arXiv subjects

P. D. Mininni

Publications and source records attributed to P. D. Mininni.

At least 55 records · Page 3Linked to original sources

arXiv2012

Inverse cascades in turbulence and the case of rotating flows

We first summarize briefly several properties concerning the dynamics of two-dimensional (2D) turbulence, with an emphasis on the inverse cascade of energy to the largest accessible scale of the system. In order to study a similar phenomenon in three-dimensional (3D) turbulence undergoing strong solid-body rotation, we test a previously developed Large Eddy Simulation (LES) model against a high-resolution direct numerical simulation of rotating turbulence on a grid of $3072^3$ points. We then describe new numerical results on the inverse energy cascade in rotating flows using this LES model and contrast the case of 2D versus 3D forcing, as well as non-helical forcing (i.e., with weak overall alignment between velocity and vorticity) versus the fully helical Beltrami case, both for deterministic and random forcing. The different scaling of the inverse energy cascade can be attributed to the dimensionality of the forcing, with, in general, either a $k_{\perp}^{-3}$ or a $k_{\perp}^{-5/3}$ energy spectrum of slow modes at large scales, perpendicular referring to the direction of rotation. We finally invoke the role of shear in the case of a strongly anisotropic deterministic forcing, using the so-called ABC flow.

physics.flu-dyn↗

arXiv2012

Isotropisation at small scales of rotating helically-driven turbulence

We present numerical evidence of how three-dimensionalization occurs at small scale in rotating turbulence with Beltrami (ABC) forcing, creating helical flow. The Zeman scale $\ell_Ω$ at which the inertial and eddy turn-over times are equal is more than one order of magnitude larger than the dissipation scale, with the relevant domains (large-scale inverse cascade of energy, dual regime in the direct cascade of energy $E$ and helicity $H$, and dissipation) each moderately resolved. These results stem from the analysis of a large direct numerical simulation on a grid of $3072^3$ points, with Rossby and Reynolds numbers respectively equal to 0.07 and $2.7\times 10^4$. At scales smaller than the forcing, a helical wave-modulated inertial law for the energy and helicity spectra is followed beyond $\ell_Ω$ by Kolmogorov spectra for $E$ and $H$. Looking at the two-dimensional slow manifold, we also show that the helicity spectrum breaks down at $\ell_Ω$, a clear sign of recovery of three-dimensionality in the small scales.

physics.flu-dyn↗

arXiv2011

On the emergence of very long time fluctuations and 1/f noise in ideal flows

This study shows the connection between three previously observed but seemingly unrelated phenomena in hydrodynamic (HD) and magnetohydrodynamic (MHD) turbulent flows, involving the emergence of fluctuations occurring on very long time scales: the low-frequency 1/f noise in the power frequency spectrum, the delayed ergodicity of complex valued amplitude fluctuations in wavenumber space, and the spontaneous flippings or reversals of large scale fields. Direct numerical simulations of ideal MHD and HD are employed in three space dimensions, at low resolution, for long periods of time, and with high accuracy to study several cases: Different geometries, presence of rotation and/or a uniform magnetic field, and different values of the associated conserved global quantities. It is conjectured that the origin of all these long-time phenomena is rooted in the interaction of the longest wavelength fluctuations available to the system with fluctuations at much smaller scales. The strength of this non-local interaction is controlled either by the existence of conserved global quantities with a back-transfer in Fourier space, or by the presence of a slow manifold in the dynamics.

physics.flu-dyn↗

arXiv2011

High Reynolds number magnetohydrodynamic turbulence using a Lagrangian model

With the help of a model of magnetohydrodynamic (MHD) turbulence tested previously, we explore high Reynolds number regimes up to equivalent resolutions of 6000^3 grid points in the absence of forcing and with no imposed uniform magnetic field. For the given initial condition chosen here, with equal kinetic and magnetic energy, the flow ends up being dominated by the magnetic field, and the dynamics leads to an isotropic Iroshnikov-Kraichnan energy spectrum. However, the locally anisotropic magnetic field fluctuations perpendicular to the local mean field follow a Kolmogorov law. We find that the ratio of the eddy turnover time to the Alfven time increases with wavenumber, contrary to the so-called critical balance hypothesis. Residual energy and helicity spectra are also considered; the role played by the conservation of magnetic helicity is studied, and scaling laws are found for the magnetic helicity and residual helicity spectra. We put these results in the context of the dynamics of a globally isotropic MHD flow which is locally anisotropic because of the influence of the strong large-scale magnetic field, leading to a partial equilibration between kinetic and magnetic modes for the energy and the helicity.

