We consider two-dimensional (2-D) free surface gravity waves in prismatic channels, including bathymetric variations uniquely in the transverse direction. Starting from the Saint-Venant equations (shallow-water equations) we derive a one-dimensional transverse averaged model describing dispersive effects related solely to variations of the channel topography. These effects have been demonstrated in Chassagne et al. 2019 J. Fluid Mech. 870, 595–616 to be predominant in the propagation of bores with Froude numbers below a critical value of approximately 1.15. The model proposed is fully nonlinear, Galilean invariant, and admits a variational formulation under natural assumptions about the channel geometry. It is endowed with an exact energy conservation law, and admits exact travelling-wave solutions. Our model generalises and improves the linear equations proposed by Chassagne et al. 2019 J. Fluid Mech. 870, 595–616, as well as in Quezada de Luna and Ketcheson, 2021 J. Fluid Mech. 917, A45. The system is recast in two useful forms appropriate for its numerical approximations, whose properties are discussed. Numerical results allow the verification of the implementation of these formulations against analytical solutions, and validation of our model against fully 2-D nonlinear shallow-water simulations, as well as the famous experiments by Treske 1994 J. Hyd. Res. 32, 355–370.

We present a theoretical framework and validation for manipulating instability growth in shock-accelerated dual-layer material systems, which feature a light–heavy interface followed by two sequential heavy–light interfaces. An analytical model is first developed to predict perturbation evolution at the two heavy–light interfaces, explicitly incorporating the effects of reverberating waves within the dual-layer structure. The model identifies five distinct control regimes for instability modulation. Shock-tube experiments and numerical simulations are designed to validate these regimes, successfully realising all five predicted states. Notably, the selective growth stagnation of a perturbation at either the upstream or downstream heavy–light interface is realised numerically by tuning the initial separation distances of the three interfaces. This work elucidates the critical role of the wave dynamics in governing interface evolution of a shocked dual layer, offering insights for mitigating hydrodynamic instabilities in practical scenarios such as inertial confinement fusion.

Studying rotating convection under geo- and astrophysically relevant conditions has proven to be extremely difficult. For the rotating Rayleigh–Bénard system, van Kan et al. (J. Fluid Mech., vol. 1010, 2025,A42)have now been able to massively extend the parameter space accessible by direct numerical simulations. Their progress relies on a rescaling of the governing Boussinesq equations, which vastly improves numerical conditioning (Julien et al., arXiv:2410.02702). This opens the door for investigating previously inaccessible dynamical regimes and bridges the gap to the asymptotic branch of rapidly rotating convection.

In this study, we obtain the continuum equations of Arctic sea ice motion starting from the dynamics of a single floe and show that the rheology that emerges from floe–floe interactions is viscous – as conjectured by Reed and Campbell (J. Geophys. Res., vol. 67 (1), 1962, pp. 281–297). The motion of the floe is principally driven by the wind and ocean currents and by inelastic collisions with the neighbouring floes. A mean-field representation of these collisions is developed, neglecting any changes in the floe thickness due to thermal growth and mechanical deformation. This mean-field representation depends on the state of the ice cover, and is expressed in terms of ice concentration and mean thickness. The resulting Langevin equation for the floe velocity, or the corresponding kinetic equation (Kramers–Chandrasekhar equation (KCE)) for its probability density, provides a complete description of the floe’s motion. We then use the floe-scale dynamics to obtain a continuum description of sea ice motion through a Chapman–Enskog analysis of the KCE. The local equilibrium solution to the kinetic equation is found to be the Laplace distribution, in qualitative agreement with observations. Our approach also allows us to establish the dependence of pressure and shear viscosity of the ice cover on ice concentration and mean thickness. Lastly, we show that our results resolve a conflict associated with the choice of the value of shear viscosity in previous idealised numerical studies of Arctic sea ice motion.

