Papers

New analytical model predicts how fluid flows around a cylinder at high speeds, capturing wake patterns, turbulence, and shock waves with less computation than full simulations.

This study presents a hybrid computational framework for simulating non-reacting inviscid high-speed flows of nitrogen gas (N$_2$) around a circular cylinder. Owing to the strongly convection-dominated nature of the compressible Euler equations, the compressible-flow streamline-upwind/Petrov–Galerkin (SUPG) formulation is combined with the YZ$\beta$ shock-capturing technique to stabilize the finite element discretization in the presence of strong discontinuities. Building upon the stabilized solution, a physics-informed neural network (PINN) is employed as a post-processing correction stage (\underline{P}INN-\underline{A}ugmented \underline{S}UPG with \underline{S}hock-\underline{C}apturing—PASSC). The network is anchored to the finite element solution through a shock-weighted data-consistency loss, while the governing equations are enforced in a conservative space–time control-volume form supplemented by macroscopic conservation windows, an entropy-admissibility penalty, and the boundary conditions of the underlying problem. Two-dimensional simulations are performed for free-stream Mach numbers ranging from $2.0$ to $12.0$, and the results are assessed against analytical normal-shock and stagnation relations, the semi-empirical Billig correlation, and reference solutions from the literature. The correction is designed to improve the numerical representation of shocks by reducing localized discretization-induced oscillations and mesh-scale serrations while preserving the agreement of the stabilized solution with the analytical and semi-empirical reference quantities.

Hypersonic flows involve extreme thermochemical non-equilibrium, where strong energy dissipation leads to tightly coupled chemical reactions, radiation, and energy exchange. In this regime, surface chemistry, particularly catalytic wall reactions, can significantly affect boundary-layer composition and surface heat transfer. Accurate simulations of such flows may require repeated evaluations of detailed thermochemical libraries, which represent a major computational bottleneck in high-fidelity reactive-flow simulations. To mitigate this cost, we employ the data-driven reduced-order framework introduced by Scherding et al. (2023), which combines nonlinear dimensionality reduction, community clustering, and local surrogate models to efficiently approximate high-dimensional thermochemical mappings. In this work, this framework is extended for the first time to hypersonic reactive flows with localized catalytic surface discontinuities, introducing sharp variations in wall chemistry and heat transfer. To address the increased complexity of the thermochemical state space, the dimensionality reduction method is enhanced with a Sammon-type stress penalty that mitigates topological folding of the latent manifold and improves the robustness of the clustering and surrogate stages. The resulting model accurately captures the effects of discontinuous catalytic properties, including sharp gradients in wall species mass fractions, diffusion fluxes, and surface heat transfer, while reducing the overall simulation cost by 50% without compromising accuracy.

We investigate the long-time behavior of optimal mixing in an advection-diffusion equation using a shell model framework. Our focus is on quantifying the decay of the scalar variance, measured by the negative Sobolev norm $H^{-1}$, under enstrophy-constrained stirring. We perform long-time computations using both local-in-time (maximizing the instantaneous mixing rate) and global-in-time (maximizing mixedness at a prescribed final time) optimization strategies. For mixing with diffusion ($\kappa>0$), the numerical results show that the scalar length scale eventually becomes limited by a generalized Batchelor scale, in close agreement with theoretical predictions. In this regime, the $H^{-1}$ mix-norm decays exponentially in time with a decay rate that is independent of the diffusivity $\kappa$. Compared with the purely advective case ($\kappa = 0$), diffusion significantly enhances the long-time mixing rate; moreover, increasing diffusivity further improves mixing efficiency by reducing the prefactor of the exponential decay. Guided by these numerical observations, we derive new conditional lower bounds on the $H^{-1}$ norm whose exponential decay rates are strictly independent of the diffusivity parameter $\kappa$, for all $\kappa > 0$. We further establish conditional upper bounds on the maximal rate of enhanced dissipation of the scalar variance, showing that the effective diffusion time scale is at least of the order $|\log\kappa|$.

