A new methodology to construct three-dimensional, temporally stationary but spatially inhomogeneous, incompressible turbulence is presented. The method combines use of the data-driven spectral proper orthogonal decomposition (SPOD) to identify and isolate large-scale coherent motions of the flow, together with a physics-based enrichment algorithm using spatiotemporally localized Gabor modes that capture the inertial subrange turbulence. This fusion of data-driven and physics-based methods enables a statistically correct reconstruction of broadband turbulent flows using fewer modes than would be required using SPOD alone. To demonstrate the approach, we consider the problem of reconstructing wake turbulence on a plane downstream of a dragging actuator disk impinged by homogeneous isotropic turbulence. The reconstructed flow has single- and two-point correlations that are consistent with the reference high-resolution simulation data and could be used to generate statistically consistent inflow boundary conditions for subsequent simulations.

Recognizing the fact that the finite-time singularity of the Navier–Stokes equations is widely accepted as a key issue in fundamental fluid mechanics, and motivated by the recent model of Moffatt & Kimura (J. Fluid Mech., vol. 861, 2019a, pp. 930–967; J. Fluid Mech., vol. 870, 2019b, R1) on this issue, we have performed direct numerical simulation (DNS) for two colliding slender vortex rings of radius $R$. The separation between the two tipping points $2s_{0}$ and the scale of the core cross-section $\unicode[STIX]{x1D6FF}_{0}$ are chosen as $\unicode[STIX]{x1D6FF}_{0}=0.1s_{0}=0.01R$; the vortex Reynolds number ($Re=\text{circulation/viscosity}$) ranges from 1000 to 4000. In contrast to the claim that the core remains compact and circular, there is notable core flattening and stripping, which further increases with $Re$ – akin to our previous finding in the standard anti-parallel vortex reconnection. Furthermore, the induced motion of bridges arrests the curvature growth and vortex stretching at the tipping points; consequently, the maximum vorticity grows with $Re$ substantially slower than the exponential scaling predicted by the model – implying that, for this configuration, even physical singularity is unlikely. Our simulations not only shed light on the longstanding question of finite-time singularities, but also further delineate the detailed mechanisms of reconnection. In particular, we show for the first time that the separation distance $s(\unicode[STIX]{x1D70F})$ before reconnection follows 1/2 scaling exactly – a significant DNS result.

Over the past two decades several attempts have been made to formulate constitutive models for slow granular flow to remedy the deficiencies of classical plasticity. All the proposed models assume the medium to be incompressible, though it is well known that density change accompanies deformation in granular materials. A particularly important aspect of density change that is distinctive of granular materials is dilatancy, or volume deformation caused by shear deformation. No constitutive model for sustained flow has thus far captured dilatancy. Here we present a non-local constitutive model wherein the deformation rate and density at a point depend on the state of stress in a mesoscopic region around it. Apart from incorporating dilatancy, our model has a physical origin that is distinct from that of the previously proposed non-local models. We test our model on simple shear flow in the absence and presence of gravity, and find its predictions to be in good agreement with particle dynamics simulations.

The kinetic energy spectrum in the atmospheric mesoscale has a - 5/3 slope, which suggests an energy cascade. But the underlying dynamics of this cascade is still not fully understood. Is it driven by inertia–gravity waves, vortices or something else? To answer these questions, it is necessary to decompose the spectrum into contributions from waves and vortices. Linear decompositions are straightforward, but can lead to ambiguous results. A recent paper by Wang & Bühler (J. Fluid Mech., vol. 882, 2020, A16) addresses this problem by presenting a nonlinear decomposition of the energy spectrum into waves and vortices using the omega equation. They adapt this method for one-dimensional aircraft data and apply it to two datasets. In the lower stratosphere, the results show a mesoscale spectrum dominated by waves. The situation in the upper troposphere is different: here vortices are just as important, or possibly more than important, as waves, although the limitations of the one-dimensional data preclude a definitive answer.

