In turbulence near a free surface, strong vortices attach to the surface, creating surface imprints visible as nearly circular ‘dimples’. By studying these imprints in direct numerical simulation (DNS) data we make two observations. First, the imprints of surface-attached vortices can be very effectively distinguished from other turbulent surface features using two physical features: they are nearly circular in shape, and persist for a long time compared with other pertinent time scales. Secondly, the instantaneous number of surface dimples from surface-attached vortices in an area, $N(t)$, is intimately related to its mean-square surface divergence, $\beta ^2(t)$. We develop a simple and physically transparent computer vision procedure which, using the properties of low eccentricity and longevity, detects and tracks vortices from their surface features only, with sensitivity and accuracy of $90\,\%$ or better. We compare $N(t)$ and $\beta ^2(t)$, finding a normalised cross-correlation of $0.90$, with changes in $N$ lagging around $0.8T_\infty$ behind those in $\beta ^2$ ($T_\infty$ is an integral time scale), confirming the common observation that vortices are spawned by strong upwelling events where $\beta ^2$ is large. These findings suggest that the rate of mass flux across the surface, being closely related to surface divergence, can be estimated remotely in some natural flows using visible free-surface dimples as proxy.

We investigate the streamwise vorticity generation mechanism and distribution pattern in an unbounded steady inertial flow past a fixed Platonic polyhedron. Three angular positions are selected: an edge facing the flow (E), a face facing the flow (F) and a vertex facing the flow (V). We provide compelling evidence that the generation of the streamwise vorticity is primarily caused by the tilting of the transverse vorticity that originates from the particle front surface. Each inclined face on the front surface generates a pair of opposite-signed streamwise vortices. They are advected to the particle wake and form a chiral vorticity pattern which preserves the symmetry of the particle front surface. Two particles at dual angular positions exhibit highly similar vorticity patterns. Our study reveals a striking similarity between the vorticity patterns and the far-field optics diffraction pattern of a light beam past a polygonal aperture. We discover the deterministic vorticity generation mechanism to predict the streamwise vorticity patterns based on the distribution of edges and inclined faces on the particle front surface. Conversely, the vorticity patterns themselves can serve as a diagnostic tool to infer the geometry of the opaque particle front surface. Additionally, the vorticity patterns can be used to predict the stable angular position of a freely settling angular particle, which tends to be such that the number of streamwise vorticity pairs in the wake is maximized.

While large-scale seafloor features (e.g. continental slopes, mid-ocean ridges) help shape the broad patterns of ocean circulation, small-scale rough topography (e.g. seamounts, abyssal hills) can also impact the large-scale dynamics in two significant ways. First, they impact the momentum budget through flow steering, flow blocking and drag force, non-local momentum transfer via the generation of radiating internal waves and momentum dissipation by topographically induced turbulence. Second, they impact the density budget. Turbulence induced by flow–topography interactions facilitates ocean overturning circulation by upwelling dense, deep waters which form in polar oceans and sink to the abyss. Rough topography and its associated dynamics are of subgrid scale in Earth systems models (ESMs) and need parameterization for the foreseeable future. A parameterization of the intertwined impacts of flow–topography interactions on momentum and density budgets is currently non-existent, although its importance is well established. Radko (J. Fluid Mech., vol. 961, 2023, A24) provides a novel analytical model for representing the impact of rough seafloor on larger-scale flows, spanning slow to fast flow-speed regimes in homogeneous and multilayer models. The proposed ‘closure’ is in remarkable agreement with high-resolution numerical simulations and provides a crucial step forward in parameterizing the impact of rough topography in coarse-resolution ocean models. Extending the model to the full Navier–Stokes equations, linking it to the density budget and considering more realistic ocean topography are three critical future steps towards implementing Radko's theory in operational ESMs.