We study optimal control problems for incompressible fluids in two-dimensional domains with a cold boundary and internal heat sources and sinks. Given a kinetic energy budget, measured by the square of a nondimensional Péclet number $\mathrm{Pe}$, the goal is to maximize a cooling efficiency inversely proportional to the mean square gradient of the fluid's temperature. Using Lagrange duality, we formulate a well-posed dual problem whose solution yields an upper bound on the maximum cooling efficiency $\mathcal{E}(\mathrm{Pe})$. We then numerically approximate the dual problem using a convergent hierarchy of semidefinite programs obtained via discretization. We illustrate this computational approach on optimal cooling problems in a square and in an annulus, explaining also how problem symmetries can be exploited to reduce computational complexity. Finally, we construct admissible points for the dual problem to obtain new analytical upper bounds on the optimal cooling efficiency $\mathcal{E}(\mathrm{Pe})$. Specifically, we prove that $\mathcal{E}(\mathrm{Pe}) \lesssim \mathrm{Pe}^{2}$ for arbitrary domains and heat distributions, and that $\mathcal{E}(\mathrm{Pe})\lesssim \mathrm{Pe}^{2}/ \ln^2\mathrm{Pe}$ for cooling flows in disks and annuli with heat source/sink distributions with a positive azimuthal average. These results generalize and improve known efficiency bounds for energy-constrained cooling flows in a disk.

The immersed boundary (IB) method models fluid–structure interaction using the natural Lagrangian and Eulerian formulations of structural mechanics and fluid dynamics, respectively, but explicit time discretization of the IB force imposes a stiffness-dependent upper bound on the time-step size. Treating these forces implicitly removes this restriction, but the resulting coupled linear systems become increasingly difficult to solve as the structural stiffness increases. Algebraically eliminating the Lagrangian degrees of freedom yields a reduced Eulerian velocity–pressure IB system. Here we introduce a coupling-aware Vanka (CAV) smoothing strategy to enable effective multigrid preconditioning of this system. CAV patches are built as unions of standard pressure-centered Vanka patches, with the graph of the Eulerian elasticity matrix determining which patches are combined. Under grid refinement, CAV patch sizes remain bounded, and the computational cost of each multigrid cycle thereby grows linearly with the number of Eulerian degrees of freedom. Tests using target-point, membrane, and beam force laws show that CAV-preconditioned FGMRES reduces the relative residual by ten orders of magnitude in $9--15$ iterations, with little growth under grid refinement. In a nonlinear benchmark modeling flow past a flexible fiber, the average number of FGMRES iterations per Newton solve increases only from $8.6$ to $9.5$ as the Eulerian grid is refined from $32\times32$ to $256\times256$ cells. To our knowledge, CAV provides the first robust multigrid strategy for time-dependent implicit IB formulations.

Fluid-structure interaction (FSI) in viscoelastic flows past deformable structures at low Reynolds numbers remains poorly understood, despite its relevance to biological systems such as cilia and flagella, and to engineered microsystems. We investigate viscoelastic FSI in side-by-side flexible cantilever arrays using a bottom-up approach that systematically varies the number of cantilevers and the rheology of the test fluid, comparing weakly shear-thinning (WS) and highly shear-thinning (HS) polyethylene oxide solutions. For both fluids, with increasing Weissenberg number (Wi), an elongated elastic wake develops behind a single isolated cantilever. For multiple cantilevers, the WS fluid undergoes a transition at a critical Weissenberg number (Wi*) from separated to merged elastic wakes, accompanied by the emergence of a divergent flow field and coordinated inward spanwise cantilever deflection. The critical Wi* increases as the number of cantilevers in the array is increased from two to three, demonstrating a strong dependence of the onset on the array configuration. For the HS fluid, wake merger, flow divergence, and inward cantilever deflection are suppressed across the full range of Wi investigated, despite comparable elasticity and the formation of elastic wakes. This contrast shows that elasticity alone promotes wake formation but is insufficient to produce the collective instability, which instead requires both shear-thinning and interactions between neighboring cantilevers. These findings demonstrate that viscoelastic FSI in flexible arrays is governed by the combined effects of fluid elasticity, shear-thinning, and geometric configuration, with elastic wake interactions mediating the collective instability and linking local elastic wakes to array-scale structural response.