Turbulent flows within and over sparse canopies are investigated using direct numerical simulations at moderate friction Reynolds numbers $Re_{\unicode[STIX]{x1D70F}}\approx 520$ and 1000. The height of the canopies studied is $h^{+}\approx 110{-}200$, which is typical of some engineering canopies but much lower than for most vegetation canopies. The analysis of the effect of Reynolds number in our simulations, however, suggests that the dynamics observed would be relevant for larger Reynolds numbers as well. In channel flows, the distribution of the total stress is linear with height. Over smooth walls, the total stress is the sum of the viscous and the Reynolds shear stresses, the ‘fluid stress’ $\unicode[STIX]{x1D70F}_{f}$. In canopies, in turn, there is an additional contribution from the canopy drag, which can dominate within. Furthermore, the full Reynolds shear stress has contributions from the dispersive, element-induced flow and from the background turbulence, the part of the flow that remains once the element-induced flow is filtered out. For the present sparse canopies, we find that the ratio of the viscous stress and the background Reynolds shear stress to their sum, $\unicode[STIX]{x1D70F}_{f}$, is similar to that over smooth walls at each height, even within the canopy. From this, a height-dependent scaling based on $\unicode[STIX]{x1D70F}_{f}$ is proposed. Using this scaling, the background turbulence within the canopy shows similarities with turbulence over smooth walls. This suggests that the background turbulence scales with $\unicode[STIX]{x1D70F}_{f}$, rather than the conventional scaling based on the total stress. This effect is essentially captured when the canopy is substituted by a drag force that acts on the mean-velocity profile alone, aiming to produce the correct $\unicode[STIX]{x1D70F}_{f}$, without the discrete presence of the canopy elements acting directly on the fluctuations. The proposed mean-only forcing is shown to produce better estimates for the turbulent fluctuations compared to a conventional, homogeneous-drag model. These results suggest that a sparse canopy acts on the background turbulence primarily through the change it induces on the mean-velocity profile, which in turn sets the scale for turbulence, rather than through a direct interaction of the canopy elements with the fluctuations. The effect of the element-induced flow, however, requires the representation of the individual canopy elements.

Turbulent flows over dense canopies consisting of rigid filaments of small size are investigated using direct numerical simulations. The effect of the height and spacing of the canopy elements on the flow is studied. The flow is composed of an element-coherent, dispersive flow and an incoherent flow, which includes contributions from the background turbulence and from the flow arising from the Kelvin–Helmholtz-like, mixing-layer instability typically reported over dense canopies. For the present canopies, with spacings $s^{+}\approx 3{-}50$, the background turbulence is essentially precluded from penetrating within the canopy. As the elements are ‘tall’, with height-to-spacing ratios $h/s\gtrsim 1$, the roughness sublayer of the canopy is determined by their spacing, extending to $y\approx 2{-}3s$ above the canopy tips. The dispersive velocity fluctuations are observed to also depend mainly on the spacing, and are small deep within the canopy, where the footprint of the Kelvin–Helmholtz-like instability dominates. The instability is governed by the canopy drag, which sets the shape of the mean velocity profile, and thus the shear length near the canopy tips. For the tall canopies considered here, this drag is governed by the element spacing and width, that is, the planar layout of the canopy. The mixing length, which determines the length scale of the instability, is essentially the sum of its height above and below the canopy tips. The former remains roughly the same in wall units and the latter is linear with $s$ for all the canopies considered. For very small element spacings, $s^{+}\lesssim 10$, the elements obstruct the fluctuations and the instability is inhibited. Within the range of $s^{+}$ of the present canopies, the obstruction decreases with increasing spacing and the signature of the Kelvin–Helmholtz-like rollers intensifies. For sparser canopies, however, the intensification of the instabilities can be expected to cease as the assumption of a spatially homogeneous mean flow would break down. For the present, dense configurations, the canopy depth also has an influence on the development of the instability. For shallow canopies, $h/s\sim 1$, the lack of depth blocks the Kelvin–Helmholtz-like rollers. For deep canopies, $h/s\gtrsim 6$, the rollers do not perceive the bottom wall and the effect of the canopy height on the flow saturates. Some of the effects of the canopy parameters on the instability can be captured by linear analysis.