Cryogenic carbon capture (CCC) can preferentially desublimate $\text {CO}_2$ out of the flue gas. A widespread application of CCC requires a comprehensive understanding of $\text {CO}_2$ desublimation properties. This is, however, highly challenging due to the multiphysics behind it. This study proposes a lattice Boltzmann (LB) model to study $\text {CO}_2$ desublimation on a cooled cylinder surface during CCC. In two-dimensional (2-D) simulations, various $\text {CO}_2$ desublimation and capture behaviours are produced in response to different operation conditions, namely, gas velocity (Péclet number $\textit {Pe}$) and cylinder temperature (subcooling degree $\Delta T_{sub}$). As $\textit {Pe}$ increases or $\Delta T_{sub}$ decreases, the desublimation rate gradually becomes insufficient compared with the $\text {CO}_2$ supply via convection/diffusion. Correspondingly, the desublimated solid $\text {CO}_2$ layer (SCL) transforms from a loose (i.e. cluster-like, dendritic or incomplete) structure to a dense one. Four desublimation regimes are thus classified as diffusion-controlled, joint-controlled, convection-controlled and desublimation-controlled regimes. The joint-controlled regime shows quantitatively a desirable $\text {CO}_2$ capture performance: fast desublimation rate, high capture capacity, and full cylinder utilization. Regime distributions are summarized on a $\textit {Pe}$–$\Delta T_{sub}$ space to determine operation parameters for the joint-controlled regime. Moreover, three-dimensional simulations demonstrate four similar desublimation regimes, verifying the reliability of 2-D results. Under regimes with loose SCLs, however, the desublimation process shows an improved $\text {CO}_2$ capture performance in three dimensions. This is attributed to the enhanced availability of gas–solid interface and flow paths. This work develops a reliable LB model to study $\text {CO}_2$ desublimation, which can facilitate applications of CCC for mitigating climate change.

We investigate the intermittency of the coupling behaviour in screeching twin round supersonic jets at low Mach numbers across a range of nozzle spacings. Application of proper orthogonal decomposition combined with time-frequency wavelet analysis and spectral proper orthogonal decomposition shows that intermittency can manifest in twin jets as either a competition between the two symmetries, or the jets uncoupling and recoupling. The time scales on which symmetry switching occurs can vary strongly, ranging from $O(10^2)$ to $O(10^3)$ screech cycles. A transition from one symmetry to another is accompanied by a slight change in the screech frequency ranging from 0.30 % to 0.63 %. It was observed that complete uncoupling occurred only at the largest nozzle spacing of $s/D=6$ and at Mach numbers close to modal staging. When the jets are uncoupled they screech at slightly different frequencies, with a disparity of approximately 0.6 %. The coupling is particularly intermittent in the transition from the A1 to A2 branch, where the A2 mode is first observed, and tends toward steady coupling with increasing Mach number.

We consider a slowly condensing droplet levitating near the surface of an evaporating layer, and develop a mathematical model to describe diffusion, heat transfer and fluid flow in the system. The method of separation of variables in bipolar coordinates is used to obtain the series expansions for temperature, vapour concentration and the Stokes stream function. This framework allows us to determine temperature profiles and condensation rates at the surface of the droplet, and to calculate the upward force that allows the droplet to levitate. Somewhat counter-intuitively, condensation is found to be the strongest near the bottom of the droplet, which faces the hot liquid layer. The experimentally observed deviations from the classical law predicting the square of the radius to grow linearly in time are explained by the model. A spatially non-uniform phase change rate results in a contribution to the force not considered in previous studies, and comparable to droplet weight and the upward force calculated from the Stokes drag law. The levitation conditions are formulated accordingly, resulting in the prediction of levitation height as a function of droplet size without any fitting parameters. A simple criterion is formulated to define the parameter ranges in which levitation is possible. The results are in good agreement with the experimental data except that the model tends to slightly underpredict the levitation height.

