The advent of fault-tolerant quantum computing (FTQC) promises to tackle classically intractable problems. A key milestone is solving the Navier-Stokes equations (NSE), which has remained formidable for quantum algorithms due to their high input-output overhead and nonlinearity. Here, we establish a full-stack framework that charts a practical pathway to a quantum advantage for large-scale NSE simulation. Our approach integrates a spectral-based input/output algorithm, an explicit and synthesized quantum circuit, and a refined error-correction protocol. The algorithm achieves an end-to-end exponential speedup in asymptotic complexity, meeting the lower bound for general quantum linear system solvers. Through symmetry-based circuit synthesis and optimized error correction, we reduce the required logical and physical resources by two orders of magnitude. Our concrete resource analysis demonstrates that solving NSE on a $2^{80}$-grid is feasible with 8.71 million physical qubits (at an error rate of $5 \times 10^{-4}$) in 42.6 days -- outperforming a state-of-the-art supercomputer, which would require over a century. This work bridges the gap between theoretical quantum speedup and the practical deployment of high-performance scientific computing.

Inspired by recent experiments demonstrating that vibrating elastic sheets can function as seemingly contactless suction cups, we investigate the elastohydrodynamic hovering of a thin elastic sheet vibrating near a rigid substrate. Previous theoretical work suggests that the hovering height results from a balance between the active forcing that triggers the vibrations, the bending forces associated with the sheet's deformation, the viscous lubrication flow between the sheet and the substrate, and the sheet's weight. Here, we extend this analysis beyond the asymptotic regime of weak forcing and explore the regime of strong forcing through numerical simulations. We further quantify the influence of fluid inertia and compressibility on the equilibrium hovering height and the maximum load that can be supported. Both effects are found to introduce repulsive contributions to the net force on the sheet, which can significantly reduce its adhesive strength. Beyond providing insights into soft contactless grippers and swimming near surfaces, our analysis is relevant to the elastohydrodynamics of squeeze films and near-field acoustic levitation.

Dense stabilized emulsions are mixtures of immiscible fluids where the high-volume fraction droplet dispersed phase is stabilized against coalescence by steric interactions. The production of emulsions involves high-shear flows and it is well known that at a critical volume fraction the emulsion loses stability, undergoing an extremely rapid process where the fluid components in the emulsion exchange roles. This process, called catastrophic phase inversion, which resembles in several respects a dynamical phase transition, has remained widely elusive from an experimental and theoretical point of view. In this work, we present state-of-the-art experimental and numerical data to support a dynamical-system framework capable of precisely highlighting the dynamics occurring in the system as it approaches the catastrophic phase inversion. Our study clearly highlights that at high volume fractions, dynamical changes in the emulsion morphology, due to coalescence and breakup of droplets, play a critical role in determining emulsion's rheology and stability. Additionally, we show that at approaching the critical volume fractions, the dynamics can be simplified as being controlled by the dynamics of a correlation length represented, in our systems, by the size of the largest droplet. This dynamics shares a close connection with non-reciprocal phase transition where two different physical mechanisms, coalescence and breakups, can get out of balance leading to large non-symmetric periodic excursions in phase space. We clarify the phenomenology observed and quantitatively explain the essential aspect of the highly complex dynamics of stabilized emulsions undergoing catastrophic phase inversion.

We investigate droplet deformation following laser-pulse impact at low Weber numbers (We ~ 0.1-100). Droplet dynamics can be characterized by two key parameters: the impact We number and the width, W, of the distribution of the impact force over the droplet surface. By varying laser pulse energy, our experiments traverse a phase space comprising (I) droplet oscillation, (II) breakup, or (III) sheet formation. Numerical simulations complement the experiments by determining the pressure width and by allowing We and W to be varied independently, despite their correlation in the experiments. A single phase diagram, integrating observations from both experiments and simulations, demonstrates that all phenomena can be explained by a single parameter: the deformation Weber number Wed=f(We, W) that is based on the initial radial expansion speed of the droplet, following impact. The resulting phase diagram separates (I) droplet oscillation for Wed<5, from (II) breakup for 560.

