Papers

We describe turbulent hydrodynamics of superfluids in two spatial dimensions via the dynamics of point-like vortices coupled to an emergent 2+1 dimensional $U(1)$ gauge field. The cascade of superfluid kinetic energy is equivalently described by a cascade of dual electric field energies. We study superfluid turbulence using the equations of motion of the dual gauge theory in the presence of a drive and dissipation. In the limit that the vortices are point-like, the dual equations of motion directly yield the hydrodynamical equations of the superfluid. We obtain a turbulent cascade consistent with Kolmogorov's scaling law for two dimensional fluid turbulence. We observe clustering of like-signed vortices and compute the kinetic energy flux to show that the turbulent regime exhibits an inverse energy cascade.

We present a stability analysis of a dark-fluid model described as a non-relativistic, rotating, non-viscous, self-gravitating fluid. We assume spherical symmetry and model the matter by a polytropic equation of state. The resulting coupled nonlinear partial differential equation system is solved using a self-similar ansatz known from the Guderley-Landau-Stanyukovich problem. We find that three of the four Lyapunov exponents are negative, while only one is positive. This indicates one unstable direction and three contracting directions in phase space. The single positive exponent is relatively small, suggesting that the self-similar solution is only weakly unstable and remains dynamically robust over the investigated interval.

Ultra-lean hydrogen flames under terrestrial gravity are governed by a coupled interaction among preferential diffusion, thermal diffusion, heat loss, and self-induced convection. This study numerically examines combustion in a quiescent 6~vol.% H$_2$–air mixture using detailed chemistry and a low-Mach-number formulation. A complete calculations set was considered, with Soret diffusion and optically thin radiative heat loss independently enabled and disabled. One-dimensional spherical calculations were used to isolate the initial post-ignition flame kernel growth, while two-dimensional planar and axisymmetric simulations described its subsequent buoyant rise, deformation, and breakup. Over the analyzed interval, the spherical flame-front radius followed $R_f^2\approx Kt$ rather than constant-speed expansion. Soret diffusion increased the effective growth coefficient $K$, whereas radiation reduced it. The axisymmetric calculations reproduced the experimentally measured leading-point trajectory substantially better than the planar formulation. Soret diffusion produced larger, faster-rising kernels and maintained a more nearly circular upper cap, whereas radiation had a weaker effect on trajectory but increased relative lateral flattening. In all cases, a toroidal vortex stretched the flame segment and caused local extinction and fragmentation. Soret diffusion delayed breakup, while radiation advanced it; their combined effect on breakup time was nearly compensating. The results show that Soret transport and radiation primarily alter kernel growth and resistance to vortex-induced extinction, while the qualitative breakup pathway remains hydrodynamically controlled.

We establish a self-consistent 2D hydrothermodynamic analytical model for high-intensity focused ultrasound tumor ablation. Expanding compressible Navier-Stokes equations to second order demonstrates that a stationary cellular matrix suppresses acoustic streaming ($\mathbf{v}_2 = 0$). This constraint forces the absorbed wave momentum flux to convert entirely into localized, time-averaged static pressure gradients ($\nabla \langle p_2 \rangle = \mathbf{F}_2$), bridging non-linear hydrodynamics with thermodynamic dissipation. Solving the non-diffusive Pennes bioheat equation under a $1.0\,\text{s}$ top-hat pulse reveals that a spherically focusing geometry ($\propto 1/r^2$) overrides exponential damping past a critical geometric threshold ($r_{\text{crit}} = 2x_0$), preventing upstream skin overheating. We derive an optimization criterion where the absorption coefficient matches half the inverse target depth ($\alpha = 1/2x_0$). Solving the non-isothermal Arrhenius integral yields a sharp lesion boundary radius at $r_b = 0.75\,w_0$, where the volume average reaches $72.1^\circ\text{C}$ while the core peaks at $90.0^\circ\text{C}$. Post-pulse 2D free-space Green's function convolution confirms immediate monotonic thermal decay ($\partial \theta/\partial t' < 0$) outside this boundary. This closed-form framework provides explicit scaling laws for non-invasive wave-matter thermal confinement, bypassing computationally heavy numerical simulations.