The precessing vortex core (PVC) is a coherent structure that can arise in swirling jets from a global instability. In this work, the PVC is investigated under highly turbulent conditions. The goal is to characterize the receptivity of the PVC to active flow control, both theoretically and experimentally. Based on stereoscopic particle image velocimetry and surface pressure measurements, the experimental studies are facilitated by Fourier decomposition and proper orthogonal decomposition. The frequency and the mode shape of the PVC are extracted and a very good agreement with the theoretical prediction by global linear stability analysis (LSA) is found. By employing an adjoint LSA, it is found that the PVC is particularly receptive inside the duct upstream of the swirling jet. Open-loop zero-net-mass-flux actuation is applied at different axial positions inside the duct with the goal of frequency synchronization of the PVC. The actuation is shown to have the strongest effect close to the exit of the duct. There, frequency synchronization is reached primarily through direct mode-to-mode interaction. Applying the actuation farther upstream, synchronization is only achieved by a modification of the mean flow that manipulates the swirl number. These experimental observations match qualitatively well with the theoretical receptivity derived from adjoint LSA. Although the process of synchronization is very complex, it is concluded that adjoint LSA based on mean-field theory sufficiently predicts regions of high and low receptivity. Furthermore, the adjoint framework promises to be a valuable tool for finding ideal locations for flow control applications.

This paper aims at characterizing the bypass transition in boundary layers subject to strong pressure gradient and curvature effects. A series of highly resolved large-eddy simulations of a high-pressure turbine vane are performed, and the primary focus is on the effects of free-stream turbulence (FST) states on transition mechanisms. The turbulent fluctuations that have convected from the inlet first interact with the blunt blade leading edge, forming vortical structures wrapping around the blade. For cases with relatively low-level FST, streamwise streaks are observed in the suction-side boundary layer, and the instabilities of the streaks cause the breakdown to turbulence. Moreover, the varicose mode of streak instability is predominant in the adverse pressure gradient region, while the sinuous mode is more common in the (weak) favourable pressure gradient region. On the other hand, for cases with higher levels of FST, the leading-edge structures are more irregularly distributed and no obvious streak instability is observed. Accordingly, the transition onset occurs much earlier, through the breakdown caused by interactions between vortical structures. Comparing between different cases, it is the competing effect between the FST intensity and the stabilizing pressure gradient that decides the path to transition and also the transition onset, whereas the integral length scale of FST affects the scales of the streamwise streaks in the boundary layer. Furthermore, while the streaks in the low-level FST cases are mainly induced by leading-edge vortical structures, the corresponding fluctuations show a stage of algebraic growth despite the weak favourable pressure gradient and curvature.

In this numerical and theoretical work, we study the turbulent channel flow of Newtonian and elastoviscoplastic fluids. The coherent structures in these flows are identified by means of higher order dynamic mode decomposition (HODMD), applied to a set of data non-equidistant in time, to reveal the role of the near-wall streaks and their breakdown, and the interplay between turbulent dynamics and non-Newtonian effects. HODMD identifies six different high-amplitude modes, which either describe the yielded flow or the yielded–unyielded flow interaction. The structure of the low- and high-frequency modes suggests that the interaction between high- and low-speed streamwise velocity structures is one of the mechanisms triggering the streak breakdown, dominant in Newtonian turbulence where we observe shorter near-wall streaks and a more chaotic dynamics. As the influence of elasticity and plasticity increases, the flow becomes more correlated in the streamwise direction, with long streaks disrupted for short times by localised perturbations, reflected in reduced drag. Finally, we present streamwise-periodic dynamic mode decomposition modes as a viable tool to describe the highly complex turbulent flows, and identify simple well-organised groups of travelling waves.