Reliable initiation of oblique detonation waves (ODWs) is crucial for the stable operation of oblique detonation engines (ODEs), especially under flight conditions of low Mach numbers and/or high altitudes. In this case, conventional initiation approaches relying solely on a fixed-angle wedge may engender risks of initiation failure, which necessitates extra initiation assistance measures. In this study, ODW initiation over a finite wedge with local energy deposition is numerically investigated to assess the thermal effects of plasma-based initiation assistance techniques. Particular emphasis is put on the effects of forms and magnitudes of energy deposition on initiation modes and flow field structures of ODWs. The results demonstrate that on-wedge initiation of ODWs fails at a low Mach number without any energy depositions. In contrast, both continuous and pulsatile local energy depositions can effectively initiate ODWs, leading to sustainable detonation on the finite wedge. As continuous energy deposition power or pulsatile single pulse energy increases, several key detonation initiation modes emerge sequentially. Analysis of the spatiotemporal evolution of the primary wave structures under single-pulse energy deposition reveals the minimum pulse repetition frequency required for sustainable on-wedge detonation, which is subsequently verified through multi-pulse energy deposition simulations. Nevertheless, it is found that sustainable on-wedge detonation can be achieved by pulsatile energy deposition with an average power consumption of less than 10% of that required for continuous energy deposition while maintaining a same initiation length, suggesting that the pulsatile one is an efficient way of energy deposition for initiation assistance of ODWs on finite wedges under extreme flight conditions.

Repetitive curling of the incompressible viscid Navier-Stokes differential equation leads to a higher-order diffusion equation. Substituting this equation into the Navier-Stokes differential equation transposes the latter into the Korteweg-de Vries-Burgers equation with the Weierstrass p-function as the soliton solution. However, a higher-order derivative of the studied variable produces the so-called N-soliton solution, which is comparable to the N-soliton solution of the Kadomtsev-Petviashvili equation.

Leonardo da Vinci's aerial screw, conceived in the 15th century, represents one of the earliest conceptualizations of lift-generating rotary flight. Despite its historical significance, the aerodynamic and aeroacoustic performance of this rotor has received limited scientific attention. In this study, we employ direct numerical simulations to analyze the aerodynamic forces and acoustic emissions of a modernized da Vinci aerial screw design across a range of Reynolds numbers (2000, 4000, and 8000). These results are compared against those from a canonical two-bladed rotor producing similar lift. The aerial screw demonstrates significantly lower mechanical power consumption and acoustic intensity per unit lift, primarily due to its larger wetted area and correspondingly lower rotational speed. Although the aerial screw exhibits a lower lift coefficient and much of its surface contributes minimally to lift generation, the net performance under iso-lift conditions highlights its efficiency and reduced noise signature. The continuous spiral geometry of the aerial screw also helps suppress blade-vortex interaction noise common in multi-bladed systems. These findings support previous scaling analyses and point toward unconventional rotor designs as viable options for low-noise aerial platforms.

From the flutter of aircraft wings to an umbrella flipping inside out in the wind, fluid-induced elastic instabilities are a major concern in aeroelastic design. However, Nature often harnesses these instabilities to achieve new functionalities, such as the mechanical snap-through of the Venus flytrap. Inspired by this, engineers and physicists have increasingly exploited elastic instabilities to enable rapid shape changes in metamaterials and soft robots, provided the structure remains elastic throughout the transition. Here, we study the fluid-induced snapping instability of a spherical elastic shell at low Reynolds numbers, the umbrella flipping problem when life is at low Reynolds numbers. We combine precision desktop-scale experiments, fluid-structure simulations, shell theory, fluid mechanics, and scaling analysis to determine the instability threshold as a function of the geometrical and material parameters of the system. Building on these findings, we devise a snapping-based valve that passively and abruptly alters the hydraulic resistance of a channel, offering robust flow control without active components. These valves could be deployed in soft robotics and, because our results are expressed in terms of key dimensionless parameters, we speculate that the system can be miniaturized for use in microfluidic circuits. Beyond the application, our study presents what we believe to be a prototypical example of fluid-induced elastic instability at low Reynolds numbers, providing a foundation for future explorations in soft hydraulics and flow-responsive structures.

