Papers

This paper develops a data-driven framework for long-term prediction of fluid–structure interaction (FSI) dynamics, focusing on the flow-induced vibration (FIV) of a flexible plate. A stiffness-conditioned neural evolution operator jointly represents the Eulerian flow field and Lagrangian structural state. The plate is represented by 101 ordered structural tokens carrying nodal coordinates and velocities, with nondimensional bending stiffness as a global conditioning variable. Bidirectional cross-attention couples fluid and structural representations within a hybrid CNN-Transformer architecture. Trained with staged multi-step autoregressive rollouts and symmetry-reflected trajectories, a single operator captures three stiffness-dependent response regimes: deflected–flapping, deflected, and flapping. The predicted trajectories preserve the principal flow structures, structural oscillations, and dominant frequencies, while blind 1000-step rollouts remain bounded. The operator also interpolates to stiffness values excluded from training. To reduce sensitivity to under-resolved near-wall gradients in force reconstruction, we develop a differentiable aerodynamic-force module based on the derivative-moment transformation (DMT). Conventional wall-stress surface integrals are replaced by an enclosed 2D curve integral around the core vortex region, enabling accurate reconstruction of lift and drag. A Signed Distance Function (SDF) and smoothed Dirac-delta formulation make the integration fully differentiable while preserving gradient flow. The proposed framework provides an accurate and differentiable surrogate for stiffness-dependent FSI dynamics, enabling efficient parameter studies and future stiffness optimization for flow-energy-harvesting applications.

Hybrid physics-machine-learning solvers improve under-resolved simulations by embedding trainable corrections into the time integration. During autoregressive inference, repeated solver-model interactions can amplify small errors, motivating multi-timestep solver-in-the-loop training. However, production solvers rarely expose the derivatives needed to backpropagate through such rollouts. We introduce Diff-NekRS, a scalable differentiable framework that embeds neural corrections directly in the GPU-accelerated NekRS incompressible-flow solver. NekRS computes the authoritative forward trajectory, a manually implemented exact discrete adjoint differentiates the supported fully discrete timestep, and LibTorch supplies neural vector-Jacobian products and parameter gradients. End-to-end Taylor and centered finite-difference tests verify the assembled gradient for two-dimensional cylinder flow (2Dcyl) and the three-dimensional Taylor-Green vortex (3DTGV) across five horizons and 12-1,020 MPI ranks. At 1,020 ranks, optimizer-enabled post-setup training updates retain 54.5%-78.0% and 80.7%-81.9% weak-scaling efficiency for 2Dcyl and 3DTGV, respectively. In 200-step autoregressive inference, the M = 50 model reduces the three-seed median terminal relative L2 velocity error by 59.2% for 2Dcyl and 12.1% for 3DTGV relative to the uncorrected coarse-grid P = 2 baseline, and retains wall-clock speedups of 5.38x and 2.49x, respectively, relative to the corresponding P = 7 configurations for equal simulated-time intervals. These results establish a verified and scalable path for multi-timestep solver-in-the-loop training that improves coarse-grid trajectory accuracy while retaining a speed advantage over the high-order reference

The classical theory of the wind-driven surface layer of a rotating ocean closes the momentum balance with a local flux-gradient law, in which the turbulent stress at a given depth is proportional to the shear at that depth. It predicts a surface current deflected forty-five degrees from the wind, which exceeds most direct measurements. This study asks what follows when locality is relaxed. Beginning from the exact integral relation between turbulent stress and mean shear, and requiring the memory kernel to carry no preferred vertical scale, we obtain a power-law kernel and therefore a stress law of fractional order. The resulting equation cannot be posed on the velocity, because the fractional derivative of a bounded profile vanishes at the surface, so the wind stress cannot be applied, while the alternative definition of the derivative leaves the surface current unbounded. Posed on the stress instead, the problem is solvable in closed form in Mittag-Leffler functions at every order between zero and one. The surface deflection then depends on the closure order alone and is smaller than forty-five degrees throughout, whereas the depth-integrated transport stays exactly normal to the wind, because that constraint follows from the momentum balance and not from the closure. The far field decays as a power law rather than exponentially, and its amplitude vanishes in the local limit, so that limit is singular. Under a suddenly applied stress the surface transient decays algebraically. Three independent algorithms agree closely, and no observational or model data are used.