Previous studies claimed that the non-monotonic effects of wettability came mainly from the heterogeneity of geometries or flow conditions on multiphase displacements in porous media. For macroscopic homogeneous porous media, without permeability contrast or obvious preferential flow pathways, most pore-scale evidence showed a monotonic trend of the wettability effect. However, this work reports transitions from monotonic to non-monotonic wettability effects when the dimension of the model system rises from two-dimensional (2-D) to three-dimensional (3-D), validated by both the network modelling and the microfluidic experiments. The mechanisms linking the pore-scale events to macroscopic displacement patterns have been analysed through direct simulations. For 2-D porous media, the monotonic effect of wettability comes from the consistent transition pattern for the full range of capillary numbers $Ca$, where the capillary fingering mode transitions to the compact displacement mode as the contact angle $\theta$ decreases. Yet, it is indicated that the 3-D porous geometries, even though homogeneous without permeability contrast or obvious preferential flow pathways, introduce a different $Ca$–$\theta$ phase diagram with new pore-scale events, such as the coupling of capillary fingering with snap-off during strong drainage, and frequent snap-off events during strong imbibition. These events depend strongly on geometric confinements and capillary numbers, leading to the non-monotonicity of wettability effects. Our findings provide new insights into the multiphase displacement dependent on wettability in various natural porous media and offer design principles for engineering artificial porous media to achieve desired immiscible displacement behaviours.

This study utilises large-eddy simulation with the actuator line model to examine the effects of the tip speed ratio (TSR) on the wake-meandering characteristics of a wind turbine in uniform and turbulent inflows. It is shown that as the TSR grows, the onset position of the wake meandering moves closer to the rotor, and the magnitude of wake oscillation is stronger. This aligns with previous work showing that a higher TSR can accelerate the instability and breakdown of tip vortices. Without a nacelle, the Strouhal number of the wake meandering is found to be independent of the TSR under both the uniform and turbulent inflows. However, with a relatively large nacelle, the Strouhal number first increases and then decreases with TSR. Therefore, the current discovery elucidates the crucial role of the nacelle and clarifies the origin of the TSR dependence of the Strouhal number in wake meandering. In addition, the characteristic frequency of the wake meandering under the turbulent inflow is much smaller than that under the uniform inflow, because of the significant influence of the freestream turbulence. Furthermore, the proper orthogonal decomposition (POD) and spectral POD (SPOD) methods are employed to study the spatiotemporal characteristics of the meandering wake and its TSR dependence. It is found that the tip and root vortices are the prominent wake structures under the uniform inflow, whereas more complex multiscale structures from the interaction between the freestream turbulence and tip/root vortices exist under the turbulent inflow. Moreover, an amplitude modulation phenomenon of the POD time coefficients at the optimal TSR is observed in the uniform inflow case. Finally, a reduced-order model is constructed for predicting the wake dynamics by combining the SPOD and the ‘sparse identification of nonlinear dynamics’ algorithm with high accuracy and interpretability.

The accurate quantification of wall-shear stress dynamics is of substantial importance for various applications in fundamental and applied research, spanning areas from human health to aircraft design and optimization. Despite significant progress in experimental measurement techniques and postprocessing algorithms, temporally resolved wall-shear stress fields with adequate spatial resolution and within a suitable spatial domain remain an elusive goal. Furthermore, there is a systematic lack of universal models that can accurately replicate the instantaneous wall-shear stress dynamics in numerical simulations of multiscale systems where direct numerical simulations (DNSs) are prohibitively expensive. To address these gaps, we introduce a deep learning architecture that ingests wall-parallel streamwise velocity fields at $y^+ \approx 3.9 \sqrt {Re_\tau }$ of turbulent wall-bounded flows and outputs the corresponding two-dimensional streamwise wall-shear stress fields with identical spatial resolution and domain size. From a physical perspective, our framework acts as a surrogate model encapsulating the various mechanisms through which highly energetic outer-layer flow structures influence the governing wall-shear stress dynamics. The network is trained in a supervised fashion on a unified dataset comprising DNSs of statistically one-dimensional turbulent channel and spatially developing turbulent boundary layer flows at friction Reynolds numbers ranging from $390$ to $1500$. We demonstrate a zero-shot applicability to experimental velocity fields obtained from particle image velocimetry measurements and verify the physical accuracy of the wall-shear stress estimates with synchronized wall-shear stress measurements using the micro-pillar shear-stress sensor for Reynolds numbers up to $2000$. In summary, the presented framework lays the groundwork for extracting inaccessible experimental wall-shear stress information from readily available velocity measurements and thus, facilitates advancements in a variety of experimental applications.