We present UniFoil, a large publicly available universal airfoil dataset based on Reynolds-averaged Navier-Stokes (RANS) simulations. It contains over 500,000 samples spanning a wide range of Reynolds and Mach numbers, capturing both transitional and fully turbulent flows across incompressible to compressible regimes. UniFoil is designed to support machine learning research in fluid dynamics, particularly for modeling complex aerodynamic phenomena. Most existing datasets are limited to incompressible, fully turbulent flows with smooth field characteristics, overlooking the critical physics of laminar\-turbulent transition and shock\-wave interactions\-features that exhibit strong nonlinearity and sharp gradients. UniFoil addresses this limitation by offering a broad spectrum of realistic flow conditions. Turbulent simulations utilize the Spalart\-Allmaras (SA) model, while transitional flows are modeled using an e^N\-based transition prediction method coupled with the SA model. The dataset includes a comprehensive geometry set comprising over 4,800 natural laminar flow (NLF) airfoils and 30,000 fully turbulent (FT) airfoils, covering a diverse range of airfoil designs relevant to aerospace, wind energy, and marine applications. This dataset is also valuable for scientific machine learning, enabling the development of data-driven models that more accurately capture the transport processes associated with laminar-turbulent transition. UniFoil is freely available under a permissive CC\-BY\-SA license.

Deep autoencoder neural networks can generate highly accurate, low-order representations of turbulence. We design a new family of autoencoders which are a combination of a 'dense-block' encoder-decoder structure (Page et al, J. Fluid Mech. 991, 2024), an 'implicit rank minimization' series of linear layers acting on the embeddings (Zeng et al, Mach. Learn. Sci. Tech. 5, 2024) and a full discrete+continuous symmetry reduction. These models are applied to two-dimensional turbulence in Kolmogorov flow for a range of Reynolds numbers $25 \leq Re \leq 400$, and used to estimate the dimension of the chaotic attractor, $d_{\mathcal A}(Re)$. We find that the dimension scales like $\sim Re^{1/3}$ -- much weaker than known bounds on the global attractor which grow like $Re^{4/3}$. In addition, two-dimensional maps of the latent space in our models reveal a rich structure not seen in previous studies, including multiple classes of high-dissipation events at lower $Re$ which guide bursting trajectories. We visualize the embeddings of large numbers of "turbulent" unstable periodic orbits, which the model indicates are distinct (in terms of features) from any flow snapshot in a large turbulent dataset, suggesting their dynamical irrelevance. This is in sharp contrast to their appearance in more traditional low-dimensional projections, in which they appear to lie within the turbulent attractor.

Surface bubbles in the ocean are critical in moderating several fluxes between the atmosphere and the ocean. In this paper, we experimentally investigate the drainage and lifetime of surface bubbles in solutions containing surfactants and salts, subjected to turbulence in the air surrounding them modelling the wind in the ocean. We carefully construct a setup allowing us to repeatably measure the mean lifetime of a series of surface bubbles, while varying the solution and the wind speed or humidity of the air. To that end, we show that renewing the surface layer is critical to avoid a change of the physical properties of the interface. We show that the drainage of the bubbles is well modelled by taking into account the outwards viscous flow and convective evaporation. The lifetime of surface bubbles in solutions containing no salt is given by the time when evaporation becomes the main draining mechanism and independent on surfactant concentration. When salt is added, the same scaling is valid only at high surfactant concentrations. At low concentrations, the lifetime is always smaller and independent of wind speed, owing to the presence of impurities triggering a thick bursting event.