We extend the Obukhov-Corrsin theory of scalar turbulence to compressible flows with spatially variable, anisotropic diffusivity. Combining density and diffusivity into a single positive matrix field, a transport landscape, permits an exact scale-by-scale balance in which the sign-indefinite commutator between filtering and diffusion is eliminated rather than estimated. If the density-weighted third-order velocity and scalar increments scale as $\ell^\alpha$ and $\ell^\beta$, respectively, we prove that anomalous scalar dissipation is impossible when $\alpha+2\beta>1$. Remarkably, this threshold is independent of the anisotropy and spatial regularity of the diffusivity, provided it remains uniformly elliptic. Codimension-one shocks in both velocity and scalar have $\alpha=\beta=1/3$ and therefore lie exactly at the critical threshold. For statistically stationary turbulence we further obtain an exact density-weighted constant-flux relation, providing a compressible analogue of the relation underlying Yaglom's law. The results apply directly to passive-scalar transport in both gases and magnetized plasmas and provide testable diagnostics for simulations of compressible magnetohydrodynamic turbulence. Because the same operator governs anisotropic heat conduction, the results carry over to the electron temperature of a magnetized plasma, and they imply that gradient statistics in such flows must be contracted with the transport landscape rather than with the density.

Under certain conditions, gravity currents spontaneously develop large-amplitude streamwise undulations on their free surfaces ('roll waves'). The effect of channel geometry on this instability is investigated herein. Via a section-averaged stability analysis conducted independently of the rheology of the flowing material, convex open channels are found to be stabilising, relative to unconfined flows. This is shown to agree with experimental observations of laterally shallow currents of water and dry granular material in trapezoidal channels. For such flows, the influence of the geometry can be characterised by a single dimensionless parameter, which predicts stabilisation as the channel width narrows. Including the cross-stream velocity profile in the analysis further stabilises predictions and can render steady flows in triangular channels unconditionally stable - a finding borne out by our experiments. Consequently, laterally tilting a trapezoidal channel can also stabilise flows by adjusting the wetted region towards a triangular one. Implications for observations in natural channels are considered by adapting an existing model of roll waves in the Illgraben, Switzerland, to incorporate channel geometry. The resulting simulations produce suitable waves for a realistic cross-section, but are stabilised by a modest narrowing of the channel. Complementary nonlinear wave solutions are then constructed and used to show that channel confinement also diminishes amplitudes of observed waves. Finally, exceptions to the analysis are discussed, including the possibility for static material to shield waves from the effects of geometry. We demonstrate this using observations of undamped granular avalanches travelling through an arrested deposit in a triangular chute.

The Stokes-flow hydrodynamics of an irregular microparticle is encoded by its grand resistance matrix, a 6x6 tensor whose translational and rotational blocks (A and C) govern settling, diffusion, and orientational transport. Empirical drag correlations compress these tensors to a single scalar, discarding drag's orientation dependence and the rotational response. We present an SO(3)-equivariant neural network that predicts the full symmetric positive-definite A and C blocks from a particle's spherical-harmonic surface representation, equivariant by construction to floating-point precision. Trained on 1.1x10^5 random shapes from near-spherical to very rough, with a sealed test set of 18,000, it achieves 1.4% and 2.7% mean relative error on the two blocks while evaluating each shape 4-5 orders of magnitude faster than the regularised-Stokeslet solver that generated its labels. A spectral-convergence study confirms the representation is faithful: truncating a shape at spherical-harmonic degree 15 changes its resistance by a median of 0.14% (translation) and 0.38% (rotation), while the training shapes, generated band-limited at degree 15, carry no truncation error. Across 1.16x10^6 orientation-sampled settling, rotation and diffusion events, the surrogate reveals lateral drift up to 11 deg, rotational misalignment up to 46 deg, and shape-induced diffusion spreads of 30% (translational) and 2.4x (rotational), all identically zero under any scalar or spheroid reduction. Even the orientation-averaged scalar friction the correlations target, accurate to 1.7-2.8% (median; 2.2-3.2% mean), carries no tensor orientation, whereas the surrogate reproduces that scalar to ~1% while supplying the full anisotropic tensors. A fast, equivariant tensor surrogate can replace both solver and scalar approximation in atmospheric dust transport, microplastic fate and colloidal Brownian dynamics.

