arXiv subjects

P. D. Mininni

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

At least 37 records · Page 2Linked to original sources

arXiv2016

Helicity, Topology and Kelvin Waves in reconnecting quantum knots

Helicity is a topological invariant that measures the linkage and knottedness of lines, tubes and ribbons. As such, it has found myriads of applications in astrophysics and solar physics, in fluid dynamics, in atmospheric sciences, and in biology. In quantum flows, where topology-changing reconnection events are a staple, helicity appears as a key quantity to study. However, the usual definition of helicity is not well posed in quantum vortices, and its computation based on counting links and crossings of vortex lines can be downright impossible to apply in complex and turbulent scenarios. We present a new definition of helicity which overcomes these problems. With it, we show that only certain reconnection events conserve helicity. In other cases helicity can change abruptly during reconnection. Furthermore, we show that these events can also excite Kelvin waves, which slowly deplete helicity as they interact nonlinearly, thus linking the theory of vortex knots with observations of quantum turbulence.

physics.flu-dyn↗

arXiv2015

The spatio-temporal spectrum of turbulent flows

Identification and extraction of vortical structures and of waves in a disorganised flow is a mayor challenge in the study of turbulence. We present a study of the spatio-temporal behavior of turbulent flows in the presence of different restitutive forces. We show how to compute and analyse the spatio-temporal spectrum from data stemming from numerical simulations and from laboratory experiments. Four cases are considered: homogeneous and isotropic turbulence, rotating turbulence, stratified turbulence, and water wave turbulence. For homogeneous and isotropic turbulence, the spectrum allows identification of sweeping by the large scale flow. For rotating and for stratified turbulence, the spectrum allows identification of the waves, precise quantification of the energy in the waves and in the turbulent eddies, and identification of physical mechanisms such as Doppler shift and wave absorption in critical layers. Finally, in water wave turbulence the spectrum shows a transition from gravity-capillary waves to bound waves as the amplitude of the forcing is increased.

physics.flu-dyn↗

arXiv2015

Passive scalars: mixing, diffusion and intermittency in helical and non-helical rotating turbulence

We use direct numerical simulations to compute structure functions, scaling exponents, probability density functions and turbulent transport coefficients of passive scalars in turbulent rotating helical and non-helical flows. We show that helicity affects the inertial range scaling of the velocity and of the passive scalar when rotation is present, with a spectral law consistent with $\sim k_{\perp}^{-1.4}$ for the passive scalar variance spectrum. This scaling law is consistent with the phenomenological argument presented in \cite{imazio2011} for rotating non-helical flows, wich states that if energy follows a $E(k)\sim k^{-n}$ law, then the passive scalar variance follows a law $V(k) \sim k^{-n_θ}$ with $n_θ=(5-n)/2$. With the second order scaling exponent obtained from this law, and using the Kraichnan model, we obtain anomalous scaling exponents for the passive scalar that are in good agreement with the numerical results. Intermittency of the passive scalar is found to be stronger than in the non-helical rotating case, a result that is also confirmed by stronger non-Gaussian tails in the probability density functions of field increments. Finally, Fick's law is used to compute the effective diffusion coefficients in the directions parallel and perpendicular to the rotation axis. Calculations indicate that horizontal diffusion decreases in the presence of helicity in rotating flows, while vertical diffusion increases. We use a mean field argument to explain this behavior in terms of the amplitude of velocity field fluctuations.

physics.flu-dyn↗

arXiv2014

Absorption of waves by large scale winds in stratified turbulence

The atmosphere is a nonlinear stratified fluid in which internal gravity waves are present. These waves interact with the flow, resulting in wave turbulence that displays important differences with the turbulence observed in isotropic and homogeneous flows. We study numerically the role of these waves and their interaction with the large scale flow, consisting of vertically sheared horizontal winds. We calculate their space and time resolved energy spectrum (a four-dimensional spectrum), and show that most of the energy is concentrated along a dispersion relation that is Doppler shifted by the horizontal winds. We also observe that when uniform winds are let to develop in each horizontal layer of the flow, waves whose phase velocity is equal to the horizontal wind speed have negligible energy. This indicates a nonlocal transfer of their energy to the mean flow. Both phenomena, the Doppler shift and the absorption of waves traveling with the wind speed, are not accounted for in current theories of stratified wave turbulence.