Small-scale gravity waves play a crucial role in atmospheric tracer transport, yet their effects remain unresolved in climate models and must be parameterized. This study investigates how gravity waves influence large-scale tracer distributions, utilizing a multiple-scale analysis to systematically identify the governing terms of gravity wave-induced tracer fluxes. The analysis reveals both leading-order and next-order impacts: the former being the inertia-gravity wave-induced tracer Stokes drift, which acts perpendicular to both the large-scale tracer gradient and the wave number, while the latter becomes significant at lower latitudes where Coriolis effects diminish. A numerical framework is developed to incorporate these fluxes into a gravity wave parameterization model, potentially enhancing climate model accuracy without requiring explicit resolution of small-scale wave dynamics. Model validation against high-resolution wave-resolving simulations confirms the effectiveness of this approach. By improving the representation of gravity wave-induced tracer transport, this research advances the accuracy of climate simulations, particularly in their depiction of microphysics and radiative processes.

Lagrangian particles in turbulence separate away from each other faster in the backward in time direction as compared to forward in time. In this work, we show that time irreversibility is kinematically rooted in the fact that, when viewed backward in time, the alignment of particles' relative velocities is better than when viewed forward in time.

Thrombosis involves processes spanning large-scale fluid flow to sub-cellular events such as platelet activation. Traditional CFD approaches often treat blood as a continuum, which can limit their ability to capture these microscale phenomena. In this paper, we introduce a neural operator-based surrogate model to bridge this gap. Our approach employs DeepONet, trained on high-fidelity particle dynamics simulations performed in LAMMPS under a single shear flow condition. The model predicts both platelet membrane deformation and accumulated stress over time, achieving a mode error of ~0.3% under larger spatial filtering radii. At finer scales, the error increases, suggesting a correlation between the DeepONet architecture's capacity and the spatial resolution it can accurately learn. These findings highlight the importance of refining the trunk network to capture localized discontinuities in stress data. Potential strategies include using deeper trunk nets or alternative architectures optimized for graph-structured meshes, further improving accuracy for high-frequency features. Overall, the results demonstrate the promise of neural operator-based surrogates for multi-scale platelet modeling. By reducing computational overhead while preserving accuracy, our framework can serve as a critical component in future simulations of thrombosis and other micro-macro fluid-structure problems.

In recent years, sub-grid models for turbulent mixing have been developed by data-driven methods for large eddy simulation (LES). Super-resolution is a data-driven deconvolution technique in which deep convolutional neural networks are trained using direct numerical simulation (DNS) data to learn mappings between the input data from a low resolution domain to the super-resolved high resolution output domain. While the technique has been of a great success in a-priori tests, the assessment of its generalization capabilities is required for further a-posteriori applications. In this study we assess the generalization capability of a super-resolution generative adversarial network (GAN) in reconstructing scalars with different distributions. Forced turbulence mixing DNS data with a fixed Reynolds number but different bulk scalar distributions, are generated and used as training/testing datasets. The results show that the velocity vector field can be reconstructed well, but the model fails to super-resolve the scalars from out-of-sample distributions. Including two extreme mixture fraction distributions, namely double Pareto and semi-Gaussian, in the training dataset significantly improves the performance of the model, not only for those distributions, but also for previously unseen bimodal distributions.

Inspired by recent experimental observations of a harmonically excited elastic foil hovering near a wall while supporting substantial weight, we develop a theoretical framework that describes the underlying physical effects. Using elastohydrodynamic lubrication theory, we quantify how the dynamic deformation of the soft foil couples to the viscous fluid flow in the intervening gap. Our analysis shows that the soft foil rectifies the reversible forcing, breaking time-reversal symmetry; the relative spatial support of the forcing determines whether the sheet is attracted to or repelled from the wall. A simple scaling law predicts the time-averaged equilibrium hovering height and the maximum weight the sheet can sustain before detaching from the surface. Numerical simulations of the governing equation corroborate our theoretical predictions, are in qualitative agreement with experiments, and might explain the behavior of organisms while providing design principles for soft robotics.