Measuring intense rotation and dissipation in turbulent flows

Forecasting small-scale dynamics of fluid turbulence using deep neural networks

Turbulence in fluid flows is characterized by a wide range of interacting scales. Since the scale range increases as some power of the flow Reynolds number, a faithful simulation of the entire scale range is prohibitively expensive at high Reynolds numbers. The most expensive aspect concerns the small-scale motions; thus, major emphasis is placed on understanding and modeling them, taking advantage of their putative universality. In this work, using physics-informed deep learning methods, we present a modeling framework to capture and predict the small-scale dynamics of turbulence, via the velocity gradient tensor. The model is based on obtaining functional closures for the pressure Hessian and viscous Laplacian contributions as functions of velocity gradient tensor. This task is accomplished using deep neural networks that are consistent with physical constraints and explicitly incorporate Reynolds number dependence to account for small-scale intermittency. We then utilize a massive direct numerical simulation database, spanning two orders of magnitude in the large-scale Reynolds number, for training and validation. The model learns from low to moderate Reynolds numbers and successfully predicts velocity gradient statistics at both seen and higher (unseen) Reynolds numbers. The success of our present approach demonstrates the viability of deep learning over traditional modeling approaches in capturing and predicting small-scale features of turbulence.

Kinematic Effects on Probability Density Functions of Energy Dissipation Rate and Enstrophy in Turbulence

Direct numerical simulation and theoretical analyses showed that the probability density functions (PDFs) of the energy dissipation rate and enstrophy in turbulence are asymptotically stretched gamma distributions with the same stretching exponent, and both the left and right tails of the enstrophy PDF are longer than those of the energy dissipation rate regardless of the Reynolds number. The differences in PDF tails arise due to the kinematics, with differences in the number of terms contributing to the dissipation rate and enstrophy. Meanwhile, the stretching exponent is determined by the dynamics and likeliness of singularities.

Extreme events and instantons in Lagrangian passive scalar turbulence models

The advection and mixing of a scalar quantity by fluid flow is an important problem in engineering and natural sciences. The statistics of the passive scalar exhibit complex behavior even in the presence of a Gaussian velocity field. This paper is concerned with two Lagrangian turbulence models that are based on the recent fluid deformation model, but adding a passive scalar field with uniform mean gradient. For a range of Reynolds numbers, these models can reproduce the statistics of passive scalar turbulence. For these models, we demonstrate how events of extreme passive scalar gradients can be recovered by computing the instanton, i.e., the saddle-point configuration of the associated stochastic field theory. It allows us to both reproduce the heavy-tailed statistics associated with passive scalar turbulence, and recover the most likely mechanism leading to such extreme events. We further demonstrate that events of large negative strain in these models undergo spontaneous symmetry breaking.

Transition of fluctuations from Gaussian state to turbulent state

Variation of the statistical properties of an incompressible velocity, passive vector and passive scalar in isotropic turbulence was studied using direct numerical simulation. The structure functions of the gradients, and the moments of the dissipation rates, began to increase at about [Formula: see text] from the Gaussian state and grew rapidly at [Formula: see text] in the turbulent state. A contour map of the probability density functions (PDFs) indicated that PDF expansion of the gradients of the passive vector and passive scalar begins at around [Formula: see text], whereas that of the longitudinal velocity gradient PDF is more gradual. The left tails of the dissipation rate PDF were found to follow a power law with an exponent of 3/2 for the incompressible velocity and passive vector dissipation rates, and 1/2 for the scalar dissipation rate and the enstrophy; they remained constant for all Reynolds numbers, indicating the universality of the left tail. The analytical PDFs of the dissipation rates and enstrophy of the Gaussian state were obtained and found to be the Gamma distribution. It was shown that the number of terms contributing to the dissipation rates and the enstrophy determines the decay rates of the two PDFs for low to moderate amplitudes. This article is part of the theme issue 'Scaling the turbulence edifice (part 1)'.