physics.flu-dyn↗

arXiv2014

Stably stratified turbulence in the presence of large-scale forcing

We perform two high resolution direct numerical simulations of stratified turbulence for Reynolds number equal to Re~25000 and Froude number respectively of Fr~0.1 and Fr~0.03. The flows are forced at large scale and discretized on an isotropic grid of 2048^3 points. Stratification makes the flow anisotropic and introduces two extra characteristic scales with respect to homogeneous isotropic turbulence: the buoyancy scale, L_B, and the Ozmidov scale, l_{oz}. The former is related to the number of layers that the flow develops in the direction of gravity, the latter is regarded as the scale at which isotropy is recovered. The values of L_B and l_{oz} depend on the Froude number and their absolute and relative size affect the repartition of energy among Fourier modes. By contrasting the behavior of the two simulated flows we identify some surprising similarities: after an initial transient the two flows evolve towards comparable values of the kinetic and potential enstrophy, and energy dissipation rate. Further similarities emerge at large scales: the same ratio between potential and total energy (~0.1) is spontaneously selected by the flows, and slow modes grow monotonically in both regimes causing a slow increase of the total energy in time. The axisymmetric total energy spectrum shows a wide variety of spectral slopes as a function of the angle between the imposed stratification and the wave vector. One-dimensional energy spectra computed in the direction parallel to gravity are flat from the forcing up to buoyancy scale. At intermediate scales a ~ k^{-3} parallel spectrum develops for the Fr ~ 0.03 run, whereas for weaker stratification, the saturation spectrum does not have enough scales to develop and instead one observes a power law compatible with Kolmogorov scaling. Finally, the spectrum of helicity is flat until L_B, as observed in the nocturnal planetary boundary layer.

physics.flu-dyn↗

arXiv2014

Magnetic field reversals and long-time memory in conducting flows

Employing a simple ideal magnetohydrodynamic model in spherical geometry,we show that the presence of either rotation or finite magnetic helicity is sufficient to induce dynamical reversals of the magnetic dipole moment. The statistical character of the model is similar to that of terrestrial magnetic field reversals, with the similarity being stronger when rotation is present.The connection between long time correlations, $1/f$ noise, and statistics of reversals is supported, consistent with earlier suggestions.

physics.flu-dyn↗

arXiv2014

Evidence for Bolgiano-Obukhov scaling in rotating stratified turbulence using high-resolution direct numerical simulations

We report results on rotating stratified turbulence in the absence of forcing, with large-scale isotropic initial conditions, using direct numerical simulations computed on grids of up to 4096^3 points. The Reynolds and Froude numbers are respectively equal to Re=5.4 x 10^4 and Fr=0.0242. The ratio of the Brunt-Väisälä to the inertial wave frequency, N/f, is taken to be equal to 4.95, a choice appropriate to model the dynamics of the southern abyssal ocean at mid latitudes. This gives a global buoyancy Reynolds number R_B=ReFr^2=32, a value sufficient for some isotropy to be recovered in the small scales beyond the Ozmidov scale, but still moderate enough that the intermediate scales where waves are prevalent are well resolved. We concentrate on the large-scale dynamics, for which we find a spectrum compatible with the Bolgiano-Obukhov scaling, and confirm that the Froude number based on a typical vertical length scale is of order unity, with strong gradients in the vertical. Two characteristic scales emerge from this computation, and are identified from sharp variations in the spectral distribution of either total energy or helicity. A spectral break is also observed at a scale at which the partition of energy between the kinetic and potential modes changes abruptly, and beyond which a Kolmogorov-like spectrum recovers. Large slanted layers are ubiquitous in the flow in the velocity and temperature fields, with local overturning events indicated by small Richardson numbers, and a small large-scale enhancement of energy directly attributable to the effect of rotation is also observed.