A fundamental problem in the field of anisotropic macromolecular materials concerns how the flow-induced orientational order connects microscopic structure to macroscopic rheological stress and optical anisotropy. This study considered cellulose nanocrystal suspensions as rigid-rod model systems for the purpose of isolating orientational effects from chain stretching. Simultaneous rheo-optical measurements of birefringence, orientation angle, and shear stress were combined with a Fokker-Planck orientation model and stress decomposition. Our results show that, at low values of the Peclet number, birefringence and total stress exhibit proportionality similar to the stress-optic rule. However, the concentration dependence indicates that this proportionality reflects stress partitioning rather than a unique material coefficient. With increasing flow strength, orientational saturation is accompanied by a reduced relative Brownian stress contribution and a corresponding change in the total stress-based relation. Referencing the optical response to an estimated Brownian stress contribution yields a substantially more unified response across concentrations and flow conditions, supporting a stress-partitioning interpretation of apparent stress-optic rule breakdown.

The equilibrium oblique-detonation polar is a fundamental gasdynamic relation. This relation links the deflection angle, the wave angle, the flow state and the heat release. However, the wave angle is usually determined by numerical iteration. There is no explicit formula to determine the wave angle from a prescribed deflection angle, referred to as the inverse problem, even for the classical oblique-detonation model: a calorically perfect gas with a constant specific-heat ratio and a fixed heat release. This is inconvenient in practical applications. In this work, we solve this inverse problem for the classical model and derive explicit formulae for the wave angle. Inspired by the derivation of the oblique-shock inverse relation, the oblique-detonation inverse relation also reduces to a cubic equation. Heat release only changes the cubic coefficients, so the equation can still be solved explicitly. We also derive the complete analytical branch structure. We further find that the detachment point and the downstream total-sonic point can be determined explicitly by solving a cubic and a quadratic equation, respectively. We extend the explicit formulae to the two-$\gamma$ model and apply them to oblique-detonation calculations with equilibrium chemistry. These explicit formulae for the wave angle and critical points promote the theoretical understanding of oblique detonations and support their practical calculation.

The transport of bubbles along a curved superhydrophobic surface is not governed by buoyancy alone, but also by the interaction between the geometric confinement, the capillary and contact-line resistance, and the hydrodynamic resistance. We systematically investigated the capillary number ($Ca$) and Bond number ($Bo$) of the transported bubble, as well as the size of the rod relative to the bubble. An analytical force-balance model was developed to predict transport velocity, accounting for buoyancy, hydrodynamic drag, and capillary resistance. The transition from transport to detachment was identified. The experiments were carried out sequentially and supplemented by axisymmetric numerical simulations to investigate wake-induced interactions between bubbles. Bubble transport is strongly influenced by rod inclination and the bubble-to-rod size ratio, demonstrating that curvature-induced confinement alters the balance between driving and resistive forces. The analytical model captured the experimental trends with deviations of less than 10% in most cases. The bubble detaches from the inclined rod at a critical Bond number that depends on rod diameter, facilitating the development of a transport regime map. The study also found that the motion of successive bubbles is strongly coupled. When a following bubble enters the wake of a preceding bubble, it speeds up and attains a higher capillary number than the leading bubble. Both experiments and numerical simulations consistently reproduce this wake-mediated acceleration, which shows that bubble transport is governed by both the force balance on individual bubbles and the hydrodynamic interactions between adjacent bubbles. These findings form the basis for controlling bubble transport, detachment, and collective motion on superhydrophobic interfaces.

Physics-Informed Neural Networks (PINNs) provide a mesh-free framework for solving partial differential equations but often struggle with sharp gradients and shock-dominated solutions. Extended Physics-Informed Neural Networks (XPINNs) address this challenge through domain decomposition; however, the effects of decomposition design, overlap, and local network capacity on solution accuracy remain insufficiently characterized. This work presents a systematic assessment of domain decomposition configurations for XPINNs applied to the one-dimensional viscous Burgers equation ($\nu=0.01/\pi$). We compare a standard PINN, a conventional XPINN, a shock-focused XPINN with increased network capacity in the shock-containing subdomain, and overlapping XPINNs with different overlap widths. All configurations are trained using a common protocol based on Adam, L-BFGS refinement, and ten Residual-based Adaptive Refinement (RAR) cycles. Performance is evaluated against a reference solution using global and shock-region relative $L_2$ and $L_\infty$ errors, maximum PDE residuals, and interface continuity errors. The results show that decomposition design strongly affects XPINN accuracy and shock resolution. Among the overlapping configurations, the smallest overlap provides the best accuracy, while larger overlaps degrade performance. The shock-focused XPINN achieves the lowest overall solution errors, indicating that increased local network capacity can provide greater benefit than increasing overlap alone. RAR produces the largest improvements during early refinement stages, followed by increasingly non-monotonic changes in accuracy. These findings highlight the importance of jointly considering decomposition, interface coupling, network capacity, and adaptive refinement for shock-dominated problems.