Vorticity-Strain Rate Dynamics and the Smallest Scales of Turbulence

Building upon the intrinsic properties of Navier-Stokes dynamics, namely the prevalence of intense vortical structures and the interrelationship between vorticity and strain rate, we propose a simple framework to quantify the extreme events and the smallest scales of turbulence. We demonstrate that our approach is in excellent agreement with the best available data from direct numerical simulations of isotropic turbulence, with Taylor-scale Reynolds numbers up to 1300. We additionally highlight a shortcoming of prevailing intermittency models due to their disconnection from the observed correlation between vorticity and strain. Our work accentuates the importance of this correlation as a crucial step in developing an accurate understanding of intermittency in turbulence.

Measuring vorticity vector from the spinning of micro-sized mirror-encapsulated spherical particles in the flow

We demonstrate a nonintrusive technique that is capable of measuring all three-components of vorticity following small tracer particles in the flow. The vorticity is measured by resolving the instantaneous spin of the microsized spherical hydrogel particles, in which small mirrors are encapsulated. The hydrogel particles have the same density and refractive index as the working fluid-water. The trajectory of the light reflected by the spinning mirror, recorded by a single camera, is sufficient to determine the 3D rotation of the hydrogel particle, and hence the vorticity vector of the flow at the position of the particle. Compared to more conventional methods that measure vorticity by resolving velocity gradients, this technique has much higher spatial resolution. We describe the principle of the measurement, the optical setup to eliminate the effect of particle translation, the calibration procedure, and the analysis of measurement uncertainty. We validate the technique by measurements in a Taylor-Couette flow. Our technique can be used to obtain the multipoint statistics of vorticity in turbulence.

Multi-spectral optical imaging of the spatiotemporal dynamics of ionospheric intermittent turbulence

Equatorial plasma depletions have significant impact on radio wave propagation in the upper atmosphere, causing rapid fluctuations in the power of radio signals used in telecommunication and GPS navigation, thus playing a crucial role in space weather impacts. Complex structuring and self-organization of equatorial plasma depletions involving bifurcation, connection, disconnection and reconnection are the signatures of nonlinear evolution of interchange instability and secondary instabilities, responsible for the generation of coherent structures and turbulence in the ionosphere. The aims of this paper are three-fold: (1) to report the first optical imaging of reconnection of equatorial plasma depletions in the South Atlantic Magnetic Anomaly, (2) to investigate the optical imaging of equatorial ionospheric intermittent turbulence, and (3) to compare nonlinear characteristics of optical imaging of equatorial plasma depletions for two different altitudes at same times. We show that the degree of spatiotemporal complexity of ionospheric intermittent turbulence can be quantified by nonlinear studies of optical images, confirming the duality of amplitude-phase synchronization in multiscale interactions. By decomposing the analyses into North-South and East-West directions we show that the degree of non-Gaussianity, intermittency and multifractality is stronger in the North-South direction, confirming the anisotropic nature of the interchange instability. In particular, by using simultaneous observation of multi-spectral all-sky emissions from two different heights we show that the degree of non-Gaussianity and intermittency in the bottomside F-region ionosphere is stronger than the peak F-region ionosphere. Our results are confirmed by two sets of observations on the nights of 28 September 2002 and 9 November 2002.

Generalization of Turbulent Pair Dispersion to Large Initial Separations

We present a generalization of turbulent pair dispersion to large initial separations (η<r_{0}<L), by introducing a new time scale, τ_{v_{0}}, that reflects the persistence of initial conditions at time τ=0. Results of 3D Lagrangian tracking experiments at moderate Reynolds numbers show that pairs, for which the new time scale is shorter than the eddy turnover time scale, separate as in the Richardson superdiffusive regime, ⟨Δr^{2}⟩∝τ^{3}. The analysis of delay times (time interval to cross Δr=ρr_{0}) of these conditionally sampled pairs exhibit ρ^{2/5} scaling.