physics.flu-dyn↗

arXiv2014

Large-scale anisotropy in stably stratified rotating flows

We present results from direct numerical simulations of the Boussinesq equations in the presence of rotation and/or stratification, both in the vertical direction. The runs are forced isotropically and randomly at small scales and have spatial resolutions of up to $1024^3$ grid points and Reynolds numbers of $\approx 1000$. We first show that solutions with negative energy flux and inverse cascades develop in rotating turbulence, whether or not stratification is present. However, the purely stratified case is characterized instead by an early-time, highly anisotropic transfer to large scales with almost zero net isotropic energy flux. This is consistent with previous studies that observed the development of vertically sheared horizontal winds, although only at substantially later times. However, and unlike previous works, when sufficient scale separation is allowed between the forcing scale and the domain size, the total energy displays a perpendicular (horizontal) spectrum with power law behavior compatible with $\sim k_\perp^{-5/3}$, including in the absence of rotation. In this latter purely stratified case, such a spectrum is the result of a direct cascade of the energy contained in the large-scale horizontal wind, as is evidenced by a strong positive flux of energy in the parallel direction at all scales including the largest resolved scales.

physics.flu-dyn↗

arXiv2014

Wave turbulence in shallow water models

We study wave turbulence in shallow water flows in numerical simulations using two different approximations: the shallow water model, and the Boussinesq model with weak dispersion. The equations for both models were solved using periodic grids with up to $2048^2$ points. In all simulations, the Froude number varies between $0.015$ and $0.05$, while the Reynolds number and level of dispersion are varied in a broader range to span different regimes. In all cases, most of the energy in the system remains in the waves, even after integrating the system for very long times. For shallow flows, non-linear waves are non-dispersive and the spectrum of potential energy is compatible with $\sim k^{-2}$ scaling. For deeper (Boussinesq) flows, the non-linear dispersion relation as directly measured from the wave and frequency spectrum (calculated independently) shows signatures of dispersion, and the spectrum of potential energy is compatible with predictions of weak turbulence theory, $\sim k^{-4/3}$. In this latter case, the non-linear dispersion relation differs from the linear one and has two branches, which we explain with a simple qualitative argument. Finally, we study probability density functions of the surface height and find that in all cases the distributions are asymmetric. The probability density function can be approximated by a skewed normal distribution as well as by a Tayfun distribution.

physics.flu-dyn↗

arXiv2014

Quantification of the strength of inertial waves in a rotating turbulent flow

We quantify the strength of the waves and their impact on the energy cascade in rotating turbulence by studying the wave number and frequency energy spectrum, and the time correlation functions of individual Fourier modes in numerical simulations in three dimensions in periodic boxes. From the spectrum, we find that a significant fraction of the energy is concentrated in modes with wave frequency $ω\approx 0$, even when the external forcing injects no energy directly into these modes. However, for modes for which the period of the inertial waves $τ_ω$ is faster than the turnover time $τ_\textrm{NL}$, a significant fraction of the remaining energy is concentrated in the modes that satisfy the dispersion relation of the waves. No evidence of accumulation of energy in the modes with $τ_ω= τ_\textrm{NL}$ is observed, unlike what critical balance arguments predict. From the time correlation functions, we find that for modes with $τ_ω< τ_\textrm{sw}$ (with $τ_\textrm{sw}$ the sweeping time) the dominant decorrelation time is the wave period, and that these modes also show a slower modulation on the timescale $τ_\textrm{NL}$ as assumed in wave turbulence theories. The rest of the modes are decorrelated with the sweeping time, including the very energetic modes modes with $ω\approx 0$.