Turbulence approaching a solid surface is strained before it arrives, and the distortion of its spectrum is often what governs the downstream response; yet reduced-order predictions, leading-edge-noise theory among them, still take the incoming spectrum as frozen. We develop a strain-coupled formulation of one-dimensional turbulence (ODT) that evolves strained turbulence with full spatial resolution at a cost compatible with parametric study, carrying the rapid distortion and the nonlinear relaxation together. The obstacle is that the rapid pressure-strain is non-local and three-dimensional while an ODT line resolves only the flow state along its own coordinate. Splitting the distortion physics by structure captures the phenomenology: the off-axis production and a spectrally closed rapid operator enter as continuous-in-time forcing along the model coordinate, while `eddy events' capture the on-line production and the turbulence-driven relaxation. Carried through to leading-edge noise, the evolved inflow shifts the predicted level by 5-20 dB at the energy-containing scales relative to the conventional frozen-spectrum assumption.

The source term of an acoustic analogy is not unique: different rearrangements of the Navier-Stokes equations attribute the same radiated sound to different apparent sources. Although this non-uniqueness has long been recognised, it has never been given a quantitative structure. We provide one by organising acoustic analogies into a fibre-like family over the space of effective media and defining transport between analogies through unique frequency-preserving, rotation-free linear space-time maps. Three exact results follow. First, the classical family of convected analogies is not closed under transport: successive uniform-flow regaugings generate effective media with anisotropic sound-speed tensors, recovering the generalised media introduced by Goldstein. Second, the discrete holonomy of analogy transport is obtained in closed form. It consists of an exact spectral dilation and a rotation that vanishes to fourth order in Mach number; transport becomes singular on a sonic horizon in analogy space. Third, in the continuum limit the boost sector is flat, while curvature is confined to anisotropy directions and is given by the commutator of sound-speed-tensor increments. The geometry does not imply any change in the physical sound field: all exact analogies yield the same far field. Its significance is operational. When an approximate source model is transported between analogies, as commonly occurs in hybrid prediction methods, the resulting far-field predictions acquire an exact, parameter-free bias consisting of a rigid spectral dilation and directivity rotation. An exact far-field law for anisotropic media extends these results to open transport paths. All identities are verified symbolically and numerically.

This investigation employs direct numerical simulations (DNS) of high-Mach-number turbulent boundary layers under three flow conditions: a low-enthalpy calorically perfect gas, and two high-temperature gas mixtures, one in chemical non-equilibrium state and the other in full thermochemical non-equilibrium state. The influences of the two-temperature model on turbulent statistics and the coupling among turbulence, chemistry, and vibrational energy are examined. It is found that while high-enthalpy effects leave the velocity statistics virtually unchanged, they dramatically modify the near-wall temperature field. A pronounced disparity between the translational-rotational temperature and the vibrational temperature arises in the near-wall region, rendering the conventional generalized Reynolds analogy (GRA) inaccurate for vibrational temperature. To remedy this, a novel composite GRA is proposed that blends a vibrational-temperature-based relation with the standard formulation, and it demonstrates excellent agreement with the DNS data. Thermal non-equilibrium effects also substantially alter near-wall chemical reactions: it suppresses O2 dissociation while promoting NO formation, leading to a corresponding decrease and increase in the mean concentrations of O and NO, respectively. Spectral analyses of the turbulence-chemistry and turbulence-vibrational relaxation interaction terms reveal that temperature fluctuations dominate these flow quantities at energy-containing scales. Integrating the resulting spectral functions, we evaluate subgrid-scale closure terms for large-eddy simulation. At small filtering scales, the magnitude of the cross-correlation term rivals or exceeds that of the temperature fluctuation term, whereas the temperature fluctuation term becomes dominant at larger filter scales.

Nonlinear stabilization is indispensable for discontinuous Galerkin (DG) discretizations of hyperbolic conservation laws, yet it typically disrupts the delicate error structure required for superconvergence analysis. Consequently, existing theory has largely been restricted to linear or semi-discrete schemes lacking oscillation control. This paper bridges this gap by proposing a Runge–Kutta (RK) aligned oscillation-eliminating (OE) DG framework that restores the superconvergence properties. By synchronizing the pseudo-time step in the OE procedure with the cumulative RK stage coefficients, we unlock a cancellation mechanism for low-order interface errors that is inaccessible to standard OEDG formulations. We rigorously prove that this fully discrete scheme achieves $(k+2)$-th order superconvergence to a tailored projection of the exact solution for linear conservation laws in both one and two dimensions, while maintaining the non-oscillatory shock-capturing capabilities of the original method. Moreover, we establish a general guiding principle for designing a class of OE-type DG schemes that exhibit such superconvergence. Key theoretical innovations include the construction of stage-aligned correction functions to compensate for nonlinear OE sources and the discovery of a two-dimensional projection operator that preserves outflow-edge averages, a property essential to close the discrete shift estimates. Numerical experiments confirm the predicted superconvergence rates and demonstrate that RK alignment preserves the parameter-free robustness of OEDG for problems with strong discontinuities.

