Quantum technologies, including computing, communication/security and sensing, have significantly advanced over the last years. Industry-specific applications are now being intensely researched and healthcare, medicine and the life sciences represent one of the focus areas.

We investigate the Benjamin–Feir (or modulational) instability of Stokes waves, i.e. small-amplitude, one-dimensional periodic gravity waves of permanent form and constant velocity, in water of finite and infinite depth. We develop a perturbation method to describe to high-order accuracy the unstable spectral elements associated with this instability, obtained by linearizing Euler's equations about the small-amplitude Stokes waves. These unstable elements form a figure-eight curve centred at the origin of the complex spectral plane, which is parametrized by a Floquet exponent. Our asymptotic expansions of this figure-eight are in excellent agreement with numerical computations as well as recent rigorous results by Berti et al. (Full description of Benjamin–Feir instability of Stokes waves in deep water, 2021, arXiv:2109.11852) and Berti et al. (Benjamin–Feir instability of Stokes waves in finite depth, 2022, arXiv:2204.00809). From our expansions, we derive high-order estimates for the growth rates of the Benjamin–Feir instability and for the parametrization of the Benjamin–Feir figure-eight curve with respect to the Floquet exponent. We are also able to compare the Benjamin–Feir and high-frequency instability spectra analytically for the first time, revealing three different regimes of the Stokes waves, depending on the predominant instability.

The dynamics of sedimenting particles under gravity are surprisingly complex due to the presence of effective long-ranged forces. When the particles are polar with a well-defined symmetry axis and non-uniform density, recent theoretical predictions suggest that prolate objects will repel and oblate ones will weakly attract. We tested these predictions using mass polar prolate spheroids, which are composed of 2 mm spheres glued together. We probed different aspect ratios ($\kappa$) and centre of mass variations ($\chi$) by combining spheres of different densities. Experiments were done in both quasi-two-dimensional (2-D) and three-dimensional (3-D) chambers. By optically tracking the motion of single particles, we found that the dynamics were well described by a reduced mobility matrix model that could be solved analytically. Pairs of particles exhibited an effective repulsion, and their separation roughly scaled as $(\kappa - 1)/\chi ^{0.39}$, i.e. particles that were more prolate or had smaller mass asymmetry had stronger repulsion effects. In three dimensions, particles with $\chi >0$ were distributed more uniformly than $\chi =0$ particles, and the degree of uniformity increased with $\kappa$, indicating that the effective 2-body repulsion manifests for a large number of particles.

Composite sweeping-enhanced resolvents, referred to as the ${\boldsymbol {R}}_s^2$ model, are proposed to predict the space–time statistics of large-scale structures in turbulent channel flows. This model incorporates two key mechanisms: (i) eddy damping is introduced to represent random sweeping decorrelation caused by nonlinear forcing, leading to a sweeping-enhanced resolvent ${{\boldsymbol {R}}_s}$; and (ii) the sweeping-enhanced resolvent ${{\boldsymbol {R}}_s}$ is composited into its iterations ${\boldsymbol {R}}_s^2$ to yield non-zero Taylor time microscales. The resulting ${\boldsymbol {R}}_s^2$ model can correctly predict the frequency spectra and two-point cross-spectra of large-scale structures. This model is compared numerically with eddy-viscosity-enhanced resolvent models. The latter are designed to represent energy transfer instead for time decorrelation, and thus underpredict the characteristic decay time scales. The ${\boldsymbol {R}}_s^2$ model correctly yields the characteristic decay time scales in turbulent channel flows.

The exhaust from combustion engines contains particulate matter (PM), which poses potential health risks to human lungs. Current emission laws place increasingly strict limitations on both PM and particle number, leading to the necessity of using wall-flow filters to separate out a significant amount of the introduced PM. As this leads to an increase in the filter's loading, it is regenerated continuously or periodically, leading to the rearrangement of individual particulate structures inside the filter channels. Such rearrangement events cause the formation of specific deposition patterns, which affect the filter's pressure drop, its loading capacity and the separation efficiency. In order to derive predictions on the formation of specific deposition patterns, the transient behaviour of individual particle structures needs to be examined. The present work investigates the detachment and transport of particle structures during filter regeneration with three-dimensional surface-resolved simulations using a lattice Boltzmann method. The goal of this work is the determination of relevant key quantities and their interpretation with respect to predictions regarding the resulting deposition patterns. In this context, it is shown that lift forces are not the predominant detachment forces for non-spherical particle structures, and that the stopping distance of such structures is too long to avoid back-end deposition.