Operators for interfacial problems are trained on reference solutions produced by the solver they are intended to replace. This work develops a data-free physics-informed neural operator for level-set interface advection, in which the interface is the equation's unknown and the operator maps an initial interface to the full spatiotemporal trajectory under a prescribed flow. Training uses only the transport residual and a geometric constraint; no reference solution enters the objective at any point. A spacetime Fourier backbone emits the entire trajectory in one pass, and the initial condition is imposed by construction rather than by penalty, which removes the competition between the anchoring term and the residual that otherwise arises when no solution data are available. Supervised and hybrid operators are trained under an identical architecture, family, budget and test set, and are reported throughout as baselines that quantify what refusing labels costs. On a reversed single vortex the data-free operator reaches 1.614 +/- 0.067% relative L2 error on 100 held-out initial interfaces against 0.369 +/- 0.035% for the supervised baseline, a factor of 4.4; on solid-body rotation the corresponding figures are 3.804 +/- 1.075% and 2.576 +/- 0.159%, a factor of 1.5. The two benchmarks rank the arms differently, and the difference is attributable to the eikonal constraint: the exact solution violates |grad phi| = 1 over 0.3% of the domain under rotation and 86.9% under the vortex. Where the constraint is valid the physics-trained operator conserves enclosed area 2.7 times better than the supervised baseline despite a larger field error, and a hybrid arm using eight reference solutions outperforms a supervised arm using sixteen.

A species-specific weighting scheme for the Natural-Sample-Size collision model within the Direct Simulation Monte Carlo method is developed and implemented in the open-source gas and plasma solver PICLas. The implemented weighting scheme places particular emphasis on chemical reactions and ionization processes of trace species in order to guarantee physically accurate and low-noise simulations of atmospheric entry processes. The successful implementation and the conservation of momentum and energy during relaxation processes and chemical reactions are verified through a reservoir simulation of a reacting air mixture. As a more sophisticated validation case, atmospheric entry simulations of a cylinder at an altitude of 108 km are investigated. In a final step, the developed weighting scheme is employed to investigate ionization processes in the shock layer surrounding the RAM-C II reentry probe during atmospheric entry. The simulations showed very good agreement with experimental flight data and reduced noise in the rarefied regions for the charged species.

We perform direct numerical simulations (DNS) to investigate how cubic-lattice porous substrates influence momentum and heat transfer in turbulent channel flows. The simulations span friction Reynolds numbers from 260 to 1500, Prandtl numbers of 0.5, 1, and 2, and substrate porosities of 50%, 71%, and 87%. We show that theories developed for rough- wall turbulence can be extended to porous surfaces by replacing the roughness height with the inverse of the streamwise Forchheimer coefficient. The shifts in the mean velocity and temperature profiles follow existing fully rough momentum and thermal theories, enabling their prediction with rough-wall models. Combining these models with synthetic temperature and velocity profiles, we derive analytical formulas for the friction coefficient and Stanton number that agree with our DNS data to within 5%. The performance enhancement factor, which measures heat-transfer augmentation relative to the pressure-drop penalty at constant pumping power, is comparable to that obtained for rough surfaces. This suggests that porous substrates provide an alternative method for enhancing heat transfer in turbulent flows.