Plasma reactors present themselves as a unique means of electrified chemical production, particularly in the conversion of greenhouse gases (e.g., CO2) back into chemical feedstocks. Warm plasmas, such as gliding arc discharges, represent a growing class of catalyst-free plasma reactors that demonstrate high energy efficiency and scalability. Here, we introduce mean discharge time as a characteristic descriptor of gliding arc dynamics, extracted directly from voltage and current waveforms. Electrical signatures for distinct plasma behaviors (modes) were established using high-speed photography, and discharge time distributions were evaluated as a function of Reynolds number. Mean discharge time is shown to decrease non-linearly with Reynolds number, providing a link between arc behavior and underlying fluid dynamics, which is otherwise neglected in traditional reactor characterization. Mean discharge time thereby provides a quantitative, operando descriptor of transient gliding arc dynamics and stability, offering insight into discharge behavior that traditional characterization approaches do not capture.

We present a deterministic discontinuous Galerkin (DG) finite-element solution of the Boltzmann equation, without moment-closure approximations, under a class of far-from-equilibrium deformations. Specifically, we consider affine flows which reduce the Boltzmann equation to a purely velocity-space problem for the reduced distribution function in a reduced velocity field. We solve the reduced equation using a tensor-product Lagrange DG discretization for four representative flows: simple shear, pressure shear, bi-directional shear, and a vortex flow. Our principal finding is that the velocity distribution is well-approximated by an anisotropic Gaussian throughout the evolution, despite the non-equilibrium conditions. Further, we show the evolution of the covariance tensor of the Gaussian distribution is equal to the inverse of the right Cauchy-Green tensor in the free-streaming limit without collisions. This prediction compares very well with the numerical solution at short times; at longer times, they grow apart, reflecting the influence of particle collisions.

Forward and inverse modeling of parametric dynamical systems requires surrogate models that are not only accurate for state prediction, but also informative for parameter calibration. However, a systematic end-to-end differentiable formulation for coupling deep-learning-based reduced-order surrogates with variational parameter estimation remains underdeveloped. In this work, we introduce a physics-aware neural-network-based latent-space framework for reduced-order forward modeling and variational parameter estimation. The proposed autoencoder-based approach yields a differentiable surrogate that maps physical parameters to predicted flow fields through a latent representation. The observable supervision is used during offline training to encourage the latent variables to retain information correlated with system parameters, while the online inverse problem is solved in the parameter space through the surrogate-induced observation operator. The method is evaluated on two computational-fluid-dynamics benchmarks. The results show that reconstruction accuracy alone is insufficient for inverse modeling, owing to the lack of end-to-end differentiability or physics awareness for variational parameter calibration. Quantitative latent-space analysis further shows that observable supervision improves case-level separability and temporal organization of latent representations. Experiments with realistic measurement settings, including noisy, low-resolution, randomly masked, and block-wise partial observations, demonstrate the robustness of the proposed framework and show that it generally reduces calibration error and variability compared with the standard surrogate models.

When a liquid thread pinches off, its neck thins as it separates into two unconnected regions. Using continuum mechanics, we can predict that the neck reaches zero radius in finite time while its curvature grows without bound. Together, the vanishing neck and diverging curvature form a finite-time singularity. However, a real fluid does not realise these mathematical limits as molecular or material physics takes over once the neck becomes sufficiently small. Similar singularities arise throughout soft matter whenever a smooth continuum description is used at vanishing length scales. This review asks what the shrinking region forgets, what it retains, and which material length, time, or stress cuts off the apparent divergence. The dynamics near a singularity often become self-similar, with profiles at different times collapsing onto one shape when rescaled by the shrinking local length. Sometimes that collapse is universal enough that the surrounding geometry and forcing no longer determine the local dynamics. Nonetheless, the measured output could still depend on how the shrinking region is fed by the surrounding flow and on the small-scale physics that finally replaces the ideal divergence. Complex fluids and active matter change the same local balance by bringing their own timescales into the shrinking region. Beyond interfaces, the same logic applies when the localised object is a stress concentration or a defect in geometry or order rather than a moving surface. Singularities matter because they show where continuum theory stops being the relevant description and how the small-scale cutoff sets the outputs that count in printing, coating, aerosols, and stretchable solids.