physics.flu-dyn↗

arXiv2013

Turbulence comes in bursts in stably stratified flows

There is a clear distinction between simple laminar and complex turbulent fluids. But in some cases, as for the nocturnal planetary boundary layer, a stable and well-ordered flow can develop intense and sporadic bursts of turbulent activity which disappear slowly in time. This phenomenon is ill-understood and poorly modeled; and yet, it is central to our understanding of weather and climate dynamics. We present here a simple model which shows that in stably stratified turbulence, the stronger bursts can occur when the flow is expected to be more stable. The bursts are generated by a rapid non-linear amplification of energy stored in waves, and are associated with energetic interchanges between vertical velocity and temperature (or density) fluctuations. Direct numerical simulations on grids of 2048^3 points confirm this somewhat paradoxical result of measurably stronger events for more stable flows, displayed not only in the temperature and vertical velocity derivatives, but also in the amplitude of the fields themselves.

physics.flu-dyn↗

arXiv2013

Sign cancellation and scaling in the vertical component of velocity and vorticity in rotating turbulence

We study sign changes and scaling laws in the Cartesian components of the velocity and vorticity of rotating turbulence, in the helicity, and in the components of vertically-averaged fields. Data for the analysis is provided by high-resolution direct numerical simulations of rotating turbulence with different forcing functions, with up to 1536^3 grid points, with Reynolds numbers between ~1100 and ~5100, and with moderate Rossby numbers between ~0.06 and ~8. When rotation is negligible, all Cartesian components of the velocity show similar scaling, in agreement with the expected isotropy of the flow. However, in the presence of rotation only the vertical components of the fields show clear scaling laws, with evidence of possible sign singularity in the limit of infinite Reynolds number. Horizontal components of the velocity are smooth and do not display rapid fluctuations for arbitrarily small scales. The vertical velocity and vorticity, as well as the vertically-averaged vertical velocity and vorticity, show the same scaling within error bars, in agreement with theories that predict that these quantities have the same dynamical equation for very strong rotation.

physics.flu-dyn↗

arXiv2013

Inverse cascade behavior in freely decaying two-dimensional fluid turbulence

We present results from an ensemble of 50 runs of two-dimensional hydrodynamic turbulence with spatial resolution of 2048^2 grid points, and from an ensemble of 10 runs with 4096^2 grid points. All runs in each ensemble have random initial conditions with same initial integral scale, energy, enstrophy, and Reynolds number. When both ensemble- and time-averaged, inverse energy cascade behavior is observed, even in the absence of external mechanical forcing: the energy spectrum at scales larger than the characteristic scale of the flow follows a k^(-5/3) law, with negative flux, together with a k^(-3) law at smaller scales, and a positive flux of enstrophy. The source of energy for this behavior comes from the modal energy around the energy containing scale at t=0. The results shed some light into connections between decaying and forced turbulence, and into recent controversies in experimental studies of two-dimensional and magnetohydrodynamic turbulent flows.

physics.flu-dyn↗

arXiv2013

Effective diffusivity of passive scalars in rotating turbulence

We use direct numerical simulations to compute turbulent transport coefficients for passive scalars in turbulent rotating flows. Effective diffusion coefficients in the directions parallel and perpendicular to the rotations axis are obtained by studying the diffusion of an imposed initial profile for the passive scalar, and calculated by measuring the scalar average concentration and average spatial flux as a function of time. The Rossby and Schmidt numbers are varied to quantify their effect on the effective diffusion. It is find that rotation reduces scalar diffusivity in the perpendicular direction. The perpendicular diffusion can be estimated from mixing length arguments using the characteristic velocities and lengths perpendicular to the rotation axis. Deviations are observed for small Schmidt numbers, for which turbulent transport decreases and molecular diffusion becomes more significant.

physics.flu-dyn↗

arXiv2013

Intermittency in Hall-magnetohydrodynamics with a strong guide field

We present a detailed study of intermittency in the velocity and magnetic field fluctuations of compressible Hall-magnetohydrodynamic turbulence with an external guide field. To solve the equations numerically, a reduced model valid when a strong guide field is present is used. Different values for the ion skin depth are considered in the simulations. The resulting data is analyzed computing field increments in several directions perpendicular to the guide field, and building structure functions and probability density functions. In the magnetohydrodynamic limit we recover the usual results with the magnetic field being more intermittent than the velocity field. In the presence of the Hall effect, field fluctuations at scales smaller than the ion skin depth show a substantial decrease in the level of intermittency, with close to monofractal scaling.