The Carrier–Greenspan hodograph transformation linearises the nonlinear shallow-water equations on a beach of constant slope. We extend the transformation to a moving bottom and identify the family of bottom motions that preserves the Carrier–Greenspan invariants. The bottom gradient must be uniform in space, that is, $h(x,t)=\rho(t)x+\mathcal{B}(t)$, and constant $\rho$ returns the classical slope. For this family a horizontally accelerating frame removes the forcing. The bottom motion then disappears from the hodograph equation, and two quadratures recover the physical variables. If the gradient varies in time, the bed displacement grows without bound offshore and the far field cannot remain at rest. The domain must therefore be finite, although the pivot may be placed anywhere. A bottom-tilting wave maker realises this family. Closed forms follow for the hinge response, for the crest-to-trough steepness of the generated wave, and for the leading nonlinear correction. The correction depends on the point to which the steepness is referred, and so differs between a leading-elevation and a leading-depression wave. Because the hinge is at the beach toe, these closed forms provide the incident wave required by the classical plane-beach solution. The run-up can therefore be predicted from the plate motion alone. The steepness is predicted without a fitted constant and agrees with the reference computations. Sixty-one runs over a level bed, reported here for the first time, carry the test to deeper water and longer plate motions. The measured run-up follows the predicted run-up, with an offset that the inviscid theory does not account for.

Frontogenesis is the process by which ocean fronts–regions of strong horizontal density gradients in the upper ocean–strengthen. It is a highly non-linear phenomenon arising from many competing effects, such as background strain, instabilities, and surface forcing. Vertical mixing plays a complicated role in governing both frontogenesis and the long-term dynamics of ocean fronts. For weak fronts, it has been shown to drive shear dispersion which further weakens the front over long timescales. However, vertical mixing also mixes the vertically-sheared thermal wind velocity, driving the front out of balance and causing a secondary circulation to develop that may strengthen the front. Here, it is shown that vertical mixing can directly act to oppose the frontogenetic secondary circulation, provided the frontal width is larger than a critical value. A non-linear iteration method is described for finding balanced states in which vertical mixing arrests frontogenesis and the parameter dependence of this regime is discussed. Further, existing asymptotic solutions for the buoyancy and velocity fields are extended and found to closely match these balanced states, even outside their region of formal validity.

Recovering high-resolution states from sparse, low-resolution observations is a central challenge in scientific machine learning and data assimilation. Classical data assimilation exploits temporal information through forecast-analysis cycles, but often requires repeated access to expensive high-resolution forecast models. Generative super-resolution can recover unresolved structure from coarse observations, but is commonly used as a one-shot mapping that does not fully exploit constraints from past states. We introduce Iterative Refinement (IR), a learned data assimilation framework that combines these perspectives. Instead of performing a single coarse-to-fine reconstruction, IR decomposes the task into resolution-wise forecast-analysis operations across a multiresolution hierarchy. At each stage, a shared neural operator with resolution-dependent spectral mode slicing provides a dynamical prior, while a shared conditional diffusion corrector uses the current coarser-resolution state to produce a refined posterior at the next finer resolution. We evaluate IR on one-dimensional stochastically forced Burgers dynamics and two-dimensional Kraichnan turbulence. On the challenging 256x256 Kraichnan benchmark, IR achieves an RMSE of 0.184 and an SSIM of 0.836, outperforming spectral upsampling, one-shot diffusion super-resolution, enhanced deep super-resolution, and an autoregressive forecaster. On the more constrained Burgers testbed, IR remains competitive with one-shot diffusion, which achieves the lowest RMSE. These results show that one-shot generative reconstruction can be effective for simpler settings, while hierarchical forecast-analysis refinement becomes advantageous in strongly multiscale and underdetermined regimes. Overall, IR combines temporal priors, generative correction, and multiresolution reconstruction for learned data assimilation in complex physical systems.

A large-eddy simulation (LES) of a laminar separation bubble (LSB) induced by an adverse pressure gradient over a flat plate is performed at an inflow displacement-thickness-based Reynolds number of 410 and a free-stream Mach number of 0.25. With a mean peak reverse flow of 21.4%, the bubble sustains self-excited vortex shedding through a local region of absolute instability, in the absence of any external forcing. Spectral proper orthogonal decomposition (SPOD) applied to the LES data identifies three dominant coherent structures within the LSB: two-dimensional and oblique Kelvin–Helmholtz (KH) waves in the separated shear layer at the vortex-shedding frequency, and stationary spanwise-periodic streaks near reattachment at near-zero frequency. Classical resolvent analysis of the mean flow identifies strong convective amplification of the KH waves over a range of spanwise wavenumbers, but predicts only weak amplification in the low-frequency, streak-forming region, where the leading gain is orders of magnitude smaller and no dominant rank-one mechanism is present. This discrepancy with the SPOD energy indicates that the streaks are not sustained by same-frequency linear amplification, but are instead energized by the intrinsic forcing, which the classical framework treats as an unexplained input. Harmonic resolvent analysis of the time-periodic base flow reveals the underlying mechanism: the base-flow unsteadiness couples the oblique KH wave at the shedding frequency to the stationary streak through cross-frequency amplification, yielding a gain far larger than that of the direct same-frequency amplification. This cross-frequency route provides a likely explanation for how the stationary streaks observed near reattachment are energized.