physics.flu-dyn↗

arXiv2011

Conformal invariance in three-dimensional rotating turbulence

We examine three--dimensional turbulent flows in the presence of solid-body rotation and helical forcing in the framework of stochastic Schramm-Löwner evolution curves (SLE). The data stems from a run on a grid of $1536^3$ points, with Reynolds and Rossby numbers of respectively 5100 and 0.06. We average the parallel component of the vorticity in the direction parallel to that of rotation, and examine the resulting $<ω_\textrm{z}>_\textrm{z}$ field for scaling properties of its zero-value contours. We find for the first time for three-dimensional fluid turbulence evidence of nodal curves being conformal invariant, belonging to a SLE class with associated Brownian diffusivity $κ=3.6\pm 0.1$. SLE behavior is related to the self-similarity of the direct cascade of energy to small scales in this flow, and to the partial bi-dimensionalization of the flow because of rotation. We recover the value of $κ$ with a heuristic argument and show that this value is consistent with several non-trivial SLE predictions.

nlin.AO↗

arXiv2011

The decay of turbulence in rotating flows

We present a parametric space study of the decay of turbulence in rotating flows combining direct numerical simulations, large eddy simulations, and phenomenological theory. Several cases are considered: (1) the effect of varying the characteristic scale of the initial conditions when compared with the size of the box, to mimic "bounded" and "unbounded" flows; (2) the effect of helicity (correlation between the velocity and vorticity); (3) the effect of Rossby and Reynolds numbers; and (4) the effect of anisotropy in the initial conditions. Initial conditions include the Taylor-Green vortex, the Arn'old-Beltrami-Childress flow, and random flows with large-scale energy spectrum proportional to $k^4$. The decay laws obtained in the simulations for the energy, helicity, and enstrophy in each case can be explained with phenomenological arguments that separate the decay of two-dimensional from three-dimensional modes, and that take into account the role of helicity and rotation in slowing down the energy decay. The time evolution of the energy spectrum and development of anisotropies in the simulations are also discussed. Finally, the effect of rotation and helicity in the skewness and kurtosis of the flow is considered.

physics.flu-dyn↗

arXiv2010

Experimental evidence of conformal invariance in soap film turbulent flows

We present experimental evidence of statistical conformal invariance in isocontours of fluid thickness in experiments of two-dimensional turbulence using soap films. A Schlieren technique is used to visualize regions of the flow with constant film thickness, and association of isocontours with Schramm-Löwner evolution (SLE) is used to identify conformal invariance. In experiments where an inverse energy cascade develops, statistical evidence is consistent with such an association. The diffusivity of the associated one-dimensional Brownian process is close to 8/3, a value previously identified in isocontours of vorticity in high-resolution numerical simulations of two-dimensional turbulence (D. Bernard et al., Nature Phys. 2, 124, 2006). In experiments where the inverse energy cascade is not sufficiently developed, no statistical evidence of conformal invariance is found.

physics.flu-dyn↗

arXiv2010

Large scale behavior and statistical equilibria in rotating flows

We examine long-time properties of the ideal dynamics of three--dimensional flows, in the presence or not of an imposed solid-body rotation and with or without helicity (velocity-vorticity correlation). In all cases the results agree with the isotropic predictions stemming from statistical mechanics. No accumulation of excitation occurs in the large scales, even though in the dissipative rotating case anisotropy and accumulation, in the form of an inverse cascade of energy, are known to occur. We attribute this latter discrepancy to the linearity of the term responsible for the emergence of inertial waves. At intermediate times, inertial energy spectra emerge that differ somewhat from classical wave-turbulence expectations, and with a trace of large-scale excitation that goes away for long times. These results are discussed in the context of partial two-dimensionalization of the flow undergoing strong rotation as advocated by several authors.

physics.flu-dyn↗

arXiv2010

Scale interactions in magnetohydrodynamic turbulence

This article reviews recent studies of scale interactions in magnetohydrodynamic turbulence. The present day increase of computing power, which allows for the exploration of different configurations of turbulence in conducting flows, and the development of shell-to-shell transfer functions, has led to detailed studies of interactions between the velocity and the magnetic field and between scales. In particular, processes such as induction and dynamo action, the damping of velocity fluctuations by the Lorentz force, or the development of anisotropies, can be characterized at different scales. In this context we consider three different configurations often studied in the literature: mechanically forced turbulence, freely decaying turbulence, and turbulence in the presence of a uniform magnetic field. Each configuration is of interest for different geophysical and astrophysical applications. Local and non-local transfers are discussed for each case. While the transfer between scales of solely kinetic or solely magnetic energy is local, transfers between kinetic and magnetic fields are observed to be local or non-local depending on the configuration. Scale interactions in the cascade of magnetic helicity are also reviewed. Based on the results, the validity of several usual assumptions in hydrodynamic turbulence, such as isotropy of the small scales or universality, is discussed.