astro-ph.SR↗

arXiv2013

Ideal evolution of MHD turbulence when imposing Taylor-Green symmetries

We investigate the ideal and incompressible magnetohydrodynamic (MHD) equations in three space dimensions for the development of potentially singular structures. The methodology consists in implementing the four-fold symmetries of the Taylor-Green vortex generalized to MHD, leading to substantial computer time and memory savings at a given resolution; we also use a re-gridding method that allows for lower-resolution runs at early times, with no loss of spectral accuracy. One magnetic configuration is examined at an equivalent resolution of $6144^3$ points, and three different configurations on grids of $4096^3$ points. At the highest resolution, two different current and vorticity sheet systems are found to collide, producing two successive accelerations in the development of small scales. At the latest time, a convergence of magnetic field lines to the location of maximum current is probably leading locally to a strong bending and directional variability of such lines. A novel analytical method, based on sharp analysis inequalities, is used to assess the validity of the finite-time singularity scenario. This method allows one to rule out spurious singularities by evaluating the rate at which the logarithmic decrement of the analyticity-strip method goes to zero. The result is that the finite-time singularity scenario cannot be ruled out, and the singularity time could be somewhere between $t=2.33$ and $t=2.70.$ More robust conclusions will require higher resolution runs and grid-point interpolation measurements of maximum current and vorticity.

physics.plasm-ph↗

arXiv2012

Helicity dynamics in stratified turbulence in the absence of forcing

A numerical study of decaying stably-stratified flows is performed. Relatively high stratification and moderate Reynolds numbers are considered, and a particular emphasis is placed on the role of helicity (velocity-vorticity correlations). The problem is tackled by integrating the Boussinesq equations in a periodic cubical domain using different initial conditions: a non-helical Taylor-Green (TG) flow, a fully helical Beltrami (ABC) flow, and random flows with a tunable helicity. We show that for stratified ABC flows helicity undergoes a substantially slower decay than for unstratified ABC flows. This fact is likely associated to the combined effect of stratification and large scale coherent structures. Indeed, when the latter are missing, as in random flows, helicity is rapidly destroyed by the onset of gravitational waves. A type of large-scale dissipative "cyclostrophic" balance can be invoked to explain this behavior. When helicity survives in the system it strongly affects the temporal energy decay and the energy distribution among Fourier modes. We discover in fact that the decay rate of energy for stratified helical flows is much slower than for stratified non-helical flows and can be considered with a phenomenological model in a way similar to what is done for unstratified rotating flows. We also show that helicity, when strong, has a measurable effect on the Fourier spectra, in particular at scales larger than the buoyancy scale for which it displays a rather flat scaling associated with vertical shear.

physics.flu-dyn↗

arXiv2012

The decay of Batchelor and Saffman rotating turbulence

The decay rate of isotropic and homogeneous turbulence is known to be affected by the large-scale spectrum of the initial perturbations, associated with at least two cannonical self-preserving solutions of the von Kármán-Howarth equation: the so-called Batchelor and Saffman spectra. The effect of long-range correlations in the decay of anisotropic flows is less clear, and recently it has been proposed that the decay rate of rotating turbulence may be independent of the large-scale spectrum of the initial perturbations. We analyze numerical simulations of freely decaying rotating turbulence with initial energy spectra $\sim k^4$ (Batchelor turbulence) and $\sim k^2$ (Saffman turbulence) and show that, while a self-similar decay cannot be identified for the total energy, the decay is indeed affected by long-range correlations. The decay of two-dimensional and three-dimensional modes follows distinct power laws in each case, which are consistent with predictions derived from the anisotropic von Kármán-Howarth equation, and with conservation of anisotropic integral quantities by the flow evolution.

physics.flu-dyn↗