The presence of sidewalls in turbulent duct flows leads to the emergence of secondary flow structures in the form of counter-rotating streamwise vortices near the corners (Prandtl's secondary flow of the second kind). This work develops reduced-order Galerkin projection models that can predict the emergence and structure of these turbulent mean secondary flows in a square duct geometry, without requiring any prior knowledge of the turbulent statistics. The models are obtained by projecting the Navier–Stokes equations onto eigenmodes of the linearised system, with the resulting systems of ordinary differential equations simulated with the addition of zero-mean forcing. We show that most models obtained using leading streamwise-constant eigenmodes predict the correct shape and direction of the secondary mean, with the minimal such model requiring only two modes. In these models, the secondary mean contribution arises due to the nonzero average coefficient of an eigenmode that possesses all of the symmetry properties expected of a secondary mean. The models are sufficiently simple such that the relationship between this mean coefficient and the joint second moment of other mode coefficients can be computed analytically. We confirm that running streamwise-constant direct numerical simulations (DNS) with the same forcing structure as used in the reduced-order models produces similar secondary-flow structures. We additionally demonstrate that our models produce qualitatively similar Reynolds stress distributions to fully resolved direct numerical simulations, with improved agreement as model dimension increases.

Clinically actionable, patient-specific hemodynamic assessment, specifically wall shear stress, vortex structure and pressure distributions, is critical for determining risky or unfavorable evolution in Abdominal Aortic Aneurysms (AAA). While Physics-Informed Deep Operator Networks (PI-DeepONets) show promising results in complementing established 5 tools such as Computational Fluid Dynamics (CFD), a persistent architectural challenge remains for complex 3D flows. In this direction, we propose a Modified Multi-Input Multi-Output PI-DeepONets (M3PI-DeepONet) designed for predicting unsteady flows in an idealized AAA geometry. Central to our model is the Aggregated Injection strategy, where latent representations from multiple input branches are fused prior to trunk injection, allowing the coordinate basis to adapt to multiple physical constraints. To the best of our knowledge, this is the first architecture to combine the layer-wise gating mechanism with a multi-branch operator-network topology, yielding an input-adaptive trunk basis. Additionally, we integrate the 3D Navier-Stokes equations as governing physical laws, so the model is trained based on physics-informed residuals, initial and boundary conditions, and only 0.3% of the labeled internal data together with the selected branch-conditioning signals. The M3PI-DeepONet simultaneously predicts unsteady 3D flow velocity and pressure fields with an average relative L2 velocity error below 4% and pressure error around 5% while achieving a conservative retained-cycle inference speedup of approximately 36x compared to reference CFD simulations once the branch inputs used for conditioning are available. This work advances the application of deep learning in cardiovascular disease modeling, marking step toward real-time, non-invasive clinical diagnostics.

Deep learning surrogates for RANS flow prediction around airfoils face two persistent bottlenecks. A single neural architecture cannot simultaneously resolve sharp near-wall boundary layers and smooth far-field potential flow. Additionally, force prediction is undermined by the numerical instability of computing wall-normal velocity gradients from continuous-field approximations. Both of these points are addressed with a DD-RNO (domain-decomposed routed neural operator), combining a spectral geometry encoder with two physics-guided innovations: (a) a differentiable domain routing mechanism that partitions the flow field into inviscid, boundary-layer, and wake regimes—dispatching query points to specialized regional decoders, and (b) learned canonical quadrature (LCQ), which replaces unstable pressure integration with flow-conditioned, learned integration weights that predict lift and drag directly from surface pressure. On the AirfRANS benchmark, DD-RNO cuts velocity field mean-square error (MSE) by 17$x$ ($u_x$) and 12$x$ ($u_y$) over the strongest baseline, widening to 23$x$ under out-of-distribution Reynolds extrapolation—evidence that the routing mechanism generalizes with the physics it encodes rather than merely fitting the training distribution. LCQ reduces drag MSE by 7.5$x$ relative to conventional pressure integration and raises drag rank correlation from $\rho = 0.250$ to $\rho = 0.997$. Ablations confirm that both components are indispensable to performance: removing domain routing increases velocity error by 8.2$x$, and removing LCQ increases relative drag error more than 40-fold. At ~144 ms per sample—a 10,000$x$ speedup over conventional RANS solvers—DD-RNO offers a surrogate accurate and fast enough for real-time aerodynamic design and optimization loops.