Offshore wind farms operate within the marine atmospheric boundary layer, where ocean waves can modify air-sea momentum transfer, turbine inflow, and wake recovery. Wave-resolved simulations can capture phase-dependent wind–wave interactions, but their computational cost and implementation complexity limit their use in large atmospheric and wind-farm domains. This study describes applications and tests of the recently proposed moving surface drag (MOSD) model, a flat-bottom wall-stress formulation for horizontally resolved moving waves, to a sequence of increasingly complex wind–wave and offshore wind-energy applications. The model is first evaluated for turbulent flow over Stokes-like waves using laboratory measurements, where it reproduces mean velocity profiles and captures the qualitative structure of wave-induced motions, although their amplitude is underpredicted. MOSD is then applied to broadband wave spectra fields and offshore wind-farm boundary layers, showing good agreement with mean velocity profiles from wave-resolved simulations across different wave ages, grid resolutions, and turbine spacings. Finally, exploratory offshore wind-farm simulations using MOSD under conventionally neutral conditions demonstrate its application at wind-farm scale. Large-scale waves leave detectable signatures in near-surface velocity spectra, but these signatures decay with height and do not produce clear peaks in temporal spectra of aggregate turbine power. Overall, the results demonstrate that the MOSD model provides a tractable framework for incorporating resolved wave effects in wind-wave and offshore wind-farm simulations.

This paper describes experiments and numerical simulations on the normal impact of a round liquid jet onto a horizontal surface, such as when water from a tap hits the bottom of a kitchen sink. In this case the liquid impacting on the surface spreads as a fast-flowing thin film and, at some distance from the point of impact, the thickness of the flow abruptly increases and the speed of the flow is reduced. In the experiments studied here the flow is axisymmetric about the axis of the jet, and the abrupt change in depth occurs at a given radius and is known as a circular hydraulic jump (CHJ). We present new experiments in which we measure the thickness of the liquid film inside and beyond the jump and use these measurements to estimate the governing parameters, the Weber, Froude and Reynolds numbers that determine the influence of surface tension, gravity and viscosity, respectively. We also carry out numerical simulations of the flow that show excellent agreement with the experiments and provide independent estimates of these dimensionless parameters. We find that, on the scale of a kitchen sink, and for water at high Reynolds number and low Bond number, at the jump the Weber number is of order unity while the Froude number is large, implying that the jump is controlled by surface tension. We also define a critical dimensionless jet flow rate at which this control no longer holds and gravity plays a significant role.

Two immiscible viscous fluids in pressure-driven channel flow can be unstable through their interface when their viscosities differ, at arbitrarily small Reynolds number — the instability Yih found in 1967. The unstable state is the interface itself: a curve inside the domain, separating the two fluids, whose displacement is governed by a partial differential equation of its own and which moves the fluid domain with it. Actuation is at one wall only, so the state to be controlled is reached across a fluid. We stabilize this interface at any rate below the limit set by the streamwise mean flow, by static feedback of the two velocity components of that wall, through a Fredholm backstepping transformation acting jointly on the two layers. The target is the two-fluid Stokes problem, shifted, with the transmission of stress between the fluids kept and the coupling of the interface into them removed. Two findings about the two-fluid spectrum carry the design: joined at the interface, the eigenvalue sequences of the two layers, which collide for a dense set of layer ratios when the layers are uncoupled, avoid each other uniformly, so no degeneracy has to be assigned; and the slowest mode left to viscosity is not a bulk mode but the capillary relaxation of the interface, whose rate is linear rather than quadratic in the wavenumber, which sets the band of actuated wavenumbers. The controller is tested on the nonlinear two-fluid channel, switched on against a saturated interfacial wave.

Active particles confined in droplets can set their host droplet into motion. This phenomenon is usually attributed to direct hydrodynamic forcing by the enclosed particles. Here we reveal a different mechanism: we show that a self-propelled raft of active colloids confined in a thin oil droplet at the surface of water typically follows an off-centered orbit, thus periodically deforming the droplet's contact line in an anisotropic way. This non-reciprocal deformation acts as a swimming stroke and propels the droplet according to the principles of low-Reynolds-number swimming. The effect is absent for a single colloid and arises from the intrinsically many-body dynamics of the raft, which we capture with a dynamical model coupling viscous hydrodynamics and many-body active dynamics. Our results show how collective internal activity can be converted into locomotion through deformation of a soft confining boundary.

Architectures with periodic activation functions have already been shown to be beneficial in comparison to monotonic counterparts for a wide range of applications of physics-informed neural networks. Here, we investigate a network architecture which uses the complex exponential function, generating pairs of sine and cosine outputs as activation functions. Testing it against comparable, sine-activated multi-layer perceptrons for the task of temperature reconstruction from sparse velocity data for cubic Rayleigh-Bénard convection reveals significant improvements in the reconstruction quality without a substantial increase in computational cost per training step. Vice versa, the improved architecture enables reaching similar reconstruction qualities for a fraction of the expense. Analyzing the mathematical structure of these networks points to the improvements being rooted in the property of passing both a sine and cosine function forward. This way, the subsequent layer is able to adapt the phase of the provided latent periodic functions, and doing it individually for each of its neurons.