In this study, we revisit the spectral transfer model for the turbulent intensity in passive scalar transport (under large-scale anisotropic forcing), and a subsequent modification to the scaling of scalar variance cascade is presented. From the modified spectral transfer model, we obtain a revised scalar transport model using a fractional-order Laplacian operator that facilitates the robust inclusion of the non-local effects originating from large-scale anisotropy transferred across the multitude of scales in the turbulent cascade. We provide an a priori estimate for the non-local model based on the scaling analysis of the scalar spectrum, and later examine our developed model through direct numerical simulation. We present a detailed analysis on the evolution of the scalar variance, high-order statistics of the scalar gradient and important two-point statistical metrics of the turbulent transport to make a comprehensive comparison between the non-local model and its standard version. Finally, we present an analysis that seamlessly reconciles the similarities between the developed model with the fractional-order subgrid-scale scalar flux model for large-eddy simulation (Akhavan-Safaei et al., J. Comput. Phys., vol. 446, 2021, 110571) when the filter scale approaches the dissipative scales of turbulent transport. In order to perform this task, we employ a Gaussian process regression model to predict the model coefficient for the fractional-order subgrid model.

Underwater stability of an air layer trapped in a micro-structure, plastron, is critical in drag reduction applications. Here, we investigate the wetting state and plastron stability of underwater superhydrophobic surfaces (SHS) under an intense acoustic drive. Flat surfaces and SHS are subjected to short acoustic pulses of different intensities. At low amplitude, the comparison between the results of various surfaces shows that plastron behaves like a water–air interface, whose presence can be detected from the phase of the reflected acoustic waves. At moderate intensity, a wetting transition towards a completely wetting state is observed and shown to be triggered by a sufficiently large acoustic radiation pressure. This wetting transition is well captured by a simplified model by balancing radiation pressure with the critical capillary pressure for the interface sliding. Cavitation clouds appear under strong excitation; their sizes and positions greatly depend on the surface acoustic boundary condition. For SHS in a Cassie–Baxter state (with an air layer), cavitation clouds appear at specific locations (from the solid surface) corresponding to the pressure anti-node of the transient standing wave generated by the reflection. This study unprecedentedly demonstrates the capability of acoustic waves to monitor and characterize plastron stability with low and moderate amplitudes, respectively.

The heterogeneity of permeability in a porous medium considerably alters the behaviour of density-driven flows from what is observed in a medium of homogeneous permeability, and significantly enhances the mixing between the dense and light fluids during the flow. In this work, we present results from laboratory experiments performed in heterogeneous media consisting of horizontal layers of different permeabilities, investigating their effects on gravity current flows. We find that the mixing in our heterogeneous experimental set-ups can be ${O}(2)$ greater than that in a homogeneous medium of similar depth-averaged properties. The enhanced mixing in this setting is primarily because of transverse gravity-driven fingers and produced blunt front, which is the direct result of the layered structure. This enhanced rate of mixing dictates the gravity current height and length, making the current lose its long and thin shape much faster than a comparable current in a homogeneous medium. We discuss the experimental observations in detail and present relevant physical interpretations. Based on the experimental measurements and dimensionless modelling, we also derive semi-empirical formulas for predicting the gravity current length, height and mixing in a heterogeneous medium. Results from this work can be used in predicting the scale of mixing between different density fluids during contaminant transport in the subsurface environment.

When two drops collide, they may either exhibit complete coalescence or selectively generate secondary drops, depending on their relative sizes and physical properties, as dictated by a decisive interplay of the viscous, capillary, inertia and gravity effects. Electric field, however, is known to induce distinctive alterations in the topological evolution of the interfaces post-collision, by influencing a two-way nonlinear coupling between electro-mechanics and fluid flow as mediated by a topologically intriguing interfacial deformation. While prior studies primarily focused on the viscous-dominated regime of the resulting electro-coalescence dynamics, several non-intuitive features of the underlying morpho-dynamic evolution over the intertio-capillary regime have thus far remained unaddressed. In this study, we computationally investigate electrically modulated coalescence dynamics along with secondary drop formation mechanisms in the inertio-capillary regime, probing the interactions of two unequal-sized drops subjected to a uniform electric field. Our results bring out an explicit mapping between the observed topological evolution as a function of the respective initial sizes of the parent drops as well as their pertinent electro-physical property ratios. These findings establish electric-field-mediated exclusive controllability of the observed topological features, as well as the critical conditions leading to the transition from partial to complete coalescence phenomena. In a coalescence cascade, an electric field is further shown to orchestrate the numbers of successive stages of coalescence before complete collapse. However, an increase of the numbers of cascade stages with the electric field strength and parent droplet size ratio is non-perpetual, and the same is demonstrated to continue until only a threshold number of cascade stages is reached. These illustrations offer significant insights into leveraging the interplay of electrical, inertial and capillary-driven interactions for controllable drop manipulation via multi-drop interactions for a variety of applications ranging from chemical processing to emulsion technology.