In this paper, we study the Couette-Taylor instability of a viscous fluid between two rotating cylinders in the small-gap, slow rescaled rotation rate, high Reynolds number regime, focusing on the very counter-rotating case $\mu < \mu_c \approx -0.8$ where the primary instability is non-axisymmetric. Starting from the Navier-Stokes equations, we derive a limit system that captures the leading-order dynamics and compute the critical Taylor number $T_c(\mu)$ together with the critical axial and azimuthal wavenumbers. Near criticality, the weakly nonlinear behaviour is governed by a system of two coupled complex Ginzburg-Landau equations. All coefficients of this amplitude system including the cubic nonlinear terms are evaluated numerically from the linearised eigenfunctions and the associated adjoint problem. The reduced equations admit helicoidal waves (travelling in both the axial and azimuthal directions) and ribbon waves (standing axially, travelling azimuthally), and their existence and stability criteria are discussed. We also examine more exotic spatially modulated solutions that satisfy a third-order dynamical system, whose complete classification remains an open challenge.

When a liquid drop impacts a solid surface, rebound and splashing are known to be suppressed by additives that induce elastic effects; however, the influence of elasticity on the maximum spreading radius remains debated. The difficulty lies in isolating elastic resistance from the enhanced spreading caused by viscous shear thinning. Here, we experimentally decouple these effects by investigating Boger fluid drops (constant-viscosity solutions with high elasticity) of polyethylene oxide (PEO) and polyacrylamide (PAAM). We demonstrate that elastic properties do not alter the maximum spreading ratio, even at high concentrations up to 1000 ppm. We formulate an energy balance that accounts for the inertial, capillary, viscous, and elastic contributions, and yields a dimensionless criterion ($\Gamma$) that estimates the degree of elastic effects. We show that $\Gamma \ll 1$ for all impact conditions tested, demonstrating that elastic effects are energetically negligible during droplet spreading, opposite to what Weissenberg and Deborah numbers would predict.

This work investigates Deep Reinforcement Learning (DRL) as a tool for model-free closed-loop active separation control in a fully turbulent wind tunnel flow over a one-sided diffuser. The agent controls an array of magnetic valves (on/off) that eject compressed air into the boundary layer, while the environmental state is reduced to the signal from a single wall-shear-stress sensor placed near the natural transitory detachment point. The control law is learned in real time using Proximal Policy Optimization. Compared to the standard learning design based on the weighted sum of all rewards following an action, we demonstrate that a horizon aligned with the convective time of the flow leads to faster convergence and a more robust control strategy. The resulting control law corresponds to a low-duty-cycle actuation pattern that yields a forward-flow fraction of approximately $53\%$. This compares favorably with conventional and optimized periodic open-loop control ($\sim 40\%$ and $\sim 51\%$, respectively). The findings of this article indicate that, when embedded into an online experiment, DRL represents an efficient tool to identify robust and interpretable active separation control strategies.

Uncertainty in wind farm layout optimization regarding model choice and the impact of global blockage always exists. This paper evaluates these interactions by extending a multi-objective approach that maximizes mean Annual Energy Production (AEP) from a model ensemble while minimizing their variance. By incorporating the Self Similar blockage model into an ensemble of five wake models, we assess the impact of blockage physics on layout robustness. Results from a linear mixed-effects model indicate that including blockage leads to a non-significant average AEP reduction of 0.0624 GWh ($p$-value = 0.323). Conversely, it caused a highly statistically significant increase in uncertainty, with model disagreement rising by 0.177 GWh ($p$-value < 0.001). Additionally, computational runtime increased nearly nine times. These findings highlight an accuracy vs. certainty paradox, where theoretically necessary physics can compromise model consensus if implemented without re-calibration. Ultimately, this work suggests that simple blockage couplings act as a diagnostic for model incompatibility, emphasizing the necessity of careful model tuning for wind farm design.

