This paper presents a numerical investigation of the turbulence transition phenomenon in the wake of wall-mounted prisms. Large-eddy simulations are performed at $Re = 1\times 10^3 {-}5\times 10^3$ for prisms with a range of aspect ratio (height to width) from $0.25$ to $1.5$, and depth ratios (length to width) between $1$ and $4$. The results show that the wake irregularity is enhanced with increasing depth ratio, evidenced by higher turbulent kinetic energy (${\approx}90\,\%$) near the leading edge, and the onset of irregular, unsteady vortex shedding. This is attributed to interactions between Kelvin–Helmholtz instability (KHI) of the shear layer and large-scale vortex shedding, and it is induced by an unsteady shear layer, resembling flapping-like motion. These interactions elevate the flow momentum due to increased turbulence intensity and mixing, contributing to the wake transition phenomenon. To this end, this study defines the role of depth ratio in the transition phenomenon by showing that increasing depth ratio (e.g. from $1$ to $4$) leads to earlier onset of KHIs in the shear layer. These instabilities intensify with depth ratio, resulting in stronger interactions between shear layer and large-scale vortex shedding. Specifically, KHI-induced vortices interact more frequently with large-scale wake structures for higher depth ratio prisms, exciting larger flow fluctuations and irregular wake patterns. This interaction alters the frequency and coherence of vortex shedding, revealing a complex coupling mechanism that drives the transition to turbulence.

This article explores how a submerged elastic plate, clamped at one edge, interacts with water waves. Submerged elastic plates have been considered as potentially effective design elements in the development of wave energy harvesters but their behaviour in a wave field remains largely unexplored, especially experimentally. Positioned at a fixed depth in a wave tank, the flexible plate demonstrates significant wave reflection capabilities, a characteristic absent in rigid plates of identical dimensions. The experiments thus reveal that plate motion is crucial for wave reflection. Sufficiently steep waves are shown to induce a change in the mean position of the plate, with the trailing edge reaching the free surface in some cases. This configuration change is found to be particularly efficient to break water waves. These findings contribute to understanding the potential of elastic plates for wave energy harvesting and wave attenuation scenarios.

This work focuses on the intensity variation mechanisms in the mean inner and outer shear layers of a premixed swirling flame. In order to close the gap between the Lagrangian vorticity transport and the Eulerian shear layer intensity ($\gamma$), we propose a combined Reynolds-vorticity transport approach to obtain the streamwise variation of $\gamma$ as the integrals of vorticity generation terms, including tilting, baroclinic torque, diffusion and dilatation. However, different from the classical vorticity (transport) equation, the vortex stretching vanishes, and the original dilatation is replaced by a shear-layer dilatation in the new model. It enables the quantitative evaluation of how the different vorticity transport terms affect the shear layer intensity; in particular, we have identified vortex tilting and baroclinic torque as the main cause of the inner shear layer enhancement in the swirling flame’s near field. Although this model is initially developed to study the flame-attached shear layers, the broader significance lies in its applicability to general axisymmetric shear flows.

The influence of irregular three-dimensional rough surfaces on the displacement of the logarithmic velocity profile relative to that of a smooth wall in turbulent flow, known as the roughness function, is studied using direct numerical simulations. Five different surface power spectral density (PSD) shapes were considered, and for each, several rough Gaussian surfaces were generated by varying the root mean square ($k_{rms}$) of the surface heights. It is shown that the roughness function ($\Delta U^{+}$) depends on both the PSD and $k_{rms}$. For a given $k_{rms}$, $\Delta U^{+}$ increases as the wavenumbers of the PSD expand to large values, but at a rate that decreases with the magnitude of the wavenumbers. Although $\Delta U^{+}$ generally does not scale with either $k_{rms}$ or the effective slope $ES$ when these variables are considered singularly, for PSDs with low wavenumbers, $\Delta U^{+}$ tends to scale with $ES$, whereas as wavenumbers increase, $\Delta U^{+}$ tends to scale with $k_{rms}$. An equivalent Nikuradse sand roughness of about eight times $k_{rms}$ is found, which is similar to that observed in previous studies for a regular three-dimensional roughness. Finally, it is shown that $k_{rms}$ and the effective slope are sufficient to describe the roughness function in the transitional rough regime.

Drag reduction induced by a polydisperse solution of polyethylene oxide is investigated by direct numerical simulations of the Navier–Stokes equations coupled with the Lagrangian evolution of the polymers, modelled as dumbbells. Simulation parameters are chosen to match the experimental conditions of Berman (1977), who measured the polymer molecular weight distribution. Drag reduction is induced only by the few high molecular weight polymers fully stretched by the turbulent flow, whilst the hundreds of parts per million of low molecular weight chains are ineffective.