The reflection and transmission of internal waves at a horizontal interface between layers of constant buoyancy frequency are treated. This interface is a simple model of the atmospheric tropopause. The waves are weakly nonlinear and obey the nonlinear Schrödinger equation away from the interface. The waves are horizontally periodic and vertically confined to a long packet. The interfacial conditions are formally taken to third order, and include higher-order linear as well as nonlinear effects. The higher-order linear affects show an instability at the interface for steep waves. Numerical results for shorter wave packets show that the higher-order linear terms result in non-physical wave generation, and are ultimately neglected for such cases. Nonlinear effects result in a decrease in the reflected wave amplitudes and an increase in the transmitted wave amplitudes when compared to linear theory. Overall, the nonlinear effects make the interface more transparent to upwardly propagating internal waves.

We report direct numerical simulations of the flow around a spanwise-flexible wing in forward flight. The simulations were performed at $Re=1000$ for wings of aspect ratio 2 and 4 undergoing a heaving and pitching motion at Strouhal number $St_c\approx 0.5$. We have varied the effective stiffness of the wing $\varPi _1$ while keeping the effective inertia constant, $\varPi _0=0.1$. It has been found that there is an optimal aerodynamic performance of the wing linked to a damped resonance phenomenon, that occurs when the imposed frequency of oscillation approaches the first natural frequency of the structure in the fluid, $\omega _{n,f}/\omega \approx 1$. In that situation, the time-averaged thrust is maximum, increasing by factor 2 with respect to the rigid case with an increase in propulsive efficiency of approximately 15 %. This enhanced aerodynamic performance results from the combination of larger effective angles of attack of the outboard wing sections and a delayed development of the leading edge vortex. With increasing flexibility beyond the resonant frequency, the aerodynamic performance drops significantly, in terms of both thrust production and propulsive efficiency. The cause of this drop lies in the increasing phase lag between the deflection of the wing and the heaving/pitching motion, which results in weaker leading edge vortices, negative effective angles of attack in the outboard sections of the wing, and drag generation in the first half of the stroke. Our results also show that flexible wings with the same $\omega _{n,f}/\omega$ but different aspect ratio have the same aerodynamic performance, emphasizing the importance of the structural properties of the wing for its aerodynamic performance.

Viscous flow around two spherical macroscopic cavities (or void spaces) in a granular material, which is exposed to an otherwise uniform flow at infinity, is investigated. The flow field is obtained analytically by solving the Stokes equation inside and the Darcy–Brinkman equation outside of the cavities, where continuity of the velocity and that of the stress are assumed on the boundary. In our previous complementary paper (Sano, Karmakar & Sekhar, J. Fluid Mech., vol. 931, 2022, A20), we obtain that two cavities of equal size in a tandem position are more prone to collapse for a shorter centre-to-centre distance with low permeability. In the present study, the asymptotic analysis of the interaction of two spherical cavities of different sizes with arbitrary configuration is presented. Particular attention is paid to the configuration dependence of two cavities of equal radius. The velocity field and the volume flux into respective cavities are calculated, which reveal that two cavities with orientation less than a certain critical angle are given a larger volume flux and are more prone to collapse. The present results are applicable to predicting the behaviour in a fixed-bed regime of a solid–gas transport system, microscale waterway formation in a granular material, onset of landslides, collapse of cliffs and river banks, etc.

Inspired by geological structures formed by magmatic intrusions that deform the Earth's crust, we investigate the elastohydrodynamic growth of a viscoplastic blister under an elastic sheet resting on a prewetted substrate. By combining experiments, scaling analysis and numerical simulations, we reveal new regimes for the elastoviscoplastic growth dynamics of the blister. The blister height and its apparent radius grow as $h(0,t) \sim t^{5/9}$ and $R(t) \sim t^{2/9}$ if the fluid pressure is set by bending of the sheet, and as $h(0,t) \sim t^{5/13}$ and $R(t) \sim t^{4/13}$ if the fluid pressure is set by stretching of the sheet. A plug-like flow inside the blister dictates its dynamics, whereas the blister takes a self-similar shape given by a balance of the fluid's yield stress and the pressure gradient induced by the deformation of the elastic sheet.