Representing flow states over a wide range of flow parameters and control inputs in a low-dimensional state space is a central challenge in fluid mechanics. Rather than representing the instantaneous flow field in a fixed subspace spanned by the leading proper orthogonal decomposition (POD) modes, this study regards the POD subspace itself as the flow state at each flow condition. The set of POD subspaces associated with flow conditions defines a state space on the Grassmann manifold. Diffusion maps identify the intrinsic low-dimensional structure of the family of POD subspaces, while Grassmannian rank-one update subspace estimation tracks the temporal evolution of a POD subspace online. The framework is experimentally demonstrated for flow around an airfoil. POD subspaces are extracted from wall-pressure fluctuations measured by a microphone array over a range of angles of attack and under different control inputs. The subspaces are found to lie on a one-dimensional submanifold of the Grassmann manifold. Moreover, the transition from separated to attached flow, induced by a plasma actuator, follows a reproducible trajectory along the same submanifold identified from statistically stationary flow data. The temporal evolution of the subspace is consistent with the transient evolution of the flow field observed using particle image velocimetry. These results show that POD subspaces can serve as representative flow states, enabling their temporal evolution across a wide range of flow conditions to be tracked online in a low-dimensional space based on wall-pressure fluctuations. This low-dimensional representation provides a basis for real-time flow-state estimation and feedback control.

High-order shock-capturing schemes often face severe computational bottlenecks due to wide stencils, stagewise nonlinear weights, and expensive local characteristic decompositions. To address this, we propose a compact finite-average-moment (FAM) framework for hyperbolic conservation laws that completely decouples the formal spatial order from the number of evolved local degrees of freedom. By evolving only a $\mathbb{P}^1$ moment state (i.e., cell averages and scaled first-order moments), we achieve up to sixth-order accuracy ($k=3, 4, 5, 6$) via compact, polynomially exact linear moment reconstructions. A key algorithmic innovation is consolidating the nonlinear stabilization into a single, derivative-free oscillation-elimination (OE) procedure applied only after the final Runge–Kutta stage. This OE procedure exactly preserves cell averages while applying an explicit exponential correction to the first-order moments, avoiding repeated stagewise nonlinear weights or limiting. Fourier analysis of the linear backbone demonstrates $k$th-order accuracy, strong spurious mode damping, and $(k+1)$th-order cell-average superconvergence. Extensive numerical experiments on scalar laws and the Euler equations verify the expected smooth accuracy and robust, nonoscillatory shock resolution. Notably, by performing componentwise reconstruction directly in conservative variables and streamlining stabilization, the FAM schemes deliver significantly lower complete-run wall-clock times compared to the multi-resolution weighted essentially non-oscillatory (MR-WENO), unified-stencil Hermite WENO (HWENO-U), and OE-HWENO methods.

We extend Thorpe successive approximation expansion to the forced, tide locked internal wave generation problem of Lamb and Dunphy, where a barotropic tide over a ridge radiates a discrete spectrum of Taylor Goldstein eigenmodes in a steady shear current. At second order in topographic steepness, each mode forces a bound second harmonic via diagonal mode pair kernels derived in closed form; both kernels vanish for uniform flow, recovering Thorpe limit. At third order, solvability of the resonant fundamental yields a nonlinear wavenumber correctionthe forced counterpart of Thorpe phase speed shift, with tidal frequency fixed. Computations at the parameters of Lamb and Dunphy show that the corrections are small but systematic, with the bound harmonic distorting the displacement profile modestly and concentrated in the surface shear layer for downstream modes. The corrections peak at modes 2 to 3, grow quadratically with ridge height and current strength, and amount to a nonlinear slow-down of every mode, explaining from within the theory why the linear discrete spectrum model agreed so well with fully nonlinear simulations. A pycnocline case with stratification colocated with the shear layer amplifies the nonlinear corrections substantially, showing that the uniform stratification verdict is not generic and that the corrections are controlled by where N2 sits relative to the shear.

