This work experimentally explores the alignment of the vorticity vector and the strain-rate tensor eigenvectors at locations of extreme upscale and downscale energy transfer. We show that the turbulent von Kármán flow displays vorticity–strain alignment behaviour across a large range of Reynolds numbers, which is very similar to previous studies on homogeneous, isotropic turbulence. We observe that this behaviour is amplified for the largest downscale energy transfer events, which tend to be associated with sheet-like geometries. These events are also shown to have characteristics previously associated with high flow field nonlinearity and singularities. In contrast, the largest upscale energy transfer events display very different structures which showcase a strong preference for vortex compression. Notably, in both cases we find that these trends are strengthened as the probed scales approach the Kolmogorov scale. We then show further evidence for the argument that strain self-amplification is the most salient feature in characterising the cascade direction. Finally, we identify possible invariant behaviour for the largest energy transfer events, even at scales near the Kolmogorov scale.

Turbulent flows exhibit large intermittent fluctuations from inertial to dissipative scales, characterised by multifractal statistics and breaking the statistical self-similarity. It has recently been proposed that the Navier–Stokes turbulence restores a hidden form of scale invariance in the inertial interval when formulated for a dynamically (nonlinearly) rescaled quasi-Lagrangian velocity field. Here we show that such hidden self-similarity extends to the large-eddy-simulation (LES) approach in computational fluid dynamics (CFD). In particular, we show that classical subgrid-scale models, such as implicit or explicit Smagorinsky closures, respect the hidden scale invariance at all scales – both resolved and subgrid. In the inertial range, they reproduce the hidden scale invariance of Navier–Stokes statistics. These properties are verified very accurately by numerical simulations and, beyond CFD, turn LES into a valuable tool for fundamental turbulence research.

The wake merging of two side-by-side porous discs with varying disc spacing is investigated experimentally in a wind tunnel. Two disc designs used in the literature are employed: a non-uniform disc and a mesh disc. Hot-wire anemometry is utilised to acquire two spanwise profiles at 8 and 30 disc diameters downstream and along the centreline between the dual-disc configuration up to 40 diameters downstream. The spanwise Castaing parameter profiles confirm the appearance of rings of internal intermittency at the outermost parts of the wakes. These rings are the first feature to interact between the discs. After this point, the turbulence develops to a state whereby an inertial range is observable in the spectra. Farther downstream, the internal intermittency shows the classical features of homogeneous, isotropic turbulence. These events are repeatable and occur in the same order for both types of porous discs. This robustness allows us to develop a general map of the merging of the two wakes.

Wall turbulence consists of various sizes of vortical structures that induce flow circulation around a wide range of closed Eulerian loops. Here we investigate the multiscale properties of circulation around such loops in statistically homogeneous planes parallel to the wall. Using a high-resolution direct numerical simulation database of turbulent channels at Reynolds numbers of $Re_\tau =180$, 550, 1000 and 5200, circulation statistics are obtained in planes at different wall-normal heights. Intermittency of circulation in the planes of the outer flow ($y^+ \gtrsim 0.1Re_\tau$) takes the form of universal bifractality as in homogeneous and isotropic turbulence. The bifractal character simplifies to space-filling character close to the wall, with scaling exponents that are linear in the moment order, and lower than those given by the Kolmogorov paradigm. The probability density functions of circulation are long-tailed in the outer bifractal region, with evidence showing their invariance with respect to the loop aspect ratio, while those in the inner region are closely Gaussian. The unifractality near the wall implies that the circulation there is not intermittent in character.

Intermittency as it occurs in fast dynamos in the magnetohydrodynamics (MHD) framework is evaluated through the examination of relations between normalized moments at third order (skewness $S$) and fourth order (kurtosis $K$) for both the velocity and magnetic field, and for their local dissipations. As investigated by several authors in various physical contexts such as fusion plasmas (Krommes 2008 Phys. Plasmas 15, 030703), climate evolution (Sura & Sardeshmukh 2008 J. Phys. Oceano. 38, 639-647), fluid turbulence or rotating stratified flows (Pouquet et al. 2023 Atmosphere 14, 01375), approximate parabolic $K(S)\sim S^\alpha$ laws emerge whose origin may be related to the applicability of intermittency models to their dynamics. The results analyzed herein are obtained through direct numerical simulations of MHD flows for both Taylor–Green and Arnold–Beltrami–Childress forcing at moderate Reynolds numbers, and for up to $3.14 \times 10^5$ turn-over times. We observe for the dissipation $0.2 \lesssim \alpha \lesssim 3.0$, an evaluation that varies with the field, the forcing and when filtering for high-skewness intermittent structures. When using the She & Lévêque (1994) Phys. Rev. Lett. 72, 336-339 intermittency model, one can compute $\alpha$ analytically; we then find $\alpha \approx 2.5$, clearly differing from a (strict) parabolic scaling, a result consistent with the numerical data.

