In this study, we develop a super-resolution (SR) model for homogeneous isotropic turbulence (HIT) inspired by the recently proposed low-inference-cost ResShift diffusion model. The training data are obtained from direct numerical simulation of two three-dimensional HIT cases with varying grid resolutions and Reynolds numbers ($ \textit{Re}_\lambda = 94$ and 173) to increase the model’s generalisability. The model is trained on two-dimensional snapshots rather than full three-dimensional fields, as training and inference on three-dimensional data would increase the computational cost significantly. Both the data from the whole domain and the data from a quarter of the domain are considered in the dataset to increase the diversity and quantity of training samples. This strategy also helps the model learn more localised flow structures and reduces dependence on global domain-specific patterns. The model is trained using single snapshots of velocity components for three upsampling factors of 4, 8 and 16. To assess the generalisability of the trained model, it is tested for flows under conditions different from those of the training data. Additionally, the high-resolution reconstruction of flow fields from low-resolution turbulent boundary layer data is performed to evaluate the model’s performance in anisotropic turbulence. The results show that the diffusion model presented in this study performs well in predicting the velocity field even for high upsampling factors, and unlike bicubic interpolation, convolutional neural network (CNN)- and U-Net-based models, it does not generate a visually blurry flow field when applied to high upsampling factors. It also outperforms bicubic interpolation, CNN- and U-Net-based models, as well as the traditional conditional denoising diffusion probabilistic model designed for SR, in predicting flow statistics. The model effectively extracts flow features, generates flow structures of varying sizes and shows strong performance in predicting vorticity. It also reproduces the energy spectrum at high wavenumbers with reasonable accuracy, indicating the recovery of small-scale structures often lost in coarse data. This capability is valuable for subgrid-scale stress estimation and helps improve the physical fidelity of large eddy simulation frameworks.

We show that spatio-temporal non-Markovianity of a Gaussian random synthetic velocity field is an essential property for modelling turbulent mixing. We demonstrate this using synthetically generated Gaussian incompressible velocity fields for passive scalar mixing. Including a separate velocity decorrelation time scale for each spatial scale (random sweeping) yields an essentially non-Markovian velocity field with a finite time memory decaying as $\tau ^{-6}$ (for a decaying spectrum) instead of an exponential decay (Markovian), which is obtained by including a constant time scale for all spatial scales, irrespective of the filtering function. We characterise the Lagrangian mixing statistics of both the Markovian and the non-Markovian synthetic fields and compare them against a corresponding incompressible direct numerical simulation (DNS). We show that the average pair dispersion is well captured by the non-Markovian fields across the ballistic, inertial and diffusive regimes. We also study diffusive passive scalar mixing in the Schmidt number range $\textit{Sc}\leqslant 1$ using the DNS and the synthetic fields. Both the synthetic fields recover the $-17/3$ scalar spectrum for low Schmidt numbers and inertial subrange in kinetic energy spectra. However, the mean fluctuation gradient magnitudes are severely under predicted by the Markovian synthetic fields compared with the non-Markovian synthetic fields. Additionally, the fluctuation gradients parallel to the mean gradient exhibit smaller skewness when stirred by the Markovian synthetic field compared with the non-Markovian fields. Finally, we show that the non-Markovian synthetic fields perform better in decaying scalar gradient simulations initialised by a concentrated sphere with high passive scalar concentration. Throughout, we compare our results with companion three-dimensional DNS to show the necessity of non-Markovianity in synthetic fields to capture mixing dynamics.

The mechanical response of elastic porous media confined within rigid geometries is central to a wide range of industrial, geological and biomedical systems. However, current models for these problems typically overlook the role of wall friction and particularly its interaction with confinement. Here, we develop a theoretical framework to describe the interplay between the mechanics of the medium and Coulomb friction at the confining walls for slow, quasistatic deformations in response to two canonical uniaxial forcings: piston-driven loading (i.e. an imposed effective stress at the top boundary) and fluid-driven loading (i.e. an imposed fluid pressure at the top boundary) followed by unloading. We find that, during compression, the stress field evolves according to a quasistatic advection–diffusion equation, extending classical poroelasticity results. The magnitude of friction is controlled by a single dimensionless number ($\mathcal{F}$) proportional to the friction coefficient and the aspect ratio of the confining geometry. During decompression, a portion of the solid matrix remains stuck due to friction, leading to hysteresis and to the propagation of a slip front. In piston-driven loading the frictional stress is directly coupled to the solid effective stress, leading to exponential damping of the loading and striking changes to the displacement field. However, this coupling limits the energy dissipated by friction. In fluid-driven loading the pressure gradient locally adds energy, decoupling elastic energy storage and frictional energy dissipation. The displacement remains qualitatively unchanged but is quantitatively reduced due to large energy dissipation. In both cases, friction can have a substantial impact on the apparent mechanical properties of the medium.