Bubble-type vortex breakdown in axial vortices is investigated numerically through a model problem of flow inside a cylinder with a top rotating lid, referred to as ‘Vogel–Escuider flow’. The parameters of the flow are Reynolds number ($Re$), based on the rotation speed of the top plate, and aspect ratio ($\unicode[STIX]{x1D6E4}$), which is the ratio of height to radius of the cylinder, depending on which the flow exhibits steady or unsteady breakdown bubble topologies. The flow is analysed for Reynolds number up to 5000 for $\unicode[STIX]{x1D6E4}=2.5$ using helicity density. In the absence of vortex breakdown, the helicity density does not change the sign in the bulk, while in the event of a breakdown, it changes the sign from positive to negative in the vicinity of the breakdown bubble. The three-dimensional flow is further represented as the sum of a two-dimensional velocity field in the $rz$ plane and an out-of-plane velocity vector based on the respective energies, referred to as two-dimensional three-component flow. Here $r$ is the radial coordinate, $z$ is the axial coordinate and $\unicode[STIX]{x1D703}$ is the azimuthal coordinate. Helicity density of the flow is then decomposed into planar helicity $(h_{r,z})$ and out-of-plane helicity $(h_{\unicode[STIX]{x1D703}})$. We show that a correlation exists between planar helicity and the vortex breakdown bubble. We also show that the topology of the breakdown bubbles is described by the planar helicity. Using only this planar helicity, the entire breakdown bubble is reconstructed for axisymmetric as well as non-axisymmetric flows.

Stereoscopic particle image velocimetry (PIV) configured in two orthogonal planes was utilised to capture the flow structure at the instant of entrainment of spherical bed particles in open-channel flow. Experiments were conducted with lightweight target particles amongst a bed of coplanar fixed spheres with diameters of 16 mm. The protrusions of the target particles were set to give an average entrainment rate of $1/60~\text{s}^{-1}$. These protrusions were established from extensive initial experiments which utilised an automated mechanism to place spheres on the bed of the flume and record the time elapsed until they were entrained by the flow. The results showed that at lower flow depth to particle diameter ratios, bed particles are more stable and require larger protrusions to entrain at the same rate as at a larger depth. This effect is consistent with observations of reduced velocity variance and reduced drag force variance for lower flow submergences. The PIV measurements indicated that particle entrainment is associated with very large-scale motions which extend up to 50 flow depths in the streamwise direction. Contributions of smaller scale velocity and pressure spatial fluctuations are suppressed by a spatial averaging effect related to the particle size, and a temporal averaging effect related to the time taken to fully entrain a particle from its resting pocket. These observations are relevant to sediment transport modelling. However, further data are required to clarify the role of particle lift forces and particle shape in the entrainment process.

A possible interaction between vortical structures in a round jet shear layer, viz. vortex rings and streamwise vortices, is explored following Davoust et al. (J. Fluid Mech., vol. 709, 2012, pp. 408–444). These authors reported a radial organization of streamwise vorticity in a jet at high diameter-based Reynolds number ($Re$), contrary to the classically observed azimuthal organization. They hypothesized that the observed weaker vortex rings in such jets could be deformed by streamwise vortices and further reoriented and stretched in the streamwise direction. As this hypothesis was based on the observations of one configuration of a jet flow, our study aims at assessing it by varying the key parameter, i.e. the relative strength of the vortex rings and the streamwise vortices, through forcing, along with various jet configurations. We first analyse a low-Mach-number, $Re=1.5\times 10^{5}$ transitional jet, using high-speed stereo particle image velocimetry in a cross-sectional plane at two jet exit diameters from the nozzle exit. The axisymmetric mode is acoustically excited at various amplitudes to increase the strength of the rings relative to streamwise vortices, at a Strouhal number ($St$) of 0.49, the most energetic frequency in the unforced jet. Starting from a radial array in the unexcited jet, a gradual shift towards an azimuthal configuration is obtained with increasing excitation level. Quantification of the relative strengths of the streamwise vortices and vortex rings confirms that a radial array is observed whenever the streamwise vortices are more intense than the rings, and conversely for the azimuthal configuration. We then extend the analysis to other jet cases in terms of $Re$, $St$ and state of the exiting boundary layer. We observe that the correlation between the radial or azimuthal organization of streamwise vortices and the relative strengths of the vortical structures holds systematically, confirming the possibility of the proposed interaction. A detailed analysis of the forced jets also sheds light on some interesting effects of acoustic excitation on the vortical organization in round jets.