Statistics of velocity and temperature fluctuations in two-dimensional Rayleigh-Bénard convection

We investigate fluctuations of the velocity and temperature fields in two-dimensional (2D) Rayleigh-Bénard (RB) convection by means of direct numerical simulations (DNS) over the Rayleigh number range 10^{6}≤Ra≤10^{10} and for a fixed Prandtl number Pr=5.3 and aspect ratio Γ=1. Our results show that there exists a counter-gradient turbulent transport of energy from fluctuations to the mean flow both locally and globally, implying that the Reynolds stress is one of the driving mechanisms of the large-scale circulation in 2D turbulent RB convection besides the buoyancy of thermal plumes. We also find that the viscous boundary layer (BL) thicknesses near the horizontal conducting plates and near the vertical sidewalls, δ_{u} and δ_{v}, are almost the same for a given Ra, and they scale with the Rayleigh and Reynolds numbers as ∼Ra^{-0.26±0.03} and ∼Re^{-0.43±0.04}. Furthermore, the thermal BL thickness δ_{θ} defined based on the root-mean-square (rms) temperature profiles is found to agree with Prandtl-Blasius predictions from the scaling point of view. In addition, the probability density functions of turbulent energy ɛ_{u^{'}} and thermal ɛ_{θ^{'}} dissipation rates, calculated, respectively, within the viscous and thermal BLs, are found to be always non-log-normal and obey approximately a Bramwell-Holdsworth-Pinton distribution first introduced to characterize rare fluctuations in a confined turbulent flow and critical phenomena.

Aggregation and fragmentation dynamics in random flows: From tracers to inertial aggregates

We investigate the aggregation and fragmentation dynamics of tracers and inertial aggregates in random flows leading to steady-state size distributions. Our objective is to elucidate the impact of changes in aggregation rates due to differences in advection dynamics, especially with respect to the influence of inertial effects. This aggregation process is, at the same time, balanced by fragmentation triggered by local hydrodynamic stress. Our study employs an individual-particle-based model, tracking the position, velocity, and size of each aggregate. We compare the steady-state size distribution formed by tracers and inertial aggregates, characterized by different sizes and densities. On the one hand, we show that the size distributions change their shape with changes in the dilution rate of the suspension. On the other hand, we obtain that the size distributions formed with different binding strengths between monomers can be rescaled to a single form with the use of a characteristic size for both dense inertial particles and tracer monomers. Nevertheless, this last scaling relation also fails if the size distribution contains aggregates that behave as tracer-like and inertial-like, which results in a crossover between different scalings.

Interparticle collision mechanism in turbulence

Direct numerical simulations of particle-laden homogeneous isotropic turbulence are performed to investigate interparticle collisions in a wide range of Stokes numbers. Dynamics of the particles are described by Stokes drag including particle-particle interactions via hard-sphere collisions, while fluid turbulence is solved using a pseudospectral method. Particular emphasis is placed on interparticle-collision-based conditional statistics of rotation and dissipation rates of the fluid experienced by heavy particles, which provide essential information on the collision process. We also investigate the collision statistics of collision time interval and angle. Based on a Lamb vortex model for a vortex structure, we claim that collision events occur in the edge region for vortical structures in the intermediate-Stokes-number regime, suggesting that the sling effect enhances collision as well as clustering.

Extreme events in computational turbulence

We have performed direct numerical simulations of homogeneous and isotropic turbulence in a periodic box with 8,192(3) grid points. These are the largest simulations performed, to date, aimed at improving our understanding of turbulence small-scale structure. We present some basic statistical results and focus on "extreme" events (whose magnitudes are several tens of thousands the mean value). The structure of these extreme events is quite different from that of moderately large events (of the order of 10 times the mean value). In particular, intense vorticity occurs primarily in the form of tubes for moderately large events whereas it is much more "chunky" for extreme events (though probably overlaid on the traditional vortex tubes). We track the temporal evolution of extreme events and find that they are generally short-lived. Extreme magnitudes of energy dissipation rate and enstrophy occur simultaneously in space and remain nearly colocated during their evolution.