Modeling stiff string vibrations is challenging due to their dispersive and high-frequency characteristics. This study investigates the effectiveness of Physics-Informed Neural Networks (PINNs) in simulating the transverse vibration of a one-dimensional linear stiff string with sharp initial conditions induced by plucking. The governing Partial Differential Equation (PDE), along with the associated initial and boundary conditions, is incorporated directly into the loss function of the neural network. For the reference measurements, a wire-breaking experiment was performed to excite the string, and its vibration response was captured using a laser profiler. The comparison between experimental measurements, finite-difference time-domain (FDTD) simulations, and PINN-based simulations shows good overall agreement, highlighting the potential of PINNs for modeling stiff-string vibrations.

Achieving sufficient near-wall resolution remains challenging for wall-bounded turbulence simulations using weakly compressible smoothed particle hydrodynamics (WCSPH), as local particle refinement imposes restrictive time-step requirements. This work proposes a multi-scale near-wall approach within the Reynolds-averaged Navier–Stokes (RANS) framework to improve near-wall predictions without refining the SPH particle distribution. A local one-dimensional sublayer solver based on the simplified steady $k$–$\omega$ equations is coupled with each wall-adjacent fluid particle. A local flow-rate constraint and a friction-velocity-based iteration scheme are developed to close and solve the sublayer system, while a two-way shear-stress coupling with local feedback improves consistency between the two scales. The proposed approach is evaluated using turbulent straight-channel flows over a wide range of Reynolds numbers and a wavy-channel flow involving separation and recirculation. The results demonstrate improved near-wall velocity, turbulent kinetic energy and friction-coefficient predictions, satisfactory convergence, and good agreement with reference solutions. In particular, the approach improves the convergence of near-wall predictions where conventional wall treatments struggle to provide consistent results, and agrees closely with reference solutions at Reynolds numbers as high as $8.0 \times 10^{7}$ without near-wall particle refinement. For separated flow, convergence comparable to that of locally refined finite-volume simulations is obtained using an approximately uniform particle distribution. These improvements are achieved with limited computational overhead, supporting the application of particle-based methods to engineering flows involving wall-bounded turbulence.

Cryogenic computing technologies are maturing rapidly, but heat removal remains a key challenge when increasing the device density and operating power. Two-phase evaporative cooling is a promising approach to solve this issue, because it can dissipate high heat fluxes while maintaining small temperature rises. Here, we numerically investigate liquid-$\mathrm{N_2}$-filled silicon micropillar wicks as a capillary-fed thin-film evaporation concept for cryogenic electronics. The model combines Young-Laplace meniscus calculations, Hertz-Knudsen-Schrage evaporation, unit-cell heat-transfer and liquid-flow simulations, and an array-level thermal and capillary-flow model. For a representative geometry with a pillar diameter of $10\,\mu\mathrm{m}$, pitch of $24\,\mu\mathrm{m}$, and pillar height of $75\,\mu\mathrm{m}$ at an applied heat flux of $20\,\mathrm{W\,cm^{-2}}$, the predicted chip-temperature rise is approximately $2.7\,\mathrm{K}$. This is substantially below the estimated temperature rises for representative conduction cooling through an indium-interlayered copper heat sink and direct liquid-$\mathrm{N_2}$ immersion. The corresponding predicted single-fed dry-out length is approximately $2.7\,\mathrm{mm}$, equivalent to an ideal double-fed coolable width of approximately $5.3\,\mathrm{mm}$. The results indicate that local thermal performance is favorable, whereas lateral scalability is primarily constrained by capillary dry-out. An approximate capillary-viscous scaling relation provides a compact framework for comparing dry-out limits across working fluids and related wick geometries and for identifying strategies to extend capillary-fed transport.