Direct numerical simulations (DNS) of temporally developing turbulent boundary layers are performed with a wide range of Reynolds numbers based on the momentum thickness $Re_{\theta } = 2000$–$13\,000$ for investigating the Reynolds number dependence of the turbulent/non-turbulent interface (TNTI) layer. The grid spacing in the DNS is determined carefully such that small-scale turbulent motions near the TNTI are well resolved. The outer edge of the TNTI layer, called the irrotational boundary, is detected with vorticity magnitude. The mean thicknesses of the TNTI layer, $\delta _{TNTI}$, turbulent sublayer, $\delta _{TSL}$, and viscous superlayer, $\delta _{VSL}$, are found to be approximately $15\eta _{TI}$, $10\eta _{TI}$ and $5\eta _{TI}$, respectively, where $\eta _{TI}$ is the Kolmogorov scale taken in the turbulent region near the TNTI layer. The mean curvature of the irrotational boundary is also characterized by $\eta _{TI}$. The shear parameter and the shear-to-vorticity ratio show that the mean shear effects near the TNTI layer are not significant for both large and small scales. The anisotropy tensors of Reynolds stress and vorticity suggest that the turbulence under the TNTI layer tends to be isotropic at high $Re_{\theta }$, for which $\eta _{TI}/\delta \sim Re_{\theta }^{-3/4}$ is valid with the boundary layer thickness $\delta$. The surface area of the irrotational boundary is consistent with the fractal analysis of the interface, where the fractal dimension $D_f$ is found to be $2.14$–$2.20$. The present results suggest that the mean entrainment rate per unit horizontal area normalized by the friction velocity varies slowly as $Re_{\theta }^{(3/4)(D_f-2)}$ for $Re_{\theta } \geq 4000$.

Drag force acting on a particle is vital for the accurate simulation of turbulent multiphase flows, but the robust drag model is still an open issue. Fully resolved direct numerical simulation (DNS) with an immersed boundary method is performed to investigate the drag force on saltating particles in wall turbulence over a sediment bed. Results show that, for saltating particles, the drag force along the particle trajectories cannot be estimated accurately by traditional drag models originally developed for an isolated particle that depends on the particle-wall separation distance or local volume fraction in addition to the particle Reynolds number. The errors between the models and DNS are especially clear during the descending phase of the particles. Through simple theoretical analysis and DNS data fitting, we present a corrected factor using the classical, particle Reynolds number dependent drag force model as the benchmark model. The new drag model, which takes the particle vertical velocity into account, can reasonably predict the mean drag force obtained by DNS along a particle trajectory.

We present new experiments of particle-laden turbulent fountains in a uniform horizontal crossflow, $u_a$, with momentum flux, $M_0$, and buoyancy flux, $B_0$. We use the ratio, $P$, of the crossflow speed to the characteristic fountain speed, $M_0^{-1/4}|B_0|^{1/2}$, and the ratio $U$, of the Stokes fall speed of the particles, $v_s$, to the characteristic fountain speed, to characterise the dynamics of a particle fountain in a crossflow. We find that the dynamics of these particle fountains can be categorised into three distinct regimes. In regime I when the fall speed of the particles is small in comparison with the characteristic fountain speed ($U\ll 1$), the particles remain well-coupled to the fountain fluid and the flow essentially behaves as a single-phase fountain in a crossflow. In the transitional regime II ($0.1< U<1$), when the fall speed of particles is comparable to the characteristic fountain speed, we observe some particles separating from the fountain fluid during the descent of the flow which leaves some fluid neutrally buoyant. As $U>1$ (regime III), we observe particles separating from the fountain as it rises from the source. We measure the average dispersal distance of the particles and the speed of the descending particles as a function of $U$ and $P$ and compare these results with models of a single-phase fountain in a crossflow. We build a regime diagram to describe the effect of $U$ and $P$ on the flow dynamics and consider our work in the context of deep-submarine volcanic eruptions.