Enhanced enstrophy generation for turbulent convection in low-Prandtl-number fluids

Turbulent convection is often present in liquids with a kinematic viscosity much smaller than the diffusivity of the temperature. Here we reveal why these convection flows obey a much stronger level of fluid turbulence than those in which kinematic viscosity and thermal diffusivity are the same; i.e., the Prandtl number Pr is unity. We compare turbulent convection in air at Pr=0.7 and in liquid mercury at Pr=0.021. In this comparison the Prandtl number at constant Grashof number Gr is varied, rather than at constant Rayleigh number Ra as usually done. Our simulations demonstrate that the turbulent Kolmogorov-like cascade is extended both at the large- and small-scale ends with decreasing Pr. The kinetic energy injection into the flow takes place over the whole cascade range. In contrast to convection in air, the kinetic energy injection rate is particularly enhanced for liquid mercury for all scales larger than the characteristic width of thermal plumes. As a consequence, mean values and fluctuations of the local strain rates are increased, which in turn results in significantly enhanced enstrophy production by vortex stretching. The normalized distributions of enstrophy production in the bulk and the ratio of the principal strain rates are found to agree for both Prs. Despite the different energy injection mechanisms, the principal strain rates also agree with those in homogeneous isotropic turbulence conducted at the same Reynolds numbers as for the convection flows. Our results have thus interesting implications for small-scale turbulence modeling of liquid metal convection in astrophysical and technological applications.

Local dissipation scales in two-dimensional Rayleigh-Taylor turbulence

We examine the distribution of the local dissipation scale η, Q(η), and its temporal evolution in two-dimensional (2D) Rayleigh-Taylor (RT) turbulence using direct numerical simulations at small Atwood number and unit Prandtl number. Within the self-similarity regime of the mixing zone evolution, distributions of η at small scales are found to be insensitive to the large-scale anisotropy of the system and independent of position and of the temporal evolution of the mixing zone. Our results further reveal that the present measured Q(η) agrees with those previously observed in homogeneous isotropic turbulence and in turbulent pipe flows, at least for the smallest scales around the classical Kolmogorov dissipation scale. However, the RT case seems to show a different trend from the other two cases for large scales, which may attributed to the absence of the inertial-range intermittency for the velocity field in 2D RT turbulence.

Rotation rate of rods in turbulent fluid flow

The rotational dynamics of anisotropic particles advected in a turbulent fluid flow are important in many industrial and natural settings. Particle rotations are controlled by small scale properties of turbulence that are nearly universal, and so provide a rich system where experiments can be directly compared with theory and simulations. Here we report the first three-dimensional experimental measurements of the orientation dynamics of rodlike particles as they are advected in a turbulent fluid flow. We also present numerical simulations that show good agreement with the experiments and allow extension to a wide range of particle shapes. Anisotropic tracer particles preferentially sample the flow since their orientations become correlated with the velocity gradient tensor. The rotation rate is heavily influenced by this preferential alignment, and the alignment depends strongly on particle shape.

Time-resolved volumetric measurement of fine-scale coherent structures in turbulence

We present full volumetric (three-dimensional) time-resolved (+one-dimensional) measurements of the velocity field in a large water mixing tank, allowing us to assess spatial and temporal rotational energy (enstrophy) and turbulent energy dissipation intermittency. In agreement with previous studies, highly intermittent behavior is observed, with intense coherent flow structures clustering in the periphery of larger vortices. However, further to previous work the full volumetric measurements allow us to separate out the effects of advection from other effects, elucidating not only their topology but also the evolution of these intense events, through the local balance of stretching and diffusion. These findings contribute toward a better understanding of the intermittency phenomenon, which should pave the way for more accurate models of the small-scale motions based on an understanding of the underlying flow physics.