Time-dependent fluid dynamics plays a crucial role in both natural phenomena and industrial applications. Understanding the flow instabilities and transitions within these dynamical systems is essential for predicting and controlling their unsteady behaviour. A classic example of time-dependent flow is the Stokes layer. To study the transition mechanism in this flow, we employ the finite-time Lyapunov exponent (FTLE) to demonstrate that a linear energy amplification mechanism may explain the intracyclic instability in the transitional Stokes layer, supported by favourable comparisons with experimental measurements of axial turbulence intensity. This complements existing theories applied to the Stokes layer in the literature, including the Floquet analysis and the instantaneous/momentary analyses, which have struggled to capture this experimental observation accurately. The FTLE analysis is closely related to the transient growth analysis, formulated as an optimisation problem of the disturbance energy growth over time. We found that the energy amplification weakens as the finite Stokes layer becomes more confined, and the oscillating frequency has a non-monotonic effect on the maximum transient growth. Based on these results, we recommend future experimental studies to validate this linear mechanism.

An experimental study was conducted in the CICLoPE long-pipe facility to investigate the correlation between wall-pressure and turbulent velocity fluctuations in the logarithmic region, at high friction Reynolds numbers ($4794 \lesssim Re_\tau \lesssim 47\,015$). Hereby, we explore the scalability of employing wall-pressure to effectively estimate off-the-wall velocity states (e.g. to be of use in real-time control of wall-turbulence). Coherence spectra for wall-pressure and streamwise (or wall-normal) velocity fluctuations collapse when plotted against $\lambda _x/y$ and thus reveals a Reynolds-number-independent scaling with distance-from-the-wall. When the squared wall-pressure fluctuations are considered instead of the linear wall-pressure term, the coherence spectra for the wall-pressure-squared and velocity are higher in amplitude at wavelengths corresponding to large-scale streamwise velocity fluctuations (e.g. at $\lambda _x/y = 60$, the coherence value increases from roughly 0.1 up to 0.3). This higher coherence typifies a modulation effect, because low-frequency content is introduced when squaring the wall-pressure time series. Finally, quadratic stochastic estimation is employed to estimate turbulent velocity fluctuations from the wall-pressure time series only. For each $Re_\tau$ investigated, the estimated time series and a true temporal measurement of velocity inside the turbulent pipe flow yield a normalised correlation coefficient of $\rho \approx 0.6$ for all cases. This suggests that wall-pressure sensing can be employed for meaningful estimation of off-the-wall velocity fluctuations and thus for real-time control of energetic turbulent velocity fluctuations at high-$Re_\tau$ applications.

In the dynamical systems approach to turbulence, unstable periodic orbits (UPOs) provide valuable insights into system dynamics. Such UPOs are usually found by shooting-based Newton searches, where constructing sufficiently accurate initial guesses is difficult. A common technique for constructing initial guesses involves detecting recurrence events by comparing past and future flow states using their $L_2$-distance. An alternative method uses dynamic mode decomposition (DMD) to generate initial guesses based on dominant frequencies identified from a short time series, which are signatures of a nearby UPO. However, DMD struggles with continuous symmetries. To address this drawback, we combine symmetry-reduced DMD (SRDMD) introduced by Marensi et al. (2023, J. Fluid Mech., vol. 954, A10), with sparsity promotion. This combination provides optimal low-dimensional representations of the given time series as a time-periodic function, allowing any time instant along this function to serve as an initial guess for a Newton solver. We also discuss how multi-shooting methods operate on the reconstructed trajectories, and we extend the method to generate initial guesses for travelling waves. We demonstrate SRDMD as a method complementary to recurrent flow analysis by applying it to data obtained by direct numerical simulations of three-dimensional plane Poiseuille flow at the friction Reynolds number $\textit{Re}_\tau \approx51$ ($\textit{Re}=802$), explicitly taking a continuous shift symmetry in the streamwise direction into account. The resulting unstable relative periodic orbits cover relevant regions of the state space, highlighting their potential for describing the flow.