In a previous paper, Oruba et al. (J. Fluid Mech., vol. 818, 2017, pp. 205–240) considered the ‘primary’ quasi-steady geostrophic (QG) motion of a constant density fluid of viscosity $\unicode[STIX]{x1D708}$ that occurs during linear spin-down in a cylindrical container of radius $r^{\dagger }=L$ and height $z^{\dagger }=H$, rotating rapidly (angular velocity $\unicode[STIX]{x1D6FA}$) about its axis of symmetry subject to mixed rigid and stress-free boundary conditions for the case $L=H$. Here, Direct numerical simulation at large $L=10H$ and Ekman numbers $E=\unicode[STIX]{x1D708}/H^{2}\unicode[STIX]{x1D6FA}$ in the range $=10^{-3}{-}10^{-7}$ reveals inertial wave activity on the spin-down time scale $E^{-1/2}\unicode[STIX]{x1D6FA}^{-1}$. Our analytic study, based on $E\ll 1$, builds on the results of Greenspan & Howard (J. Fluid Mech., vol. 17, 1963, pp. 385–404) for an infinite plane layer $L\rightarrow \infty$. In addition to QG spin-down, they identify a ‘secondary’ set of quasi-maximum frequency $\unicode[STIX]{x1D714}^{\dagger }\rightarrow 2\unicode[STIX]{x1D6FA}$ (MF) inertial waves, which is a manifestation of the transient Ekman layer, decaying algebraically $\propto 1/\surd \,t^{\dagger }$. Here, we acknowledge that the blocking of the meridional parts of both the primary-QG and the secondary-MF spin-down flows by the lateral boundary $r^{\dagger }=L$ provides a trigger for other inertial waves. As we only investigate the response to the primary QG-trigger, we call the model ‘reduced’ and for that only inertial waves with frequencies $\unicode[STIX]{x1D714}^{\dagger }<2\unicode[STIX]{x1D6FA}$ are triggered. We explain the ensuing organised inertial wave structure via an analytic study of the thin disc limit $L\gg H$ restricted to the region $L-r^{\dagger }=O(H)$ far from the axis, where we make a Cartesian approximation of the cylindrical geometry. Other than identifying a small scale fan structure emanating from the corner $[r^{\dagger },z^{\dagger }]=[L,0]$, we show that inertial waves, on the gap length scale $H$, radiated (wave energy flux) away from the outer boundary $r^{\dagger }=L$ (but propagating with a phase velocity towards it) reach a distance determined by the mode with the fastest group velocity.

This paper investigates the receptivity of a supersonic boundary layer to slow acoustic waves whose characteristic frequency and wavelength are on the triple-deck scales, and the phase speed is thus asymptotically small. Acoustic waves on these scales are of special importance as they have the interesting property that a perturbation with a magnitude of $O(\unicode[STIX]{x1D716}_{u})$ in the free stream generates much larger, $O(\unicode[STIX]{x1D700}_{u}R^{1/8})$, velocity fluctuations inside the boundary layer, where $R$ is the Reynolds number based on the distance to the leading edge. Their interaction with streamwise localized roughness elements, leading to stronger receptivity, is studied using triple-deck theory and direct numerical simulations (DNS). The receptivity coefficient, defined as the ratio of the streamwise-velocity amplitude of the instability mode excited to that of the incident free-stream acoustic wave, serves to characterize receptivity efficiency. Its dependence on the roughness width, the Reynolds number $R$, the free-stream Mach number $M$ and the incident angle of the acoustic wave is examined. The theoretical predictions, obtained assuming $R\gg 1$, are found to be in quantitative agreement with the DNS results at moderate values of $R$ when the roughness elements are located near the lower branch of the instability. The receptivity is sensitive to the incident angle (or the phase speed) of the acoustic wave, being highly effective within a small range of angles close to $\cos ^{-1}(1/M)$ and $\unicode[STIX]{x03C0}+\cos ^{-1}(1/M)$ for downstream and upstream propagating sound waves, respectively. The amplitude of the instability mode excited is proportional to the streamwise-velocity amplitude of the acoustic signature inside the boundary layer, and scales with the roughness height $h^{\ast }$ as $(h^{\ast }/\unicode[STIX]{x1D6FF}^{\ast })R^{1/4}$, where $\unicode[STIX]{x1D6FF}^{\ast }$ is the boundary-layer thickness.