Advanced air mobility operations hold the potential to enhance and expand regional transportation of both people and goods in populated areas. However, hazardous flight conditions arising from interactions between wind and the built environment remain a significant challenge for aerial vehicles in urban settings. This work proposes a novel framework towards safe flight planning of aerial vehicles in windy urban environments. A learning-based surrogate model is trained to rapidly predict flow fields from readily available information such as building geometry and incident wind. This surrogate prediction is used to calculate a volumetric flight challenge scalar field based on critical flow parameters and proximity to structures. A safe, flow-informed flight trajectory is then identified through a cost-minimizing pathfinder. The complete system is demonstrated experimentally through flight tests of a micro aerial vehicle through a model urban geometry placed in a large fan-array wind tunnel. Comparing this approach to trajectories generated without knowledge of the wind field, we find the flow-informed approach reduces undesired vehicle displacement and improves flight stability. This work is among the first practical demonstrations of safe, wind-aware methodologies for advanced air mobility in urban environments.

Natural transition from laminar to turbulent flow can be modeled by using only the Spalart-Allmaras (SA) working variable. The variable serves as its own transition indicator, in a one-equation Reynolds-averaged Navier-Stokes (RANS) closure. Its sub-O(1) range is dynamically inert in the baseline model. That range becomes a Tollmien-Schlichting amplification factor. A blended production term then drives the SA transport equation through laminar instability growth and turbulent eddy-viscosity production. Computations with this formulation on a zero-pressure-gradient flat plate, the NLF(1)-0416 and Eppler 387 airfoils, a two-element section, a circular cylinder through the drag crisis, the Daedalus human-powered-aircraft wing, and a 6:1 prolate spheroid are compared with experimental data and with other transition models.

Gravity driven sediment flows are responsible for a major portion of sediment redistribution within oceans, reservoirs, and lakes, with important implications in coastal erosion, siltation, carbon burial, and contaminant migration in aquatic systems. Despite the ubiquity of this phenomenon, current mechanistic understanding of sediment gravity flows (SGFs) remains limited. This knowledge gap is particularly acute in the case of cohesive, fine-grained sediments (i.e., muds) due to the complex properties of the clay matrix, including low permeability, viscoplastic rheology, and flocculation. In this work, we develop a computational fluid dynamics model that accurately predicts key features of cohesive, clay-rich SGFs based on independent measurements of the relation between sediment solid fraction and rheological yield stress. In particular, the model captures the four primary flow regimes (low density turbidity currents, high density turbidity currents, mudflows, and mudslides) observed in lock-exchange experiments with slurries containing smectite or kaolinite clay. The model is validated through comparison with previous experimental observations of sediment flow morphology, speed, and runout distance. Overall, we demonstrate the ability to predict the influence of intrinsic (particle size, grain density, and rheology) and extrinsic sediment properties (sediment topography and solid fraction) in the development of self-sustaining cohesive SGFs.

The discretization of second-order (viscous) terms in Discontinuous Spectral Element Methods (DSEMs) typically relies on an auxiliary gradient variable, whose treatment at element interfaces affects the accuracy and stability of the scheme. The Bassi-Rebay (BR1) formulation is attractive for its simplicity and parameter-free character, but suffers from sub-optimal convergence at even polynomial orders and requires an extended five-element stencil. Inspired by Huynh's Flux Reconstruction formulation, we develop a compact, fully-centered scheme for second-order fluxes within the Spectral Difference (SD) method. The proposed approach modifies the reconstruction of the auxiliary gradient using interface-dependent, one-sided continuous fluxes, reducing the stencil from five to three elements while preserving the centered and parameter-free nature of BR1. The formulation is developed in one dimension and extended to multiple dimensions. Temporal eigenanalysis is used to characterize its dissipation and dispersion properties, including the effects of interior penalty terms. Numerical tests consider the linear diffusion equation, an under-resolved localized Dirac's delta, the nonlinear porous medium equation, and implicit large-eddy simulations of the three-dimensional Taylor-Green vortex at $\mathrm{Re}=1600$ and $5000$. The compact scheme restores the expected convergence order for all polynomial degrees, including even orders, and reduces spurious oscillations in under-resolved and nonlinear regimes. It also remains stable in turbulent cases where the standard formulation fails, owing to improved damping of high-wavenumber numerical modes. The proposed approach provides an attractive compact alternative to BR1 for second-order fluxes in the SD method.