Accurate prediction of unsteady aerodynamic loads remains a major challenge in turbomachinery design. High-fidelity Computational Fluid Dynamics (CFD) simulations are expensive, while aeroelastic Quantities of Interest (QoI) depend sensitively on the temporal evolution of the pressure field. This work introduces periodic Fourier Neural Mapping (p-FNM), a neural-operator framework for predicting unsteady pressure distributions on turbine rotor blades simulated using the chorochronic numerical hypothesis. The architecture embeds temporal periodicity into the model and learns a continuous mapping from operating conditions and time to pressure fields. Unlike sequential latent-space approaches, p-FNM predicts pressure fields independently at any time, avoiding error accumulation while preserving temporal continuity. The model is evaluated on a database of unsteady rotor-blade simulations and compared with a reduced-order baseline based on a variational autoencoder and recurrent neural network, refered as the Temporal Prediction Model (TPM). Performance is assessed for pressure fields and Generalized Aerodynamic Forces (GAFs), the primary aeroelastic QoI. Across all training datasets, p-FNM consistently outperforms TPM. On the largest dataset, p-FNM achieves a pressure-field mean absolute percentage error of 0.46% and a GAF-magnitude prediction error of 4.42%, corresponding to improvements of 60.7% and 77.6%, respectively. The minimum weighted phase error reaches 0.060 rad, demonstrating accurate preservation of the temporal characteristics of the aerodynamic response. The results show that GAF prediction is more challenging than pressure-field prediction and that temporal coherence is critical for accurately predicting spectral aerodynamic quantities. These findings demonstrate the potential of periodic neural operators for reduced-order modeling and aeroelastic analysis in turbomachinery.

The relative velocity between a particle and the surrounding fluid is a key quantity that determines the various phenomena of particle-laden turbulence, such as particle clustering and turbulence modulation due to particles. We theoretically derive the expression for the relative velocity of a particle laden in turbulence by extending the argument of Balachandar (2009). This derivation provides a simplified form of the analytical model of Berk and Coletti (2024), and it makes the underlying physical assumptions explicit. Using direct numerical simulation data of turbulence in a periodic cube and turbulent channel flow, we demonstrate the validity of the derived expression, and show that it also holds for non-spherical particles and droplets.

We propose a method to overcome the difficulties encountered when applying reinforcement learning to fluid mixing processes. The proposed method has two main features: (i) it does not require detailed measurements of the flow state, and (ii) by effectively exploiting a stable limit cycle of a two-dimensional dynamical system (the Li'enard system), it can stably perform optimization without imposing explicit constraints on the control parameters. As an illustrative example, we optimize a process in which a fluid contained in a cylindrical vessel is mixed by periodically rotating the vessel. The resulting optimal vessel motion is physically reasonable: it reverses its direction of rotation before a solid-body rotation state is established. Furthermore, even when the fluid viscosity increases with time during the mixing process, the method can continuously adapt the control parameters to the changing viscosity.

We derive a thermodynamically-consistent model of fluid flow through a poroelastic medium. Starting from elastic and fluid free-energy densities, an energy-dissipation rate, and a kinematic constraint, the force-balance equations are derived using variational principles, with the pressure–density constitutive relation emerging as a direct consequence of the variational structure; the same kinematic constraint also supplies the total-flux transport structure. In the ideal-gas limit, the model linearization recovers the classical linear Biot equations. For power-law fluid energies, it yields isentropic pressure–density relations. A key advantage of the variational formulation is that extensions to richer physics, such as thermal effects, chemical reactions, or multi-component fluids, can be incorporated systematically by augmenting the energy and dissipation functionals without redesigning the force-balance or transport closure. We support the model with an energy-compatible two-field discretization and study consolidation under a surface load with three lateral-boundary treatments and three fluid-compressibility exponents.

At high Peclet number, the classical Taylor-Aris dispersion model becomes inadequate for early-time contrast-agent transport in arteries, while an explicit closure model and a clear physical interpretation of this regime remain lacking. In this study, we develop a novel explicit-closure one-dimensional (1-D) effective dispersion model for this regime, with its functional structures identified through symbolic regression. Analysis of the resulting model reveals that, in the high-Peclet-number regime, axial transport is redistributed between the effective convection flux and the dispersive flux, resulting in a reduction of the effective convective transport velocity in the dispersion model. This redistribution gives rise to a transition from the classical quadratic scaling to a linear scaling of the effective diffusivity with radial Peclet number. Numerical validation demonstrates close agreement with the convection-diffusion model over the investigated high-Peclet-number conditions, while the classical Taylor-Aris model exhibits substantial deviations. Application of the proposed model to averaged flow velocity inversion further demonstrates improved velocity estimation, particularly in the high-Peclet-number regime. These results highlight the importance of accounting for non-classical dispersion for reliable contrast-agent-based arterial blood flow velocimetry and provide new insight into high-Peclet-number mass transport.