The development of the governing equations for fluid flow in a surface-following coordinate system is essential to investigate the fluid flow near an interface deformed by propagating waves. In this paper, the governing equations of fluid flow, including conservation of mass, momentum and energy balance, are derived in an orthogonal curvilinear coordinate system relevant to surface water waves. All equations are further decomposed to extract mean, wave-induced and turbulent components. The complete transformed equations include explicit extra geometric terms. For example, turbulent stress and production terms include the effects of coordinate curvature on the structure of fluid flow. Furthermore, the governing equations of motion were further simplified by considering the flow over periodic quasi-linear surface waves wherein the wavelength of the disturbance is large compared to the wave amplitude. The quasi-linear analysis is employed to express the boundary layer equations in the orthogonal wave-following curvilinear coordinates with the corresponding decomposed equations for the mean, wave and turbulent fields. Finally, the vorticity equations are also derived in the orthogonal curvilinear coordinates in order to express the corresponding velocity–vorticity formulations. The equations developed in this paper proved to be useful in the analysis and interpretation of experimental data of fluid flow over wind-generated surface waves. Experimental results are presented in a companion paper.

Various systems of moment equations – consisting of up to $(d+3)(d^{2}+6d+2)/6$ moments – in a general dimension $d$ for a dilute granular gas composed of Maxwell molecules are derived from the inelastic Boltzmann equation by employing the Grad moment method. The Navier–Stokes-level constitutive relations for the stress and heat flux appearing in the system of mass, momentum and energy balance equations are determined from the derived moment equations. It has been shown that the moment equations only for the hydrodynamic field variables (density, velocity and granular temperature), stress and heat flux – along with the time-independent value of the fourth cumulant – are sufficient for determining the Navier–Stokes-level constitutive relations in the case of inelastic Maxwell molecules, and that the other higher-order moment equations do not play any role in this case. The homogeneous cooling state of a freely cooling granular gas is investigated with the system of the Grad $(d+3)(d^{2}+6d+2)/6$-moment equations and its various subsystems. By performing a linear stability analysis in the vicinity of the homogeneous cooling state, the critical system size for the onset of instability is estimated through the considered Grad moment systems. The results on critical system size from the presented moment theories are found to be in reasonably good agreement with those from simulations.

We present an exploratory study of the hydrodynamical interaction between two bubbles rising at high Reynolds numbers in a thin-gap cell. When they are isolated, the bubbles exhibit oscillatory motions and develop an unsteady wake with periodic release of vortices. Experiments combine bubble tracking and measurements of the liquid velocity field through volumetric time-resolved particle image velocimetry. This enabled us to analyse the kinematics of the bubbles during their interaction in relationship with the liquid flow field induced by their motion and governing their behaviour. We first investigate how the kinematics of a bubble, already submitted to the intrinsic instability of its path and wake, is modified by the interaction, i.e. by the presence of a liquid flow field generated by the companion bubble. Two main effects are highlighted in association with (i) the role of the ascending flow generated by the leading bubble, and of its spatial evolution, leading to a slowly varying vertical entrainment of the trailing bubble, and (ii) the role of the vortices released by the leading bubble inducing strong localized horizontal deviations on a bubble in line or in oblique positioning. In the latter case, two major scenarios are identified: deviations of the trailing bubble towards the wake centre line (centring in the wake) or away from it (ejection from the wake). We also show that a regular succession of ejections and re-alignments events may take place (cyclic alternation of ejections and centrings). The analysis is built on the knowledge of the behaviour of isolated bubbles, which is used as the basis for comparison to characterize the effect of the interaction, for the modelling of the vertical entrainment, and for the definition of a criteria on a dimensionless parameter characterizing the ability of a vortex to drive the bubble motion. In turn, we investigate the effect of a bubble passage in the liquid flow field generated by the companion bubble, highlighting the destruction or reinforcement of vortices. We show in particular that both effects can occur without a significant impact on the bubble kinematics.