Memory is traditionally incorporated into transport theory as a constitutive correction acting on an already prescribed kinematic structure. Here we develop a different framework in which finite memory itself generates the geometry of transport. By reconstructing deformation from causal transport histories, the instantaneous velocity gradient is replaced by a memory-dependent transport connection whose ordered evolution gives rise to noncommutativity, curvature, and holonomy in transport-history space. We show that finite memory generates a nonvanishing geometric contribution to transport even in time-periodic, irrotational flows, providing a purely kinematic mechanism for irreversible Lagrangian transport without invoking vorticity, constitutive nonlinearities, stochastic forcing, or explicit symmetry breaking. We introduce an intrinsic curvature invariant, independent of the transport representation that measures the accumulated geometric structure generated by transport history. The framework predicts universal scaling governed by the dimensionless parameter (\omega\tau_m), identifies a characteristic memory scale (tau_c) separating rapid geometric accumulation from asymptotic saturation, and reveals a monotonically decreasing memory susceptibility with globally concave accumulation dynamics. Numerical simulations confirm these predictions and show that geometric irreversibility emerges through progressive curvature accumulation rather than resonance-driven amplification. These results establish finite memory as a generator of an intrinsic geometric structure rather than merely a modifier of dynamical evolution, revealing causal history as the microscopic origin of curvature, holonomy, and irreversible transport across a broad class of non-Markovian systems.

We provide an exact and complete solution for the dynamics of a rigid particle of uniform density with $C_{2v}$ and $S_4$ symmetry, settling under gravity in a viscous fluid at a Reynolds number much smaller than unity. The $S_4$ symmetry renders the problem exactly integrable, with all orbits labelled by a single conserved quantity $0\le C\le 1$. We show that, for $0<C<1$, there are two different time scales, which lead to quasi-periodic evolution, with a significant time-dependent horizontal displacement. We obtain the tilt $\theta$ and spin $\psi$ Euler angles as periodic Jacobi elliptic functions of time, and the azimuthal angle $\phi$ through an incomplete elliptic integral of the third kind with a complex characteristic, which splits $\phi$ into a uniform drift and a strictly periodic modulation. The orientation period and the drift rate (corresponding to a constant angular velocity around the gravity direction) follow in a closed form. The vertical centre-of-mass displacement is obtained in terms of periodic in time incomplete elliptic integrals, and the periodic orbit-averaged settling velocity reduces to a single ratio of complete elliptic integrals. The horizontal component of the motion in the laboratory frame of reference is obtained exactly and algebraically in terms of all three Euler angles, so it is quasi-periodic. The horizontal component of the centre-of-mass position traces rosette-like, in general open curves confined by two concentric `envelope' circles. We determine very simple exact expressions for radii of both envelopes and demonstrate that they tend to infinity for a family of shapes with the rotation-translation coupling decreasing to zero. We also explain the origin of cusps at the rosette-like trajectory and provide a commensurability condition selecting strictly periodic rosettes.

A discrete entropy inequality is the principal nonlinear stability estimate available for systems of conservation laws, and evaluating it presupposes a physically admissible state. So far, however, the two have been secured separately. Entropy-stable schemes are almost always semi-discrete, are built around one selected entropy pair, and take for granted the positivity of density and pressure that makes the entropy well defined in the first place, whereas bound-preserving limiters keep the solution admissible but deliver no entropy estimate. For the special relativistic Euler equations, the two cannot be separated at all, since the conservative-to-primitive map is implicit, and an inadmissible state therefore has no entropy to correct. Here we construct high-order discontinuous Galerkin and finite volume schemes that, to our knowledge, for the first time, are entropy stable in the fully discrete sense for an arbitrary prescribed finite family of convex entropy pairs, a property we call multi-entropy stability, and are provably admissible wherever an entropy is evaluated. All of this is achieved by a single cellwise projection, and neither conservation nor the design order is lost. The construction rests on relativistic causality, which bounds every characteristic speed by the speed of light. Consequently, the numerical viscosity can be fixed once for all states and all equations of state, and one two-point building block then serves the whole entropy family. Since only the convexity of the admissible set and this speed bound are used, the same route remains open for related systems. Finally, in computations with four equations of state, the schemes retain high-order accuracy close to vacuum, produce no inadmissible state in strong shocks, near-vacuum shock–vortex interaction or jets with Lorentz factor above $70$, and confirm the monotone decay of every enforced discrete entropy.