The manuscript provides a description of a theoretical analysis of a non-Newtonian Prandtl fluid subject to peristaltic flow through an inclined asymmetric channel. We explore the effect of an inclined magnetic field on the peristaltic flow. This is relevant for applications involving fluid flow in narrow, inclined (tilted) tubes similar to blood vessels or the digestive system. The model also includes thermodynamic aspects such as heat diffusion (the Soret effect) and viscous dissipation resulting from wall-fluid slip conditions, which may help optimize medical devices such as lab-on-a-chip systems and dialysis machines. In this study, the concentration of a generic chemical, temperature, and fluid velocity are taken into account through mass, heat, and momentum balances, respectively. The solution is approximated using numerical techniques suitable for long wavelengths (low frequency) and low Reynolds numbers. The study also discusses trapping phenomena, which are crucial from a clinical point of view. The developed insights can improve the understanding of physiological flows in the gastrointestinal tract and blood vessels. By understanding how the fluid moves and how particles are trapped, these insights may contribute to the design of improved medical pumps and artificial organs. Graphical visualizations are provided for the fluid velocity profile, temperature distribution, and concentration of a generic chemical. Furthermore, the numerical results are validated through comparison with a closed-form solution from a benchmark problem.

Exact periodic solutions of the incompressible Navier-Stokes equations arise when the convective field is a pure gradient and can be absorbed into the pressure. We construct solutions outside this class, in arbitrary spatial dimension, by an iteration in which each step solves a linear diffusion problem forced by the transverse part of the preceding convective field. The construction is dimension-independent, and for a cyclic family of initial fields the first two iterates are available in closed form. Carried out numerically in three dimensions, the iteration converges: at Re=10 successive iterates contract with an observed factor 0.57 and the limit satisfies the mild equation with relative defect 1.0 x 10^-3. The observed factor exceeds unity by Re=30, which identifies the practical range of the iteration rather than a proved convergence boundary. We also show what goes wrong when the projection is omitted, as it was in an earlier iteration of the author's: the iterates cease to be divergence-free and an apparent growth appears that belongs to the expansion and not to the flow. For an n-dimensional generalisation of the initial field the fraction of the convective field not absorbed by pressure is 2sqrt(2)/3, independently of n over the range examined. Divergence and cell kinetic energy provide simple diagnostics that detect failure at the step where it occurs.

Pretraining a neural PDE surrogate can reduce the amount of new CFD data needed when geometry or modeled physics changes. However, it remains unclear how different components of distribution shift affect this benefit. We pretrain a surrogate on 254,909 RANS solutions from one airfoil family and fine-tune it on a new family under two target settings with matched freestream ranges: the same Spalart-Allmaras (SA) modeling and SA with added $e^N$ transition modeling. At $N=1000$, the pretrained model matches the accuracy of a model trained from scratch on $3.25\times$ as many samples for the same-SA target, but $2.58\times$ as many for the transition-modeled target. By $N=5000$, this ordering reverses ($1.56\times$ versus $1.86\times$). At $N=1000$, sampling more distinct airfoils lowers error on both targets, but only for the same-SA target is the gain increase larger than the observed draw-to-draw variation ($3.3\times$ to $4.0\times$). These results show that pretraining value depends jointly on target-data budget, target-data coverage, and whether source and target differ in modeled physics.

Considering triads in helical decomposition of three dimensional Navier-Stokes turbulence, three consecutive triads of the same shape and class, where the reference wave-number appears as the smallest, the middle and the largest wave-numbers respectively, constitutes an interesting object called the triad triplet that allows tracing the local transfer in wave-number space due to a given shape and class of triads. It is shown that, evolution equations for the triad triplet can be obtained from the equations of the three legs of a single triad that are put together via affine transformations involving scaling, rotation and reflection. Known power law solutions corresponding to constant flux of energy and helicity appear as exact solutions of a chain of triad triplets, with particular implications for the triadic phases. More interestingly, an exact, time dependent solution is available on an isolated triad triplet, that can be expressed using what appears to be straightforward generalization of Jacobi elliptic functions. These solutions, constitute novel exact nonlinear solutions of the inviscid limit of the Navier-Stokes equations.