Regularity and singularity in solutions of the three-dimensional Navier–Stokes equations

Higher moments of the vorticity field Ω m ( t ) in the form of L 2 m -norms ( ) are used to explore the regularity problem for solutions of the three-dimensional incompressible Navier–Stokes equations on the domain . It is found that the set of quantities provide a natural scaling in the problem resulting in a bounded set of time averages 〈 D m 〉 T on a finite interval of time [0,  T ]. The behaviour of D m +1 / D m is studied on what are called ‘good’ and ‘bad’ intervals of [0,  T ], which are interspersed with junction points (neutral) τ i . For large but finite values of m with large initial data ( Ω m (0)≤ ϖ 0 O ( Gr 4 )), it is found that there is an upper bound which is punctured by infinitesimal gaps or windows in the vertical walls between the good/bad intervals through which solutions may escape. While this result is consistent with that of Leray (Leray 1934 Acta Math. 63 , 193–248 ( doi:10.1007/BF02547354 )) and Scheffer (Scheffer 1976 Pacific J. Math. 66 , 535–552),— this estimate for Ω m corresponds to a length scale well below the validity of the Navier–Stokes equations.

Alignment of velocity and vorticity and the intermittent distribution of helicity in isotropic turbulence

We provide an observation suggesting a strong correlation between helicity and enstrophy in fluid turbulence. Helicity statistics were obtained in a direct numerical simulation of forced isotropic turbulence. An investigation of coherent structures revealed that intermittently large local helicity was found in the core region of the coherent rotational structures, thus showing a strong correlation with local enstrophy, not dissipation. Statistics regarding the relative helicity and the correlation between velocity and vorticity conditioned on different levels of enstrophy clearly suggest that velocity and vorticity tend to be aligned in the core of the coherent structures.

Measurements of the thermal dissipation field in turbulent Rayleigh-Bénard convection

A systematic study of the thermal dissipation field and its statistical properties is carried out in turbulent Rayleigh-Bénard convection. A local temperature gradient probe consisting of four identical thermistors is made to measure the normalized thermal dissipation rate epsilonN(r) in two convection cells filled with water. The measurements are conducted over varying Rayleigh numbers Ra (8.9x10(8)<approximately Ra<approximately 9.3x10(9)) and spatial positions r across the entire cell. It is found that epsilonN(r) contains two contributions; one is generated by thermal plumes, present mainly in the plume-dominated bulk region, and decreases with increasing Ra. The other contribution comes from the mean temperature gradient, being concentrated in the thermal boundary layers, and increases with Ra. The experiment provides a complete physical picture about the thermal dissipation field and its statistical properties in turbulent convection.

Do microscopic organisms feel turbulent flows?

Microscopic organisms in aquatic environments are continuously exposed to a variety of physical and chemical conditions. Traditionally, it is accepted that due to their small size the physiology of microscopic organisms is not affected by the moving fluid at their scale. In this study, we demonstrate that the small-scale turbulence significantly modulates algal and bacterial nutrient uptake and growth in comparison to still-water control. The rate of energy dissipation emerges as a physically based scaling parameter integrating turbulence across a range of scales and microscopic organism responses at the cell level. Microbiological laboratory tests and bioassays do not consider fluid motion as an important variable in quantifying the physiological responses of microorganisms. A conceptual model of how to integrate the fluid motion in Monod-type kinetics is proposed. We anticipate our findings will encourage researchers to reconsider the laboratory protocols and modeling procedures in the analysis of microorganism physiological responses to changing physical and chemical environments by integrating the effect of turbulence.

Velocity statistics distinguish quantum turbulence from classical turbulence

By analyzing trajectories of solid hydrogen tracers, we find that the distributions of velocity in decaying quantum turbulence in superfluid 4He are strongly non-Gaussian with 1/v(3) power-law tails. These features differ from the near-Gaussian statistics of homogenous and isotropic turbulence of classical fluids. We examine the dynamics of many events of reconnection between quantized vortices and show by simple scaling arguments that they produce the observed power-law tails.