We report the formation of an original dome-shaped air-water cavity at the impact site of closely-packed plunging water jets. The injector assembly consists of concentric rings of circular jets, similar to a shower-head configuration. We infer from high-speed imaging, LASER-induced fluorescence, and optical phase detection probes that the cavity consists of multiple stems and sheets of air that stretch, retract and pinch off to produce bubbles. We also illustrate various bubble production mechanisms in the cavity, along with coalescence and bubble breakup scenarios in the subsequent bubble cloud. Thereby, we describe the wide range of bubble sizes generated by such jets, from a few micrometers up to about $5$~mm. Measurements of the cavity size are carried out for varying impact velocity, number of jets, and jet spacing. We propose that this distinctive air-water cavity is generated by liquid entrainment when successive rings of plunging jets progressively mix with the pool water.

A lattice Boltzmann scheme for the three-dimensional compressible Navier–Stokes–Fourier equations, derived automatically from the declared system by a symbolic compiler, is validated against exact solutions and published reference data. The declared system carries the viscous stress and the heat flux as transported state, and is discretized on a D3Q7 lattice in single precision. Against the exact Sod and Becker solutions the captured shock thickness converges at first order. On the supersonic Taylor-Green vortex at $M_0 = 1.25$ the scheme at $512^3$ matches the reference dilatational dissipation more closely than seven compared solvers, by thirty percent over the next best. Every operator in this solver, the generated collision and constitutive closure and the added shock sensor alike, reads only the cell it acts on, and data reaches a neighbor only by streaming along the lattice characteristics.

Aerodynamic unsteadiness is inherent to the operation of many engineering applications, especially those that involve large-scale rotating blades, such as modern wind turbines. Over the past few decades, wind turbine rotors have grown rapidly and are now exceeding 200 meters in diameter, causing them to operate in conditions where limited empirical data are available, and where models have not been validated. Here, we use a highly pressurized wind tunnel to probe these conditions and evaluate the quasi-steady approximation, often used to simplify the modeling of the unsteady aerodynamic response of an airfoil to slow changes in inflow conditions. We find that the quasi-steady approximation is not valid for a large range of frequencies where it is normally applied. This finding suggests that the loading on wind turbine blades will be significantly underestimated when using conventional models, especially near stalling conditions, which modern wind turbines typically encounter.

Intermittent departures from nominal Kelvin–Helmholtz shedding can produce rare and pronounced drag excursions in transitional airfoil flow. We examine these events using two-dimensional direct numerical simulations of flow over a NACA0012 airfoil at an angle of attack of $5^\circ$, a freestream Mach number of $0.4$, and chord-based Reynolds numbers of $5\times10^4$ and $5\times10^5$. At the lower Reynolds number, event-resolved analysis shows that individual primary vortices are released from the separated shear layer through the eruption of wall-generated, opposite-signed secondary vorticity. Each eruption interrupts the connection between a developing primary vortex and its feeding shear layer, releasing the vortex downstream. During nominal shedding, the vortex reaching the trailing-edge region is associated with a single such release and remains sufficiently isolated to pass the trailing edge without strong collective interaction. Extreme events instead arise through clustered vortex release, in which several secondary-vorticity eruptions occur within a short interval and produce a compact group of primary vortices with small initial streamwise spacing. Differential convection further reduces their spacing and promotes strong near-trailing-edge interactions, where the combined pressure footprint of these vortices produces a localized suction peak and a sharp increase in drag. These interactions range from prolonged deformation and filamentation to rapid core coalescence. Similar compact vortex organization and near-trailing-edge interactions are recovered at $Re=5\times10^5$, indicating that the downstream event pathway persists despite the smaller vortical scales.These findings suggest that controlling vortex-release timing through secondary-vorticity dynamics may provide a route to disrupt clustered release and mitigate extreme aerodynamic loading.