Dispersion in spatio-temporal random flows is dominated by the competition between spatial and temporal velocity resets along particle paths. This competition admits a range of normal and anomalous dispersion behaviours characterised by the Kubo number, which compares the relative strength of spatial and temporal velocity resets. To shed light on these behaviours, we develop a Lagrangian stochastic approach for particle motion in spatio-temporally fluctuating flow fields. For space–time separable flows, particle motion is mapped onto a continuous time random walk (CTRW) for steady flow in warped time, which enables the upscaling and prediction of the large-scale dispersion behaviour. For non-separable flows, we measure Lagrangian velocities in terms of a new sampling variable, the average number of velocity transitions (both temporal and spatial) along pathlines, which renders the velocity series Markovian. Based on this, we derive a Lagrangian stochastic model that represents particle motion as a coupled space–time random walk, that is, a CTRW for which the space and time increments are intrinsically coupled. This approach sheds light on the fundamental mechanisms of particle motion in space–time variable flows, and allows for its systematic quantification. Furthermore, these results indicate that alternative strategies for the analysis of Lagrangian velocity data using new sampling variables may facilitate the identification of (hidden) Markov models, and enable the development of reduced-order models for otherwise complex particle dynamics.

Dust storms are a unique form of high-Reynolds-number particle-laden turbulence associated with intense electrical activity. Using a wavelet-based analysis method on field measurement data, Zhang et al. (2023 J. Fluid Mech. 963, A15) found that wind velocity intermittency intensifies during dust storms, but it is weaker than both dust concentration and electric field. However, the linear and nonlinear multifield coupling characteristics, which significantly influence particle transport and turbulence modulation, remain poorly understood. To address this issue, we obtained high-fidelity datasets of wind velocity, dust concentration, and electric field at the Qingtu Lake Observation Array. By extending the wavelet-based data analysis method, we investigated localised linear and quadratic nonlinear coupling characteristics in strong turbulence–particle–electrostatics coupling regimes. Our findings reveal that linear coupling behaviour is largely dominated by the multifield intermittent components. At small scales, due to very high intermittency, no strong phase synchronisation can be formed, and the interphase linear coupling is weak and notably intermittent. At larger scales, however, perfect phase synchronisation emerges, and dust concentration and electric field exhibit strong, non-intermittent linear coupling, suggesting that large-scale coherent structures play a dominant role in driving the coupling. Importantly, the multifield spectra show well-developed $-1$ and $-5/3$ power-law regions, but the spectral breakpoints for dust concentration and electric field are two decades lower than that for streamwise wind velocity. This difference is due to the broader range and stronger intensity of quadratic nonlinear coupling in dust concentration and electric field, which leads to the broadening of Kolmogorov’s $-5/3$ power-law spectrum.

We investigate flame–acoustic interactions in a turbulent combustor during the state of intermittency before the onset of thermoacoustic instability using complex networks. Experiments are performed in a turbulent bluff-body stabilised dump combustor where the inlet airflow rate is varied quasi-statically and continuously. We construct a natural visibility graph from the local heat release rate fluctuations ($\dot {q}'$) at each location. Comparing the average degree during epochs of high- and low-amplitude acoustic pressure oscillations ($p'$) during the state of intermittency, we detect frequency modulation in $\dot {q}'$. Through this approach, we discover unique spatial patterns of cross-variable coupling between the frequency of $\dot {q}'$ and the amplitude of $p'$. The frequency of $\dot {q}'$ increases in regions of flame anchoring owing to high-frequency excitation of the flow and flame during epochs of high-amplitude $p'$ dynamics. However, the frequency of $\dot {q}'$ decreases in regions associated with flame-front distortions by large coherent vortices. In experiments with continuously varying airflow rates, the spatial pattern of frequency modulation varies with an increase in the average amplitude of $p'$ owing to an increase in the epochs of periodic $p'$ dynamics and the size of vortices forming in the flow. Dynamic shifts in the location of flame anchoring induce low-frequency fluctuations in $\dot {q}'$ during very-high-amplitude intermittent $p'$ dynamics. Our approach using conditional natural visibility graphs thus reveals the spatial pattern of amplitude-frequency coupling between the co-evolving flame and the acoustic field dynamics in turbulent reacting flows.