Local and nonlocal strain rate fields and vorticity alignment in turbulent flows

Local and nonlocal contributions to the total strain rate tensor S(ij) at any point x in a flow are formulated from an expansion of the vorticity field in a local spherical neighborhood of radius R centered on x. The resulting exact expression allows the nonlocal (background) strain rate tensor S(ij)(B)(x) to be obtained from S(ij)(x). In turbulent flows, where the vorticity naturally concentrates into relatively compact structures, this allows the local alignment of vorticity with the most extensional principal axis of the background strain rate tensor to be evaluated. In the vicinity of any vortical structure, the required radius R and corresponding order n to which the expansion must be carried are determined by the viscous length scale lambda(nu). We demonstrate the convergence to the background strain rate field with increasing R and n for an equilibrium Burgers vortex, and show that this resolves the anomalous alignment of vorticity with the intermediate eigenvector of the total strain rate tensor. We then evaluate the background strain field S(ij)(B)(x) in direct numerical simulations of homogeneous isotropic turbulence where, even for the limited R and n corresponding to the truncated series expansion, the results show an increase in the expected equilibrium alignment of vorticity with the most extensional principal axis of the background strain rate tensor.

Lagrangian temperature, velocity, and local heat flux measurement in Rayleigh-Bénard convection

We have developed a small, neutrally buoyant, wireless temperature sensor. Using a camera for optical tracking, we obtain simultaneous measurements of position and temperature of the sensor as it is carried along by the flow in Rayleigh-Bénard convection, at Ra approximately 10;{10}. We report on statistics of temperature, velocity, and heat transport in turbulent thermal convection. The motion of the sensor particle exhibits dynamics close to that of Lagrangian tracers in hydrodynamic turbulence. We also quantify heat transport in plumes, revealing self-similarity and extreme variations from plume to plume.

Onset of spatiotemporal chaos in a nonlinear system

We describe the onset of spatiotemporal chaos in a spatially extended nonlinear dynamical system as a result of the loss of transversal stability of an invariant manifold representing a spatially homogeneous and temporally chaotic state. The onset of spatiotemporal chaos is characterized by the switching between spatially homogeneous and nonhomogeneous states with statistical properties of on-off intermittency.

Multiscale model of gradient evolution in turbulent flows

A multiscale model for the evolution of the velocity gradient tensor in turbulence is proposed. The model couples "restricted Euler" (RE) dynamics describing gradient self-stretching with a cascade model allowing energy exchange between scales. We show that inclusion of the cascade process is sufficient to regularize the finite-time singularity of the RE dynamics. Also, the model retains geometrical features of real turbulence such as preferential alignments of vorticity and joint statistics of gradient tensor invariants. Furthermore, gradient fluctuations are non-Gaussian, skewed in the longitudinal case, and derivative flatness coefficients are in good agreement with experimental data.

Statistics of three-dimensional lagrangian turbulence

We consider a superstatistical model for a Lagrangian tracer particle in a high-Reynolds-number turbulent flow. The analytical model predictions are in excellent agreement with recent experimental data for flow between counter-rotating disks. In particular, the predicted Lagrangian scaling exponents zeta_{j} agree well with the measured exponents reported in H. Xu et al. [Phys. Rev. Lett.10.1103/PhysRevLett.96.114503 96, 114503 (2006)]. The model also correctly predicts the shape of acceleration probability densities, correlation functions, statistical dependencies between components, and explains the fact that enstrophy lags behind dissipation.

Origin of transient and intermittent dynamics in spatiotemporal chaotic systems

Nonattracting chaotic sets (chaotic saddles) are shown to be responsible for transient and intermittent dynamics in an extended system exemplified by a nonlinear regularized long-wave equation, relevant to plasma and fluid studies. As the driver amplitude is increased, the system undergoes a transition from quasiperiodicity to temporal chaos, then to spatiotemporal chaos. The resulting intermittent time series of spatiotemporal chaos displays random switching between laminar and bursty phases. We identify temporally and spatiotemporally chaotic saddles which are responsible for the laminar and bursty phases, respectively. Prior to the transition to spatiotemporal chaos, a spatiotemporally chaotic saddle is responsible for chaotic transients that mimic the dynamics of the post-transition attractor.