physics.flu-dyn↗

arXiv2009

Where we observe that helical turbulence prevails over inertial waves in forced rotating flows at high Reynolds and low Rossby numbers

We present a study of spectral laws for helical turbulence in the presence of solid body rotation up to Reynolds numbers Re~1*10^5 and down to Rossby numbers Ro~3*10^-3. The forcing function is a fully helical flow that can also be viewed as mimicking the effect of atmospheric convective motions. We test in the helical case variants of a model developed previously (Baerenzung et al. 2008a) against direct numerical simulations (DNS), using data from a run on a grid of 15363 points; we also contrast its efficiency against a spectral Large Eddy Simulation (LES) (Chollet and Lesieur 1981) as well as an under-resolved DNS. The model including the contribution of helicity to the spectral eddy dissipation and eddy noise behaves best, allowing to recover statistical features of the flow. An exploration of parameter space is then performed beyond what is feasible today using DNS. At fixed Reynolds number, lowering the Rossby number leads to a regime of wave-mediated inertial helicity cascade to small scales. However, at fixed Rossby number, increasing the Reynolds number leads the system to be dominated by turbulent energy exchanges where the role of inertial waves is to weaken the direct cascade of energy while strengthening the large scales. We find that a useful parameter for partitioning the data is NC = ReRo = U2rms/[nu Omega], with Urms, nu and Omega the rms velocity, the viscosity and the rotation rate respectively. The parameter that determines how much the energy cascade is direct or inverse in which case the cascade to small scales is predominantly that of helicity is linked to Ro.

physics.flu-dyn↗

arXiv2009

Large scale effects on the decay of rotating helical and non-helical turbulence

Decaying three-dimensional (3D) turbulence is studied via direct numerical simulations (DNS) for an isotropic non-rotating flow and for rotating flows with and without helicity. We analyze the cases of moderate Rossby number and large Reynolds number focusing on the behavior of the energy spectrum at large scales and studying its effect on the time evolution of the energy and integral scales for $E(k) \sim k^4$ initial conditions. In the non-rotating case we observe the classical energy decay rate $t^{-10/7}$ and a growth of the integral length proportional to $t^{2/7}$ in agreement with the prediction obtained assuming conservation of the Loitsyanski integral. In the presence of rotation we observe a decoupling in the decay of the modes perpendicular to the rotation axis from the remaining 3D modes. These slow modes show a behavior similar to that found in two-dimensional (2D) turbulence whereas the 3D modes decay as in the isotropic case. We phenomenologically explain the decay considering integral conserved quantities that depend on the large scale anisotropic spectrum. The decoupling of modes is also observed for a flow with a net amount of helicity. In this case, the 3D modes decay as an isotropic fluid with a constant, constrained integral length, and the 2D modes decay as a constrained rotating fluid with maximum helicity.

physics.flu-dyn↗

arXiv2009

The interplay between helicity and rotation in turbulence: implications for scaling laws and small-scale dynamics

Invariance properties of physical systems govern their behavior: energy conservation in turbulence drives a wide distribution of energy among modes, observed in geophysical or astrophysical flows. In ideal hydrodynamics, the role of helicity conservation (correlation between velocity and its curl, measuring departures from mirror symmetry) remains unclear since it does not alter the energy spectrum. However, with solid body rotation, significant differences emerge between helical and non-helical flows. We first outline several results, like the energy and helicity spectral distribution and the breaking of strict universality for the individual spectra. Using massive numerical simulations, we then show that small-scale structures and their intermittency properties differ according to whether helicity is present or not, in particular with respect to the emergence of Beltrami-core vortices (BCV) that are laminar helical vertical updrafts. These results point to the discovery of a small parameter besides the Rossby number; this could relate the problem of rotating helical turbulence to that of critical phenomena, through renormalization group and weak turbulence theory. This parameter can be associated with the adimensionalized ratio of the energy to helicity flux to small scales, the three-dimensional energy cascade being weak and self-similar.

physics.flu-dyn↗

arXiv2009

Rotating helical turbulence. Part I. Global evolution and spectral behavior

We present results from two 1536^3 direct numerical simulations of rotating turbulence where both energy and helicity are injected into the flow by an external forcing. The dual cascade of energy and helicity towards smaller scales observed in isotropic and homogeneous turbulence is broken in the presence of rotation, with the development of an inverse cascade of energy now coexisting with direct cascades of energy and helicity. In the direct cascade range, the flux of helicity dominates over that of energy at low Rossby number. These cascades have several consequences for the statistics of the flow. The evolution of global quantities and of the energy and helicity spectra is studied, and comparisons with simulations at different Reynolds and Rossby numbers at lower resolution are done to identify scaling laws.

physics.flu-dyn↗

arXiv2009

Helical rotating turbulence. Part II. Intermittency, scale invariance and structures

