamics of magnetic and kinetic helicities both in fully developed turbulence and in laminar flows.

A model equation for the Reynolds number dependence of the dimensionless dissipation rate in freely decaying homogeneous magnetohydrodynamic turbulence in the absence of a mean magnetic field is derived from the real-space energy balance equation, leading to Cε = Cε,∞ + C/R− + O(1/R 2 − )), where R− is a generalized Reynolds number. The constant Cε,∞ describes the total energy transfer flux. This flux depends on magnetic and cross helicities, because these affect the nonlinear transfer of energy, suggesting that the value of Cε,∞ is not universal. Direct numerical simulations were conducted on up to 2048 3 grid points, showing good agreement between data and the model. The model suggests that the magnitude of cosmological-scale magnetic fields is controlled by the values of the vector field correlations. The ideas introduced here can be used to derive similar model equations for other turbulent systems.PACS numbers: 47.65. 52.30.Cv, 47.27.Jv, 47.27.Gs Magnetohydrodynamic (MHD) turbulence is present in many areas of physics, ranging from industrial applications such as liquid metal technology to nuclear fusion and plasma physics, geo-, astro-and solar physics, and even cosmology. The numerous different MHD flow types that arise in different settings due to anisotropy, alignment, different values of the diffusivities, to name only a few, lead to the question of universality in MHD turbulence, which has been the subject of intensive research by many groups [1][2][3][4][5][6][7][8][9][10][11][12]. The behavior of the (dimensionless) dissipation rate is connected to this problem, in the sense that correlation (alignment) of the different vector fields could influence the energy transfer across the scales [2,13,14], and thus possibly the amount of energy that is eventually dissipated at the small scales.For neutral fluids it has been known for a long time that the dimensionless dissipation rate in forced and freely decaying homogeneous isotropic turbulence tends to a constant with increasing Reynolds number. The first evidence for this was reported by Batchelor [15] in 1953, while the experimental results reviewed by Sreenivasan in 1984 [16], and subsequent experimental and numerical work by many groups, established the now wellknown characteristic curve of the dimensionless dissipation rate against Reynolds number: see [17][18][19][20] and references therein. For statistically steady isotropic turbulence, the theoretical explanation of this curve was recently found to be connected to the energy balance equation for forced turbulent flows [19], where the asymptote describes the maximal inertial transfer flux in the limit of infinite Reynolds number.For freely decaying MHD, recent results suggest that the temporal maximum of the total dissipation tends to a constant value with increasing Reynolds number. The first evidence for this behavior in MHD was put forward in 2009 by Mininni and Pouquet [21] using results from direct numerical simulations (DNSs) of isotropic MHD turbulence. The temporal maximum of the total ...

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 onefluid 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.