We perform a computational study on the effects of localized arc filament plasma actuator based control on the flow field and acoustics of a supersonic 2:1 aspect ratio rectangular jet. Post validation of the baseline jet, effects of control in the context of noise reduction are studied at experimentally guided forcing parameters, including frequencies $St=0.3, 1.0$ and $St=2.0$ with duty cycles of $20\,\%$ and $50\,\%$. In general, high-frequency forcing reduces noise in the downstream direction, with the actuator signature appearing mostly in the sideline direction. Here $St=1$, ${\rm DC}=50\,\%$ yields an optimum balance between peak noise reduction (of ${\sim }1.5$ dB) and actuator tones, with control being most effective on the major axis plane that bisects the shorter edges of the nozzle. Shear layer response to the most effective forcing includes generation of successive arrays of mutually interacting staggered lambda vortices, which eventually energize streamwise vortical elements. Causal mechanisms of noise mitigation are further elucidated as follows. First, the control reduces the energy within the supersonic phase speed regime of peak radiating frequencies by redistributing a part of it into a high-frequency band. Second, it enhances azimuthal percolation of energy into the first and second helical modes at frequencies where noise reduction is seen, thus weakening the radiatively efficient axisymmetric mode. Finally, sound-producing intermittent events in the jet are significantly reduced, thereby minimizing the high-intensity acoustic emissions. This small-perturbation-based control strategy results in only minor variations in the mean flow properties. However, reduced production and enhanced convection attenuate turbulent kinetic energy within the spreading shear layer in the controlled jet.

Due to the curvature of the droplet surface, the propagation of transmitted waves is complex inside a droplet impacted by an incident shock wave. The wave converging phenomena inside a two-dimensional water column impacted by different curved shock waves are explored in this paper by means of theoretical ray analysis and high-resolution numerical simulations. An analytical method describing the wave structure evolution characteristics inside the shocked water column is established. Hence, the morphological pattern and focus locations of these waves are theoretically obtained. The analysis shows that both the first and the second reflected waves focus inside the water column regardless of the convergent, planar or divergent nature of the incident shock wave shape. The dimensionless distances from focusing points to the column centre are derived as ${\kappa }/{( 3\kappa -{{M}_{0}}{{f}_{s}} )}$ for the former and ${\kappa }/{( 5\kappa -{{M}_{0}}{{f}_{s}})}$ for the latter, respectively. Here, $\kappa$, $M_0$ and $f_s$ represent the sound-speed ratio of the two phases, the incident shock wave strength and a function characterising the shock wave shape effect, respectively. Moreover, highly negative pressures due to the first reflected wave focusing and significant pressure oscillations due to the second reflected wave focusing are numerically tracked for three shapes of the incident shock. The effects of the incident shock wave intensity on the pressure variations at focus points are further studied. As the incident shock wave intensity increases, stronger negative pressure and higher pressure oscillation are induced. The converged incident shock wave can enhance the above phenomena, but the diverged one can weaken them.

Multifidelity models (MFMs) can be used to construct predictive models for flow quantities of interest (QoIs) over the space of uncertain/design parameters, with the purpose of uncertainty quantification, data fusion and optimization. For numerical simulation of turbulence, there is a hierarchy of methodologies ranked by accuracy and cost, where each methodology may have several numerical/modelling parameters that control the predictive accuracy and robustness of its resulting outputs. Compatible with these specifications, the present hierarchical MFM strategy allows for simultaneous calibration of the fidelity-specific parameters in a Bayesian framework as developed by Goh et al. (Technometrics, vol. 55, no. 4, 2013, pp. 501–512). The purpose of the MFM is to provide an improved prediction, mainly interpolation over the range covered by training data, by combining lower- and higher-fidelity data in an optimal way for any number of fidelity levels; even providing confidence intervals for the resulting QoI. The capabilities of the MFM are first demonstrated on an illustrative toy problem, and it is then applied to three realistic cases relevant to engineering turbulent flows. The latter include the prediction of friction at different Reynolds numbers in turbulent channel flow, the prediction of aerodynamic coefficients for a range of angles of attack of a standard airfoil and the uncertainty propagation and sensitivity analysis of the separation bubble in the turbulent flow over periodic hills subject to geometrical uncertainties. In all cases, based on only a few high-fidelity data samples, the MFM leads to accurate predictions of the QoIs. The result of the uncertainty quantification and sensitivity analyses are also found to be accurate compared with the ground truth in each case.