Lagrangian dynamics and statistical geometric structure of turbulence

The local statistical and geometric structure of three-dimensional turbulent flow can be described by the properties of the velocity gradient tensor. A stochastic model is developed for the Lagrangian time evolution of this tensor, in which the exact nonlinear self-stretching term accounts for the development of well-known non-Gaussian statistics and geometric alignment trends. The nonlocal pressure and viscous effects are accounted for by a closure that models the material deformation history of fluid elements. The resulting stochastic system reproduces many statistical and geometric trends observed in numerical and experimental 3D turbulent flows, including anomalous relative scaling.

Origin of non-Gaussian statistics in hydrodynamic turbulence

Turbulent flows are notoriously difficult to describe and understand based on first principles. One reason is that turbulence contains highly intermittent bursts of vorticity and strain rate with highly non-Gaussian statistics. Quantitatively, intermittency is manifested in highly elongated tails in the probability density functions of the velocity increments between pairs of points. A long-standing open issue has been to predict the origins of intermittency and non-Gaussian statistics from the Navier-Stokes equations. Here we derive, from the Navier-Stokes equations, a simple nonlinear dynamical system for the Lagrangian evolution of longitudinal and transverse velocity increments. From this system we are able to show that the ubiquitous non-Gaussian tails in turbulence have their origin in the inherent self-amplification of longitudinal velocity increments, and cross amplification of the transverse velocity increments.

Cluster formation in complex multi-scale systems

Based on the competition between members of a hierarchy of length scales in complex multi-scale systems, it is shown how clustering of active quantities into concentrated sets, like bubbles in a Swiss cheese, is a generic property that dominates the intermittent structure. The halo-like surfaces of these clusters have scaling exponents lower than that of their kernels, which can be as high as the domain dimension. Possible examples include spots in fluid turbulence and droplets in spin-glasses.

Intermittency of acceleration in isotropic turbulence

The intermittency of acceleration is investigated for isotropic turbulence using direct numerical simulation. Intermittently found acceleration of large magnitude always points towards the rotational axis of a vortex filament, indicating that the intermittency of acceleration is associated with the rotational motion of the vortices that causes centripetal acceleration, which is consistent with the reported result for the near-wall turbulence. Furthermore, investigation on movements of such vortex filaments provides some insights into the dynamics of local dissipation, enstrophy and acceleration. Strong dissipation partially covering the edge of a vortex filament shows weak correlation with enstrophy, while it is strongly correlated with acceleration.

Statistics of intense turbulent vorticity events

We investigate statistical properties of vorticity fluctuations in fully developed turbulence, which are known to exhibit a strong intermittent behavior. Taking as the starting point the Navier-Stokes equations with a random force term correlated at large scales, we obtain in the high Reynolds number regime a closed analytical expression for the probability distribution function of an arbitrary component of the vorticity field. The central idea underlying the analysis consists in the restriction of the velocity configurational phase-space to a particular sector where the rate of strain and the rotation tensors can be locally regarded as slow and fast degrees of freedom, respectively. This prescription is implemented along the Martin-Siggia-Rose functional framework, whereby instantons and perturbations around them are taken into account within a steepest-descent approach.

Intermittent nature of acceleration in near wall turbulence

Using direct numerical simulation of a fully developed turbulent channel flow, we investigate the behavior of acceleration near a solid wall. We find that acceleration near the wall is highly intermittent and the intermittency is in large part associated with the near wall organized coherent turbulence structures. We also find that acceleration of large magnitude is mostly directed towards the rotation axis of the coherent vortical structures, indicating that the source of the intermittent acceleration is the rotational motion associated with the vortices that causes centripetal acceleration.