We study the intermittency properties of the energy and helicity cascades in two 1536^3 direct numerical simulations of helical rotating turbulence. Symmetric and anti-symmetric velocity increments are examined, as well as probability density functions of the velocity field and of the helicity density. It is found that the direct cascade of energy to small scales is scale invariant and non-intermittent, whereas the direct cascade of helicity is highly intermittent. Furthermore, the study of structure functions of different orders allows us to identify a recovery of isotropy of strong events at very small scales in the flow. Finally, we observe the juxtaposition in space of strong laminar and persistent helical columns next to time-varying vortex tangles, the former being associated with the self-similarity of energy and the latter with the intermittency of helicity.

physics.flu-dyn↗

arXiv2009

On the lack of universality in decaying magnetohydrodynamic turbulence

Using computations of three-dimensional magnetohydrodynamic (MHD) turbulence with a Taylor-Green flow, whose inherent time-independent symmetries are implemented numerically, and in the absence of either a forcing function or an imposed uniform magnetic field, we show that three different inertial ranges for the energy spectrum may emerge for three different initial magnetic fields, the selecting parameter being the ratio of the Alfven to the eddy turnover time. Equivalent computational grids range from 128^3 to 2048^3 points with a unit magnetic Prandtl number and a Taylor Reynolds number of up to 1500 at the peak of dissipation. We also show convergence of our results with Reynolds number. Our study is consistent with previous findings of a variety of energy spectra in MHD turbulence by studies performed in the presence of both a forcing term with a given correlation time and a strong, uniform magnetic field. In contrast to the previous studies, however, the ratio of characteristic time scales here can only be ascribed to the intrinsic nonlinear dynamics of the flows under study.

physics.flu-dyn↗

arXiv2009

The dynamics of unforced turbulence at high Reynolds number for Taylor-Green vortices generalized to MHD

We study decaying magnetohydrodynamics (MHD) turbulence stemming from the evolution of the Taylor-Green (TG) flow generalized recently to MHD, with equal viscosity and magnetic resistivity and up to equivalent grid resolutions of 2048^3 points. A pseudo-spectral code is used in which the symmetries of the velocity and magnetic fields have been implemented, allowing for sizable savings in both computer time and usage of memory at a given Reynolds number. The flow is non-helical, and at initial time the kinetic and magnetic energies are taken to be equal and concentrated in the large scales. After testing the validity of the method on grids of 512^3 points, we analyze the data on the large grids up to Taylor Reynolds numbers of ~2200. We find that the global temporal evolution is accelerated in MHD, compared to the corresponding neutral fluid case. We also observe an interval of time when such configurations have quasi-constant total dissipation, time during which statistical properties are determined after averaging over of the order of two turn-over times. A weak turbulence spectrum obtains which is also given in terms of its anisotropic components. Finally, we contrast the development of small-scale eddies with two other initial conditions for the magnetic field and briefly discuss the structures that develop, and which display a complex array of current and vorticity sheets with clear rolling-up and folding.

physics.flu-dyn↗

arXiv2009

Finite dissipation and intermittency in magnetohydrodynamics

We present an analysis of data stemming from numerical simulations of decaying magnetohydrodynamic (MHD) turbulence up to grid resolution of 1536^3 points and up to Taylor Reynolds number of 1200. The initial conditions are such that the initial velocity and magnetic fields are helical and in equipartition, while their correlation is negligible. Analyzing the data at the peak of dissipation, we show that the dissipation in MHD seems to asymptote to a constant as the Reynolds number increases, thereby strengthening the possibility of fast reconnection events in the solar environment for very large Reynolds numbers. Furthermore, intermittency of MHD flows, as determined by the spectrum of anomalous exponents of structure functions of the velocity and the magnetic field, is stronger than for fluids, confirming earlier results; however, we also find that there is a measurable difference between the exponents of the velocity and those of the magnetic field, as observed recently in the solar wind. Finally, we discuss the spectral scaling laws that arise in this flow.

astro-ph.SR↗

arXiv2009

Persistent cyclonic structures in self-similar turbulent flows

Invariance properties of a physical system govern its behavior: energy conservation in turbulence drives a wide distribution of energy among modes, as observed in geophysics, astrophysics and engineering. In hydrodynamic turbulence, the role of helicity (which measures departures from mirror symmetry) remains unclear since it does not alter this distribution. However, the interplay of rotation and helicity leads to significant differences. Using numerical simulations we show the occurence of long-lived laminar cyclonic vortices together with turbulent vortices, reminiscent of recent tornado observations. Furthermore, the small scales are completely self-similar with no deviations from Gaussianity. This result points to the discovery of a small parameter in rotating helical turbulence.

physics.flu-dyn↗