Turbulent flows in three dimensions are characterized by the transport of energy from large to small scales through the energy cascade. Since the small scales are the result of the nonlinear dynamics across the scales, they are often thought of as universal and independent of the large scales. However, as famously remarked by Landau, sufficiently slow variations of the large scales should nonetheless be expected to impact small-scale statistics. Such variations, often termed large-scale intermittency, are pervasive in experiments and even in simulations, while differing from flow to flow. Here, we evaluate the impact of temporal large-scale fluctuations on velocity, vorticity and acceleration statistics by introducing controlled sinusoidal variations of the energy injection rate into direct numerical simulations of turbulence. We find that slow variations can have a strong impact on flow statistics, raising the flatness of the considered quantities. We discern three contributions to the increased flatness, which we model by superpositions of statistically stationary flows. Overall, our work demonstrates how large-scale intermittency needs to be taken into account in order to ensure comparability of statistical results in turbulence.

Predicting and perhaps mitigating against rare, extreme events in fluid flows is an important challenge. Due to the time-localised nature of these events, Fourier-based methods prove inefficient in capturing them. Instead, this paper uses wavelet-based methods to understand the underlying patterns in a forced flow over a 2-torus which has intermittent high-energy burst events interrupting an ambient low-energy ‘quiet’ flow. Two wavelet-based methods are examined to predict burst events: (i) a wavelet proper orthogonal decomposition (WPOD) based method which uncovers and utilises the key flow patterns seen in the quiet regions and the bursting episodes; and (ii) a wavelet resolvent analysis (WRA) based method that relies on the forcing structures which amplify the underlying flow patterns. These methods are compared with a straightforward energy tracking approach which acts as a benchmark. Both the wavelet-based approaches succeed in producing better predictions than a simple energy criterion, i.e. earlier prediction times and/or fewer false positives and the WRA-based technique always performs better than WPOD. However, the improvement of WRA over WPOD is not as substantial as anticipated. We conjecture that this is because the mechanism for the bursts in the flow studied is found to be largely modal, associated with the unstable eigenfunction of the Navier–Stokes operator linearised around the mean flow. The WRA approach should deliver much better improvement over the WPOD approach for generically non-modal bursting mechanisms where there is a lag between the imposed forcing and the final response pattern.

This work presents an experimental investigation of the effects of vortex shedding suppression on the properties and recovery of turbulent wakes. Four plates, properly modified so that they produce different vortex shedding strengths, are tested using high speed particle image velocimetry and hot-wire anemometry, and analysed using spectral proper orthogonal decomposition, mean-flow linear stability analysis and various turbulence statistics. When present, vortex shedding is found to exhibit a characteristic frequency that scales with the mean shear, providing a link between the mean flow and the main turbulent motion. To achieve full suppression of shedding, we combine the effects of porosity and fractal perimeter. The mean shear is then decreased to the point where the flow becomes convectively unstable and shedding vanishes. In that case, the onset of self-similarity is delayed, compared with the case with vortex shedding, and appears after another large-scale structure, the secondary vortex street, emerges. It is also found that both large- and small-scale intermittency are starkly reduced when shedding is absent. A simple theoretical representation of the wake dynamics explains the evolution of the wake properties and its connection to the coherent structures in the flow.

Heavy particles suspended in turbulent flow possess inertia and are ejected from violent vortical structures by centrifugal forces. Once piled up along particle paths, this small-scale mechanism leads to an effective large-scale drift. This phenomenon, known as ‘turbophoresis’, causes particles to leave highly turbulent regions and migrate towards calmer regions, explaining why particles transported by non-homogeneous flows tend to concentrate near the minima of turbulent kinetic energy. It is demonstrated here that turbophoretic effects are just as crucial in statistically homogeneous flows. Although the average turbulent activity is uniform, instantaneous spatial fluctuations are responsible for inertial-range inhomogeneities in the particle distribution. Direct numerical simulations are used to probe particle accelerations, specifically how they correlate to local turbulent activity, yielding an effective coarse-grained dynamics that accounts for particle detachment from the fluid and ejection from excited regions through a space- and time-dependent non-Fickian diffusion. This leads to cast fluctuations in particle distributions in terms of a scale-dependent Péclet number ${\textit {Pe}}_\ell$, which measures the importance of turbulent advection compared with inertial turbophoresis at a given scale $\ell$. Multifractal statistics of energy dissipation indicate that $ {\textit {Pe}}_\ell \sim \ell ^\delta /\tau _{p}$ with $\delta \approx 0.84$. Numerical simulations support this behaviour and emphasise the relevance of the turbophoretic Péclet number in characterising how particle distributions, including their radial distribution function, depends on $\ell$. This approach also explains the presence of voids with inertial-range sizes, and the fact that their volumes have a non-trivial distribution with a power-law tail $p(\mathcal {V}) \propto \mathcal {V}^{-\alpha }$, with an exponent $\alpha$ that tends to 2 as ${\textit {Pe}}_\ell \to 0$.