The Dynamic Mode Decomposition (DMD) has been consolidated as a basic tool for data-driven analysis of dynamical systems, allowing simultaneous identification of coherent structures and their dynamics from time-resolved measurements. However, with a linear regression at its core, DMD is unable to produce accurate models from recordings of dynamics that are inherently nonlinear, such as the response to large perturbations and the evolution on chaotic attractors. Recent approaches attempt to simultaneously fit the linear and nonlinear contributions to the dynamics by performing a regression onto a physically motivated model structure. However, although the resulting nonlinear models can produce accurate short-term predictions, their linearization does not necessarily agree with that of the original system. In this work, we introduce a novel data-driven method — nonlinearity-subtracted DMD (NSDMD) — that focuses on producing an accurate linearization of a system when the nonlinear contribution to its dynamics are available while the linear part is not. This scenario is encountered, for example, when the nonlinear terms in the governing equations are known, while the linear operator contains uncertain material properties or it accounts for the closure of unresolved dynamics. This also arises when the data is generated by a black-box simulation code that is able to output the nonlinearity, but not the action of the linear operator on the snapshots. NSDMD leverages data snapshots of the nonlinearity to explicitly account for the purely nonlinear contributions to the dynamics and formulate a regression problem that finds a low-rank approximation of the underlying linear operator. We demonstrate the approach on several numerical examples, showcasing its improved capabilities for data-driven linear analysis of chaotic, partially observed, advection-dominated, and high-dimensional dynamics.

Thermal transport in dielectric, non-magnetic crystals is mediated by quantized lattice vibrations, which drift and interact when driven out of equilibrium by a temperature gradient. This phenomenon can be described at multiple theoretical levels, ranging from fully quantum descriptions to semiclassical and mesoscopic continuum approaches. This review rigorously discusses the theoretical steps and approximations connecting these levels, bridging quantum phonon Dyson and Kadanoff-Baym equations and semiclassical Boltzmann transport formalism, and discussing the coarse-graining procedures that yield mesoscopic viscous heat equations for non-diffusive, hydrodynamic heat transport in devices. We show how the Guyer-Krumhansl and dual-phase-lag equations emerge as special linear-isotropic-band and inviscid limits of the viscous heat equations, respectively; most importantly, we demonstrate that these equations predict not only Poiseuille flow and second sound, but also more exotic effects such as negative thermal resistance, steady-state thermal backflow and vortices. We highlight how combining these frameworks with first-principles simulations connects microscopic phonon physics to observable non-diffusive heat-transport phenomena and guides their detection, amplification, and control. We recast the viscous heat equations in terms of Helmholtz and biharmonic equations solved analytically, and use this to discuss similarities and differences between the macroscopic behavior of the phonon fluid and other hydrodynamic systems, such as classical and electron fluids, focusing on compressibility, vorticity, and their influence on phonon hydrodynamics. We conclude with a roadmap to generalize the tools used to describe phonon hydrodynamics to other quasiparticles, motivating future advances in collective quantum transport phenomena in solids.

For the 2-D incompressible Euler equation, we prove the existence of $m$-fold symmetric uniformly rotating vortex patches with 90-degree corners for all $m\geq 12$. Properties of these patches and the induced stationary flows in the co-rotating frame are characterized. Our construction is based on a novel fixed-point method.

Particle resuspension models are commonly evaluated using the macroscopic resuspended fraction, although this integrated observable may conceal the temporal dynamics leading to detachment. Here, a second-order Markovian Lagrangian stochastic model is developed by augmenting the angular-velocity state with a finite-correlated tangential acceleration. The model is examined over turbulent channel flows with ($Re_\tau \in [60, 430]$) and compared with an established first-order formulation. The two models produce nearly overlapping resuspended fractions, revealing a macroscopic degeneracy between distinct stochastic descriptions. Multiscale trajectory statistics break this degeneracy. The acceleration-augmented formulation changes the short-time regularity from $S_2(\tau) \propto \tau$ to $S_2(\tau) \propto \tau^2$, sustains angular-velocity correlation, and produces stronger directional asymmetry and heavier increment tails. The survivor-conditioned mean square displacement exposes a Reynolds-number-dependent anomalous-transport window, in which the attached-particle ensemble grows more rapidly than the diffusive reference and locally approaches ballistic and super-ballistic scaling before crossing toward diffusion-like transport. This finite-time pathway records how particles approach detachment and is compressed out of the macroscopic resuspended fraction. At $Re_\tau \approx 60$, the trajectories enter a distinct low-Reynolds-number statistical state characterized by converging velocity and acceleration decorrelation and near-Gaussian increments. These results establish multiscale trajectory statistics as essential discriminants between stochastic resuspension models and identify finite acceleration correlation as a source of dynamical information beyond macroscopic detachment kinetics.