The extreme heat fluxes characteristic of hypersonic flows significantly limit the flight envelope of hypersonic vehicles. The role of hydrodynamic instability and the onset of laminar-to-turbulent boundary layer transition is of notable importance. The effect of streaks on the suppression of planar (second Mack mode) instabilities has been previously investigated, but a potentially passive and non-intrusive control method has not been established yet. Recent work shows that streaks can be generated through a spanwise variation in surface temperature. This method exploits the aerothermodynamic characteristics of the flow, and therefore promises to be robust. This work uses direct numerical simulations to determine and quantify the effectiveness of this novel control method in the suppression of second Mack mode instability for a hypersonic boundary layer over a flat plate. The computational analyses cover a range of Mach numbers, 4.8–6, and wall temperature ratios representative of both wind tunnel testing and flight scenarios. Among the range of configurations investigated, the energy of the second Mack mode is reduced by up to approximately 60 % by the steady streaks. The streak wavelength parameter plays a significant role in the stabilisation benefits. For a Mach 6 configuration, for the most linearly amplified second Mack mode disturbance frequency, nearly optimum performance is achieved for a spanwise wavelength of approximately 8–10 times the local boundary layer thickness. These findings open new avenues for controlling hypersonic boundary layers and offer valuable guidance for future experimental campaigns aimed at validating this novel control strategy.

We consider the response of a flexibly mounted square prism placed in inertial-viscoelastic fluid flow with one degree-of-freedom in the cross-flow direction. Under these flow conditions, both inertia and elastic effects are significant. We model the system numerically using a two-way coupling scheme to simulate the interaction between the fluid and the spring–mass system at a Reynolds number of $\textit{Re}=200$ for two mass ratios of $m^* = 2$ and 20, and a Weissenberg number of $\textit{Wi}=2$, across a range of reduced velocities. We demonstrate that introducing fluid elasticity suppresses vortex-induced vibrations of square prisms, consistent with prior findings for circular bluff bodies. However, we find that fluid elasticity amplifies the galloping response in comparison with the response in a Newtonian fluid, leading to larger oscillation amplitudes and the onset of galloping at lower reduced velocities. The predicted enhancement in galloping is significant, particularly at low mass ratios, where no galloping is observed over the wide reduced velocity range tested for Newtonian fluids. We show that this enhancement of galloping is likely the result of the observation that the addition of viscoelasticity increases the magnitude of the rate of change of the transverse flow-induced force on the prism with increasing angle of attack of the incoming flow.

We perform direct numerical simulations of continuously growing broadband surface waves forced by a turbulent atmospheric boundary layer coupled with a developing underwater current. We resolve and analyse the multiscale space–time evolution of the waves by considering the wave spectrum in frequency and wavenumber space and describe the kinematics of nonlinear gravity–capillary waves under a current initially described by a viscous boundary layer and transitioning to turbulence at later times under the wind-wave forcing. The wave speed experiences a scale-dependent Doppler shift, with shorter waves shifted by currents closer to the surface, in agreement with the framework from Stewart & Joy (1974 Deep Sea Res. Oceanogr. Abstracts 21(12), 1039–1049). At low wave slopes, the wave energy concentrates along the linear dispersion relation. When the wave slope is high enough, we observe wave energy located in multiple branches associated with nonlinear bound harmonics travelling at the speed of a carrier mode. These nonlinear branches are well described by a generalized nonlinear dispersion relation that links each harmonic to the effective velocity of the carrier mode to which they are bound, and are found to be Doppler shifted with the carrier mode. The generalized Doppler-shifted nonlinear dispersion relation remains valid as the underwater current becomes turbulent, and the depth-varying mean current profile can be systematically reconstructed from the measured phase velocities from waves at different scales.