A bio-inspired, passively deployable flap attached to an airfoil by a torsional spring of fixed stiffness can provide significant lift improvements at post-stall angles of attack. In this work, we describe a hybrid active–passive variant to this purely passive flow control paradigm, where the stiffness of the hinge is actively varied in time to yield passive fluid–structure interaction of greater aerodynamic benefit than the fixed-stiffness case. This hybrid active–passive flow control strategy could potentially be implemented using variable-stiffness actuators with less expense compared with actively prescribing the flap motion. The hinge stiffness is varied via a reinforcement-learning-trained closed-loop feedback controller. A physics-based penalty and a long–short-term training strategy for enabling fast training of the hybrid controller are introduced. The hybrid controller is shown to provide lift improvements as high as 136 % and 85 % with respect to the flapless airfoil and the best fixed-stiffness case, respectively. These lift improvements are achieved due to large-amplitude flap oscillations as the stiffness varies over four orders of magnitude, whose interplay with the flow is analysed in detail.

We numerically study the melting process of a solid layer heated from below such that a liquid melt layer develops underneath. The objective is to quantitatively describe and understand the emerging topography of the structures (characterized by the amplitude and wavelength), which evolve out of an initially smooth surface. By performing both two-dimensional (achieving Rayleigh number up to $Ra=10^{11}$) and three-dimensional (achieving Rayleigh number up to $Ra=10^9$) direct numerical simulations with an advanced finite difference solver coupled to the phase-field method, we show how the interface roughness is spontaneously generated by thermal convection. With increasing height of the melt the convective flow intensifies and eventually even becomes turbulent. As a consequence, the interface becomes rougher but is still coupled to the flow topology. The emerging structure of the interface coincides with the regions of rising hot plumes and descending cold plumes. We find that the roughness amplitude scales with the mean height of the liquid layer. We derive this scaling relation from the Stefan boundary condition and relate it to the non-uniform distribution of heat flux at the interface. For two-dimensional cases, we further quantify the horizontal length scale of the morphology, based on the theoretical upper and lower bounds given for the size of convective cells known from Wang et al. (Phys. Rev. Lett., vol. 125, 2020, 074501). These bounds agree with our simulation results. Our findings highlight the key connection between the morphology of the melting solid and the convective flow structures in the melt beneath.

In the context of transition analysis, linear input–output analysis determines the worst-case disturbances to a laminar base flow based on a generic right-hand-side volumetric/boundary forcing term. The worst-case forcing is not physically realizable, and, to our knowledge, a generic framework for posing physically realizable worst-case disturbance problems is lacking. In natural receptivity analysis, disturbances are forced by matching (typically local) solutions within the boundary layer to outer solutions consisting of free-stream vortical, entropic and acoustic disturbances. We pose a scattering formalism to restrict the input forcing to a set of realizable disturbances associated with plane-wave solutions of the outer problem. The formulation is validated by comparing with direct numerical simulations of a Mach 4.5 flat-plate boundary layer. We show that the method provides insight into transition mechanisms by identifying those linear combinations of plane-wave disturbances that maximize energy amplification over a range of frequencies. We also discuss how the framework can be extended to accommodate scattering from shocks and in shock layers for supersonic flow.

Understanding and predicting the dynamics of dispersed micro-objects in microfluidics is crucial in numerous natural, industrial and technological situations. In this paper, we experimentally characterized the equilibrium velocity $V$ and lateral position $\varepsilon$ of various dispersed micro-objects, such as beads, bubbles and drops, in a cylindrical microchannel over an unprecedentedly wide range of parameters. By varying the dimensionless object size ($d \in [0.1; 1]$), the viscosity ratio ($\lambda \in [10^{-2}; \infty [$), the density ratio ($\varphi \in [10^{-3}; 2]$), the Reynolds number ($Re \in [10^{-2}; 10^2]$) and the capillary number ($Ca \in [10^{-3}; 0.3]$), we offer an exhaustive parametric study exploring various dynamics from the non-deformable viscous regime to the deformable inertial regime, thus enabling us to highlight the sole and combined roles of inertia and capillary effects on lateral migration. Experiments are compared and agree well with a steady three-dimensional Navier–Stokes model for incompressible two-phase fluids, including the effects of inertia and possible interfacial deformations. This model enables us to propose a correlation for the object velocity $V$ as functions of $d$, $\varepsilon$ and $\lambda$, obtained in the ${Re}={Ca}=0$ limit, but valid for a larger range of values of ${Re}$ and ${Ca}$ delimited by the validity of the linear regime. Next, we present stability maps for the centred position showing that non-deformable objects dominated by inertial effects are only stable if large enough, typically for $d \gtrsim 0.7$, whereas deformable objects dominated by capillary effects can be stable for much smaller sizes, provided the viscosity ratio is outside the range $0.7 \lesssim \lambda \lesssim 10$, in which deformability also plays a destabilizing effect, as for inertia.