As a non-contact control approach, electric field (EF) can be utilised to drive droplet dynamics on a lubricant-infused surface (LIS), with numerous potential applications ranging from drug manufacturing to 3D printing. However, the resulting droplet dynamics remain poorly understood, especially as there are several possible droplet lubrication states on LIS. Here, we develop a lattice Boltzmann scheme that fully captures the interplay between the interfacial flows and electrohydrodynamics and harness it to investigate EF driven droplets on micropillar LIS. Combining simulations and analytical calculations, we establish quantitative expressions for the drag force and the electric force acting on a moving droplet. We demonstrate that the models can accurately capture droplet dynamics during programmable manipulation, including periodic motion and long-distance transport. Such reliable theoretical models can potentially transform precision control of droplet dynamics by removing the reliance on trial and error tests.

Dimples offer a promising route to reducing drag on aerodynamic surfaces. However, whether such shallow concavities yield a net benefit depends sensitively on their topography, which demands systematic mapping and exploration of their comprehensive design space. In this study, dimple design is examined as a mixed-variable optimization over four design variables: dimple type, depth, in-plane scale, and streamwise stretch. The design space is explored using MixMOBO, a Bayesian optimizer, coupled with immersed-boundary large eddy simulations of channel flows at a constant flow rate corresponding to a flat channel at a friction Reynolds number of 180. The optimal solution, a relatively deep, fully packed, streamwise-elongated diamond dimple, attains a 13.2% drag reduction, notably above previously reported values. A Gaussian process metamodel sensitivity analysis identifies dimple topology as the dominant factor, with coverage and elongation acting mainly through interactions, and depth itself carrying no universal sign. A near-wall flow analysis links the leading designs to fully attached, groove-like flow, whereas poorer designs tend to produce local flow separation that incurs adverse form drag. From these findings, key design insights for drag-reducing dimples are provided.

This paper is associated with a poster winner of a 2025 American Physical Society's Division of Fluid Dynamics (DFD) Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available online at the Gallery of Fluid Motion, at https://doi.org/10.1103/APS.DFD.2025.GFM.P012

We describe two open-source, 3D-printable, flexure-based tools for the quantitative measurement of extensional properties of viscoelastic fluids. These low-cost, portable, and scalable devices (which we have termed “PocketCaBER” and “PocketDoS”) are particularly applicable for use in the field and in graduate-level teaching environments due to their low cost, printability on hobby 3D printers, compatibility with cell phone cameras, portability and user-friendly operation. We characterize and benchmark each device's performance against its lab-equivalent counterpart and provide downloadable STL files for rapid fabrication. We discuss experimental limitations of these devices compared with their bench-top counterparts. Finally, we illustrate the use of such tools in facilitating student engagement in polymer science and complex fluids classes—specifically, how progress in learning goals can be uniquely and effectively accelerated by providing the necessary rheological instruments directly to each individual student (especially for advanced modules such as nonlinear extensional rheology). By giving students personal, indefinite access to laboratory-level instrumentation through these open-source frugal science tools, we discuss our efforts to expand participation and engagement within the field of nonlinear rheology.

Motivated by the application of spray combustion in aviation industry, this work investigates the dispersion of non-spherical droplets in turbulence. The most common strategy for modeling sprays relies on LPT method, which represents the spray as a discrete collection of spherical particles. One limitation of LPT is that it neglects the influence of droplet deformation on spray dynamics. Prior studies have highlighted the importance of non-sphericity in droplet vaporization, combustion and drag coefficient. However, these works are restricted to idealized configurations such as an isolated droplet in a uniform flow. To study droplet deformation in a more realistic configuration, we adopt homogeneous isotropic turbulence (HIT) as the framework to investigate its effect on droplet dispersion. Droplets of various Stokes number are studied to investigate the interplay between deformation and inertia. Analysis of droplet statistics reveals that the impact of droplet deformation on both dispersion and clustering is dependent on the inertia regime. For weakly-inertial droplets, deformation weakens both dispersion and preferential concentration, whereas for strongly-inertial droplets, deformation tends to enhance preferential concentration while weakening dispersion. The results also suggest that to achieve the same level of clustering, deformed droplets require a higher Stokes number. Interestingly, for non-inertial droplets, the deformation seems to induce an effective inertia. This is verified by a comparison between the full unsteady TAB model and its steady-state limit, which suggests that unsteady shape dynamics affect temporal correlation statistics, but leave the mean clustering pattern unchanged. These findings demonstrate that accounting for droplet deformation and its unsteady shape oscillation is essential for accurately predicting droplet dispersion and clustering in turbulence.