Body-force modelling in the lattice Boltzmann method (LBM) has been studied extensively in the incompressible limit but rarely discussed for thermal compressible flows. Here we present a systematic approach of incorporating body force in the LBM which is valid for thermal compressible and non-equilibrium flows. In particular, a LBM forcing scheme accurate for the energy equation with second-order time accuracy is given. New and essential in this scheme is the third-moment contribution of the force term. It is shown via Chapman–Enskog analysis that the absence of this contribution causes an erroneous heat flux quadratic in Mach number and linear in temperature variation. The theoretical findings are verified and the necessity of the third-moment contribution is demonstrated by numerical simulations.

It is generally believed that the temperature and the velocity fields are highly coupled in compressible wall-bounded turbulence. In the present study, we employ a linear model, i.e. the two-dimensional spectral linear stochastic estimation (SLSE), to study this coupling from the perspective of the multi-scale energy-containing eddies. Particular attention is paid to the relevant statistical characteristics of the temperature field. The connections of the two fields are found to be varied with the wall-normal position in the boundary layer. In a nutshell, their entanglement is strongest in the near-wall region, and only the extreme thermal events cannot be captured by SLSE. In the logarithmic region, only the scales that correspond to the attached eddies and the very large-scale motions (VLSMs) are firmly coupled. The near-wall footprints of the former are organized in an additive manner and fulfil the predictions of the celebrated attached-eddy model. In the outer region, the two fields are linearly coupled only at the scales corresponding to VLSMs. These findings are demonstrated to be insensitive to the Mach number effects and ascribed to the similarity between the momentum and the heat transfer in compressible wall turbulence. It is also shown that it is the Reynolds number rather than Mach number that acts as a key similarity parameter in constructing their coupling. The framework built in the present study may pave a way for investigating the multi-physics coupling in turbulence, and reinforcing our analysing and modelling capability to the interrelated problems.

Low Reynolds number turbulence in wall-bounded shear flows en route to laminar flow takes the form of spatially intermittent turbulent structures. In plane shear flows, these appear as a regular pattern of alternating turbulent and quasi-laminar flow. Both the physical and the spectral energy balance of a turbulent–laminar pattern in plane Couette flow are computed and compared to those of uniform turbulence. In the patterned state, the mean flow is strongly modulated and is fuelled by two mechanisms: primarily, the nonlinear self-interaction of the mean flow (via mean advection), and secondly, the extraction of energy from turbulent fluctuations (via negative spectral production, associated with an energy transfer from small to large scales). Negative production at large scales is also found in the uniformly turbulent state. Important features of the energy budgets are surveyed as a function of $Re$ through the transition between uniform turbulence and turbulent–laminar patterns.

Low Reynolds number turbulence in wall-bounded shear flows en route to laminar flow takes the form of oblique, spatially intermittent turbulent structures. In plane Couette flow, these emerge from uniform turbulence via a spatio-temporal intermittent process in which localised quasi-laminar gaps randomly nucleate and disappear. For slightly lower Reynolds numbers, spatially periodic and approximately stationary turbulent–laminar patterns predominate. The statistics of quasi-laminar regions, including the distributions of space and time scales and their Reynolds-number dependence, are analysed. A smooth, but marked transition is observed between uniform turbulence and flow with intermittent quasi-laminar gaps, whereas the transition from gaps to regular patterns is more gradual. Wavelength selection in these patterns is analysed via numerical simulations in oblique domains of various sizes. Via lifetime measurements in minimal domains, and a wavelet-based analysis of wavelength predominance in a large domain, we quantify the existence and nonlinear stability of a pattern as a function of wavelength and Reynolds number. We report that the preferred wavelength maximises the energy and dissipation of the large-scale flow along laminar–turbulent interfaces. This optimal behaviour is due primarily to the advective nature of the large-scale flow, with turbulent fluctuations playing only a secondary role.