Gas turbine combustors are susceptible to thermoacoustic instability, which manifests as large amplitude periodic oscillations in acoustic pressure and heat release rate. The transition from a stable operation characterized by combustion noise to thermoacoustic instability in turbulent combustors has been described as an emergence of order (periodicity) from chaos in the temporal dynamics. This emergence of order in the acoustic pressure oscillations corresponds to a loss of multifractality in the pressure signal. In this study, we investigate the spatiotemporal dynamics of a turbulent flame in a bluff-body stabilized combustor during the transition from combustion noise to thermoacoustic instability. During the occurrence of combustion noise, the flame wrinkles due to the presence of small-scale vortices in the turbulent flow. On the other hand, during thermoacoustic instability, large-scale coherent structures emerge periodically. These large-scale coherent structures roll up the wrinkled flame surface further and introduce additional complexity in the flame topology. We perform multifractal analysis on the flame contours detected from high-speed planar Mie scattering images of the reactive flow seeded with non-reactive tracer particles. We find that multifractality exists in the flame topology for all the dynamical states during the transition to thermoacoustic instability. We discuss the variation of multifractal parameters for the different states. We find that the multifractal spectrum oscillates periodically during the occurrence of thermoacoustic instability at the time scale of the acoustic pressure oscillations. The loss of multifractality in the temporal dynamics and the oscillation of the multifractal spectrum of the spatial dynamics go hand in hand.

At sufficiently high Reynolds numbers, shear-flow turbulence close to a wall acquires universal properties. When length and velocity are rescaled by appropriate characteristic scales of the turbulent flow and thereby measured in inner units, the statistical properties of the flow become independent of the Reynolds number. We demonstrate the existence of a wall-attached non-chaotic exact invariant solution of the fully nonlinear three-dimensional Navier–Stokes equations for a parallel boundary layer that captures the characteristic self-similar scaling of near-wall turbulent structures. The branch of travelling wave solutions can be followed up to $Re=1\,000\,000$. Combined theoretical and numerical evidence suggests that the solution is asymptotically self-similar and exactly scales in inner units for Reynolds numbers tending to infinity. Demonstrating the existence of invariant solutions that capture the self-similar scaling properties of turbulence in the near-wall region is a step towards extending the dynamical systems approach to turbulence from the transitional regime to fully developed boundary layers.

A focused laser can cause local optical breakdown of a gas, which leads to rapid deposition of energy into a high-temperature plasma kernel that expands and induces a complex flow. For some conditions, hot gas is rapidly ejected along the laser axis up to distances several times the kernel size, with a particularly curious feature: relatively small changes in, for example, initial pressure can cause the direction of this ejection to reverse. Detailed axisymmetric simulations of a model energy kernel in an inert gas provide a hydrodynamic description of this phenomenon, reproducing key observations in corresponding experiments, including the vortex-ring-like features that constitute the ejection. These simulations are analysed to show how changes in the early-time kernel can lead to ejection or its reversal via alteration in the relative strength and position of the vorticity produced. A corresponding semi-infinite geometry is used to isolate two mechanisms: vorticity production by the generated shock and by baroclinic torque at the kernel boundary. Dependence on the initial kernel asymmetry is quantified, as it ultimately determines whether the vorticity, upon its subsequent evolution, develops into the ring-like structure that ejects. Even simple elongation of the energy kernel alone can reverse the direction.