At every scale they occupy, magnetic fields affect various phenomena, including star formation, cosmic ray transport, charged particle acceleration, space weather, transport in planetary atmospheres, and laboratory plasmas. These fields are often generated and sustained by turbulent flows in a process called the dynamo. In 1955, E. N. Parker parameterized the effects of small-scale turbulence to propose a mean-field dynamo theory. The widely used theory reproduces observed large-scale fields but suffers from difficulty in tuning parameters as they are not justified from first principles: Studies of turbulent flows show tangled magnetic fields, which are folded and fragmented into small-scale structures due to shear-flow straining. Here, considering a shear flow that is unstable and driven, we develop analytic theory and perform three-dimensional (3D), advanced computer simulations of turbulence with up to 4096 x 4096 x 8192 grid points, showing ab initio generation of quasi-periodic, large-scale magnetic fields. The generation occurs via the mean-vorticity effect—an additional mean-field dynamo process postulated in 1990. Crucial to this dynamo is the prior generation of large-scale 3D jets, robustly produced as topologically protected and exact nonlinear solutions of the magnetohydrodynamic equations. The jet-driven dynamo applies to shear-driven laboratory and astrophysical systems. These include binary neutron star mergers, where the reported dynamo likely operates on microsecond timescales to produce in milliseconds some of the strongest magnetic fields in the Universe, providing signals for multimessenger astronomy.

Accurate numerical simulation of rarefied hypersonic plasmas is increasingly important for optimization of re-entry spacecraft design and the development of advanced aerospace technologies. For kinetic simulation methods, it is convention to enforce ions and electrons to diffuse at the same rate, known as the ambipolar diffusion approximation. This approach circumvents costly resolution of fast electron motion, but neglects the complex plasma dynamics of ions and electrons. Almost all studies that investigated the efficacy of the ambipolar diffusion approximation in hypersonics report noticeable differences in flowfield properties when electrostatic modeling is used, including increases in vehicle surface heat flux and decreases in electron temperature. However, it is unknown whether these reported differences originate directly from acceleration and deceleration of charged species through the electric fields and momentum-exchange collisions between charged and neutral species, defined as first-order effects, or from subsequent interactions with particles experiencing first-order effects, defined as second-order effects. Kinetic hypersonic flow simulations with electrostatic modeling are performed with argon to quantify the validity of the ambipolar diffusion approximation in terms of capturing first-order plasma effects along a one-dimensional stagnation streamline. Three different plasma diffusion regimes are studied under two sets of rarefied freestream flow conditions. The approximation is evaluated in terms of predicting plasma density distributions, electron temperature, and stagnation point heat flux. New criteria are proposed for identification of plasma diffusion regimes in hypersonic flows and use of the ambipolar diffusion approximation.

Wave-assisted propulsion (WAP) systems harvest ocean wave energy to generate propulsive thrust, offering a promising approach for improving endurance and energy efficiency of marine vehicles. Previous studies have focused primarily on monochromatic or unimodal wave conditions, leaving WAP performance in realistic ocean environments largely unexplored. This study investigates the hydrodynamic and hydroelastic response of a submerged flapping hydrofoil operating in bimodal sea states generated by the coexistence of swell and wind-sea wave systems. High-fidelity fluid–structure interaction simulations are performed for representative calm, transitional, and storm conditions, with passive pitching provided through a torsional spring. Simulations show that, despite increased complexity of bimodal wave forcing, propulsion performance follows the same effective peak frequency scaling previously established for monochromatic and unimodal waves, demonstrating the robustness of this scaling framework across a broad range of sea states. The findings further reveal that while the optimal normalized tuning ratio remains within a narrow range, dimensional torsional spring stiffness varies with sea state characteristics, highlighting the need for adaptive hydroelastic tuning to maximize thrust. Overall, the results demonstrate that WAP systems provide a robust means of generating wave-powered thrust under realistic ocean conditions while providing practical guidance for improved design of wave-powered marine propulsion systems.