High-fidelity numerical simulations of bubble-laden, vertical channel flow in the upward configuration, where the bubbles undergo topological changes (breakup and coalescence), were performed with the purpose of exploring the effect of the surface tension on the turbulence anisotropy in the carrier phase. A qualitative analysis shows that velocity fluctuations are enhanced in the wake of large bubbles. Moreover, as shown by the velocity spectra, these structures seem to scale with bubble size and interact with those closer to the wall. Finally, a barycentric map and other indicators of turbulence anisotropy clarify that, except at the core of the channel where the largest bubbles reside, the multiphase flow cases are actually more isotropic than the single-phase flow at a matching friction Reynolds number. This unexpected behavior is attributed to a better redistribution of energy due to an enhancement of sweep events (high-speed fluid towards the wall) in the presence of large bubbles.

The deformation of viscoelastic drops in alternating electric fields is relevant to electrohydrodynamic applications such as microfluidics, inkjet printing, and drop manipulation. We investigate the dynamics of a neutrally buoyant Oldroyd-B drop subjected to a uniform alternating electric field using asymptotic analysis and direct numerical simulations with the open-source solver Basilisk. An analytical solution is derived for small deformation and weak elasticity for an Oldroyd-B drop suspended in an Oldroyd-B medium, with both fluids modeled as leaky dielectrics under axisymmetric Stokes flow. Depending on the conductivity and permittivity ratios, six electrohydrodynamic regions are identified, characterized by distinct deformation modes, flow directions, and nonlinear responses; while some exhibit stable spheroidal deformation, others undergo pointed-tip, multi-lobed, or oblate breakup beyond a critical electric capillary number. Across high-, intermediate-, and low-frequency regimes, the deformation oscillates at twice the applied field frequency, with its mean and amplitude governed by the field frequency and viscoelasticity. For cases that produce prolate deformation under a steady field, the drop remains prolate at high frequency, exhibits brief oblate excursions at intermediate frequency, and undergoes large-amplitude oscillations between near-spherical and highly deformed states at low frequency. The mean deformation varies monotonically or non-monotonically with $De$, depending on frequency and electrical property ratios. For cases producing oblate deformation under a steady field, the drop remains oblate at high frequency, develops dimples at intermediate frequency, and breaks up at low frequency for sufficiently large $De$ and $Ca_E$; the mean deformation increases monotonically with $De$.

Fluids with nonvanishing antisymmetric components of the transport coefficient tensor are named odd fluids. In our previous works, we proposed a mesoscale simulation model for isotropic two-dimensional odd fluids and then extended it to the three-dimensional case to model an anisotropic odd fluid with cylindrical symmetry. The Navier-Stokes equation and the viscosity tensor of this three-dimensional mesoscale odd fluid were derived previously via a kinetic theory. Herein, we derive the heat conduction and self-diffusion equations, along with the corresponding thermal conductivity and self-diffusivity tensors. These theoretical results are validated by simulations. We further investigate heat and mass transport behaviors of three-dimensional odd fluids in a confined geometry through our mesoscale model. In striking contrast to normal isotropic fluids, the steady-state temperature and density distributions of confined odd fluids are significantly deformed by the odd transport coefficients.

Micromixing of non-Newtonian fluids remains challenging because laminar flow at microscales restricts transverse transport primarily to molecular diffusion. In this study, we investigate the transport mechanisms governing passive micromixing of a Carreau–Yasuda fluid in two-dimensional sinusoidal converging–diverging microchannels and develop a surrogate-assisted framework for their multi-objective design. We perform high-fidelity finite-volume simulations by systematically varying the wall-amplitude ratio, phase offset, and wave count under creeping-flow conditions. The results show that successive contraction–expansion units enhance mixing through the combined effects of interface stretching, elevated shear rates, and shear-thinning-induced viscosity reduction. These mechanisms improve scalar transport but simultaneously increase pressure drop, creating an inherent trade-off between mixing performance and hydraulic resistance. To efficiently explore the multidimensional design space, we construct surrogate models from high-fidelity numerical simulations and identify Gaussian Process Regression (GPR) as the most accurate predictor of both the mixing index and pressure drop. Coupling the validated GPR surrogate with Non-dominated Sorting Genetic Algorithm II (NSGA-II) accurately reproduces the Pareto front obtained from the high-fidelity simulations and identifies optimal microchannel geometries that balance mixing enhancement against pressure loss. The proposed machine learning framework provides a fast, accurate, and physically consistent strategy for the multi-objective design of passive micromixers for non-Newtonian fluids.