Morphodynamic descriptions of fluid deformable surfaces are relevant for a range of biological and soft matter phenomena, spanning materials that can be passive or active, as well as ordered or topological. However, a principled, geometric formulation of the correct hydrodynamic equations has remained opaque, with objective rates proving a central, contentious issue. We argue that this is due to a conflation of several important notions that must be disambiguated when describing fluid deformable surfaces. These are the Eulerian and Lagrangian perspectives on fluid motion, and three different types of gauge freedom: in the ambient space; in the parameterisation of the surface; and in the choice of frame field on the surface. We clarify these ideas, and show that objective rates in fluid deformable surfaces are time derivatives that are invariant under the first of these gauge freedoms, and which also preserve the structure of the ambient metric. The latter condition reduces a potentially infinite number of possible objective rates to only two: the material derivative and the Jaumann rate. The material derivative is invariant under the Galilean group, and therefore applies to velocities, whose rate captures the conservation of momentum. The Jaumann derivative is invariant under all time-dependent isometries, and therefore applies to local order parameters, or symmetry-broken variables, such as the nematic $Q$-tensor. We provide examples of material and Jaumann rates in two different frame fields that are pertinent to the current applications of the fluid mechanics of deformable surfaces.

In this work, we investigate the mixing of active scalars in two dimensions by the stirring action of stochastically generated weak shock waves. We use Fourier pseudospectral direct numerical simulations of the interaction of shock waves with two non-reacting species to analyse the mixing dynamics for different Atwood numbers (At). Unlike passive scalars, the presence of density gradients in active scalars alters the molecular diffusion term and makes the species diffusion nonlinear, introducing a concentration gradient-driven term and a density gradient-driven nonlinear dissipation term in the concentration evolution equation. We show that the direction of concentration gradient causes the interface across which molecular diffusion occurs to expand outwards or inwards, even without any stirring action. Shock waves enhance the mixing process by increasing the perimeter of the interface and by sustaining concentration gradients. Negative Atwood number mixtures sustain concentration gradients for a longer time than positive Atwood number mixtures due to the so-called nonlinear dissipation terms. We estimate the time until that when the action of stirring is dominant over molecular mixing. We also highlight the role of baroclinicity in increasing the interface perimeter in the stirring dominant regime. We compare the stirring effect of shock waves on mixing of passive scalars with active scalars and show that the vorticity generated by baroclinicity is responsible for the folding and stretching of the interface in the case of active scalars. We conclude by showing that lighter mixtures with denser inhomogeneities ($At\lt 0$) take a longer time to homogenise than the denser mixtures with lighter inhomogeneities ($At\gt 0$).

Elastoinertial turbulence (EIT) is a chaotic state that emerges in the flows of dilute polymer solutions. Direct numerical simulation (DNS) of EIT is highly computationally expensive due to the need to resolve the multiscale nature of the system. While DNS of two-dimensional (2-D) EIT typically requires $O(10^6)$ degrees of freedom, we demonstrate here that a data-driven modelling framework allows for the construction of an accurate model with 50 degrees of freedom. We achieve a low-dimensional representation of the full state by first applying a viscoelastic variant of proper orthogonal decomposition to DNS results, and then using an autoencoder. The dynamics of this low-dimensional representation is learned using the neural ordinary differential equation (NODE) method, which approximates the vector field for the reduced dynamics as a neural network. The resulting low-dimensional data-driven model effectively captures short-time dynamics over the span of one correlation time, as well as long-time dynamics, particularly the self-similar, nested travelling wave structure of 2-D EIT in the parameter range considered.

When a droplet impacts onto a superheated liquid pool, vapour generation and drainage within the gas cushion play a crucial role in postponing or even preventing contact between the droplet and the pool surface. Through direct numerical simulations, we closely examine the transient dynamics of vapour flow confined within the thin film, with a particular focus on the minimum thickness of this film under a range of impact conditions. Our numerical findings manifest the significant influence of evaporation on the vertical motion of the liquid–vapour interface, revealing how the minimum film thickness evolves in response to variations in impact velocity and degree of superheat. In our numerical simulations, we have identified two distinct evolution laws for the minimum film thickness, corresponding to moderate and high superheat regimes, respectively. These regimes are differentiated by the dominance of evaporation effects within the vapour film during the early falling stage. Subsequently, we establish scaling relations to characterize these regimes by carefully balancing inertial, pressure and evaporation effects within the thin vapour film. Furthermore, we observe that the vapour pressure eventually reaches equilibrium with the rapid increase in capillary pressure at the spreading front, thereby controlling the minimum thickness of the vapour layer in both moderate and high superheat regimes. We derive self-similar solutions based on this equilibrium, and the predicted minimum film thickness aligns remarkably well with our numerical results. This provides compelling evidence that evaporation alone is insufficient to prevent droplet–pool coalescence.

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.