This study investigates the influence of surface wave characteristics, specifically wave steepness and directional spreading, on intermittency in deep-water gravity wave turbulence through long-term numerical simulations of three-dimensional potential fully nonlinear periodic gravity waves. We conducted this investigation by estimating the scaling exponent of the surface elevation under different sea state conditions. With our numerical methods, we were able to evaluate the scaling exponents of the structure-function up to 12th order. The observed increased intermittency in directionally narrower sea states and in higher steepness conditions aligns with known effects of quasi-resonant wave–wave interactions and wave breaking. Comparative analyses reveal that both the conventional She–Leveque model and the multifractal models, also used to represent intermittency in wave turbulence of a different nature, exhibit a strong correlation in this study. This observation underscores the universality of intermittency phenomena within wave turbulence.

Turbulent entrainment at the turbulent/non-turbulent interface (TNTI) plays an important role in understanding the turbulent diffusion. While entrainment in fully developed canonical turbulent flows has been extensively studied, the evolution of entrainment in spatially developing flows remains poorly understood. In this work, characteristics of entrainment and the effect of vortices on entrainment of the shear layer separated from a wall-mounted fence are studied by the experiment in a water channel. The shedding vortex experiences a series of stages, including generation, growth, deformation and breakdown into smaller vortices. With the development of the flow, entrainment varies correspondingly. The prograde vortex near the TNTI is found to suppress entrainment but have little effect on the detrainment process, while the retrograde vortex promotes entrainment and suppresses detrainment as well. Consequently, the local entrainment velocity is decreased by the prograde vortex and increased more significantly by the retrograde vortex. Along the streamwise direction, the time-mean entrainment velocity is smallest where the prograde vortex is strongest in the vortex deformation stage. However, the largest time-mean entrainment velocity is located where the enstrophy gradient near the TNTI is greatest after reattachment, rather than where the retrograde vortex is strongest shortly after the breakdown of the shedding vortex, because the scarcity of retrograde vortices in the vicinity of the TNTI makes their long-time cumulative contribution not as significant as their local enhancement. The present study reveals how entrainment evolves in the separated and reattaching flow, and improves our understanding of the effect of vortices on entrainment.

Velocity gradient tensor, $A_{ij}\equiv \partial u_i/\partial x_j$, in a turbulence flow field is modelled by separating the treatment of intermittent magnitude ($A = \sqrt {A_{ij}A_{ij}}$) from that of the more universal normalised velocity gradient tensor, $b_{ij} \equiv A_{ij}/A$. The boundedness and compactness of the $b_{ij}$-space along with its universal dynamics allow for the development of models that are reasonably insensitive to Reynolds number. The near-lognormality of the magnitude $A$ is then exploited to derive a model based on a modified Ornstein–Uhlenbeck process. These models are developed using data-driven strategies employing high-fidelity forced isotropic turbulence data sets. A posteriori model results agree well with direct numerical simulation data over a wide range of velocity-gradient features and Reynolds numbers.

A spatially developing flat-plate boundary layer free from and two-way coupled with inertial solid particles is simulated to investigate the interaction between particles and the turbulent/non-turbulent interface. Particle Stokes numbers based on the outer scale are $St=2$ (low), 11 (moderate) and 53 (high). The Eulerian–Lagrangian point-particle approach is deployed for the simulation of particle-laden flow. The outer edge of the turbulent/non-turbulent interface layer is detected as an iso-surface of vorticity magnitude. Results show that the particles tend to accumulate below the interface due to the centrifugal effect of large-scale vortices in the outer region of wall turbulence and the combined barrier effect of potential flow. Consequently, the conditionally averaged fluid velocity and vorticity vary more significantly across the interface through momentum exchange and the feedback of force in the enstrophy transport. The large-scale structures in the outer layer of turbulence become smoother and less inclined in particle-laden flow due to the modulation of turbulence by the inertial particles. As a result, the geometric features of the interface layer are changed, namely, the spatial undulation increases, the fractal dimension decreases and the thickness becomes thinner in particle-laden flow as compared with unladen case. These effects become more pronounced as particle inertia increases.