In this work, we develop a state estimation framework for two-dimensional Rayleigh-Bénard (RB) convection that combines a stable Galerkin reduced-order model (ROM) with an extended Kalman filter (EKF). The ROM, constructed from controllability modes of the linearised Boussinesq equations, provides the nonlinear dynamical model for the filter prediction step. Direct numerical simulations (DNS) are used to generate synthetic measurements for data assimilation. We assess filter performance across periodic, quasiperiodic, and chaotic regimes, demonstrating that the filter tracks the most energetic modes with high fidelity and achieves time-averaged reconstruction errors below $14\%$ for velocity and $9\%$ for temperature. We apply the ROM-based EKF to a hybrid simulation scenario where the system state is assimilated from coarse PIV-like velocity measurements. It is shown that velocity observations alone suffice to reconstruct the state, including the temperature field. Finally, we exploit the Kalman gain matrix to develop a greedy sensor placement strategy that progressively removes the least informative sensors. The algorithm reveals a clear hierarchy among sensor types and can be used to derive skeletal observation configurations. It also provides guidance on which measurement variables and spatial locations are most informative for state correction. The present framework is general, and may be applied to other quadratic Galerkin ROMs for state estimation.

We analyze planar Lagrangian transport and scalar-gradient organization in a supersonic, reacting hydrogen-air temporal mixing layer using time-resolved mid-plane data from a three-dimensional direct numerical simulation. The analysis combines forward/backward finite-time Lyapunov exponent (FTLE) fields, operational FTLE-ridge skeletons, Cauchy-Green deformation measures, shear-LCS metrics, and planar hyperbolic geodesic-LCS extraction to examine how finite-time stretching structures the reacting shear layer. The time-resolved FTLE ridges identify repelling and attracting finite-time transport skeletons in the constrained two-dimensional slice, from which ridge geometry, intersection occupancy, persistence, and scalar-conditioned transport are quantified. Hyperbolic geodesic LCS are extracted from Cauchy-Green tensors reconstructed from planar flow maps as strainlines seeded at high-$λ_{\max}$ normal maxima, providing a variational counterpart to the operational FTLE-ridge skeleton. We then relate the transport skeleton to temperature, mixture fraction, and a reaction intermediate. The results show localized forward/backward ridge overlap, strong scalar-gradient enrichment, finite-time geodesic LCS that occupy the same high-strain transport skeleton, residual direction-dependent separation from a time- and cross-stream-stratified null model, and scalar-response lags that remain compact relative to decorrelation and FTLE-integration scales. Together, these results provide a transport-oriented characterization of coherent structures and their role in mid-plane mixing within a compressible reacting shear flow.

Recent evidence on the sustainment of wall-normal-velocity bursts in wall-bounded turbulence challenges the classical streak-dependent picture, suggesting that the problem should be approached relying on no a priori knowledge regarding other flow structures. This paper discusses the restarts of bursts in a log-minimal channel within the framework of a linearised Navier-Stokes system with forcing terms encapsulating the nonlinear effects of all other structures. Two generic issues are addressed. The first concerns the conditions for burst-restart-like solutions for the forced linearised system itself. We formulate optimisation problems to understand the 'minimal requirements' for burst restarting. The solutions illustrate three conceptual periods in a typical restarting process, distinguished by the behaviour of spanwise vorticity structures: breakup, counter-rotating catch-up, and co-rotating catch-up. External forces promote this process by breaking up forward-inclined vortices and merging co-rotating, catching-up vortices. A quantity termed linearly available energy (LAE) is accordingly proposed to parameterise the restarting process. The second issue concerns the contributory features to the observed burst restarts in real turbulence. We show that an essential role of nonlinearity in restarting a burst is to increase a decaying state's LAE to a level sufficient for the onset of the subsequent burst. Flow patterns extracted during the restarting stage exhibit breakup and merging effects, both facilitated by nonlinearity. This suggests that the two effects observed in both the linearised models and real turbulence are manifestations of real flow structures that cause burst restarts.

The accurate prediction of laminar-to-turbulent transition is critical for the design of aerodynamic and turbomachinery systems, yet widely used experimental benchmarks, such as the ERCOFTAC T3 series, lack the full-field, three-dimensional, and time-resolved data required for modern model development. To address these limitations, this study presents a high-fidelity numerical database of bypass transition in boundary layers, generated using wall-resolved implicit Large Eddy Simulations (iLES) to rigorously mimic the ERCOFTAC T3 flat-plate experiments. Computations are performed using a high-order compressible Navier-Stokes solver across multiple configurations, encompassing a range of freestream turbulence intensities and both zero and varying pressure gradients. The numerical results demonstrate satisfactory agreement with legacy experimental data for skin friction, mean velocity, and fluctuation profiles. Finally, the resulting database is utilized to evaluate the predictive capabilities of standard Reynolds-Averaged Navier-Stokes (RANS) transition models (SA-BCM and $k-ω-γ$), revealing systemic flaws in predicting transition onset and length. This highlights the dataset's value as a foundational resource for the calibration, assessment, and development of next-generation, physics-informed machine learning transition closures.

Velocity slip at the solid--fluid (SF) interface plays a key role in fluid transport at the nanoscale, and the SF friction coefficient has been extensively studied because it indicates the degree of slippage. Owing to the scale of this phenomenon, molecular dynamics (MD) simulations are commonly employed using two major approaches: the Green-Kubo integral method in equilibrium MD (EMD), and the direct calculation of friction force and slip velocity in non-equilibrium MD (NEMD) systems under shear. Regarding the latter, a strict definition of the slip velocity is missing due to the nonzero thickness of the boundary at the microscale, and the average velocity of the first adsorption layer or the velocity at the boundary obtained by extrapolation or interpolation is often used. In this study, we propose an alternative description of the slip velocity based on a thermal perspective from the two different scales, i.e., at the macroscale, frictional heat is defined as the product of the friction force and slip velocity, whereas at the microscale, it can be expressed as the sum of the works exerted on the fluid and solid by each other. By combining the two different scales, we defined the slip velocity based on the dissipation induced at the SF interface under shear, which avoids the arbitrariness in the slip velocity at the microscale.

We present a forcing-informed (FI) resolvent analysis framework to identify input-output relations for statistically stationary self-sustained unsteady flows. The central idea of this method is to inform the resolvent operator about the spatiotemporal structures of the nonlinear terms that act as exogenous forcing with respect to the mean flow. To construct the FI resolvent operator, we estimate the basis vectors for the input subspace spanned by forcing snapshots and, similarly, for the output subspace, from simulation data. The extracted FI response and forcing modes are expressed through the estimated bases of the output and input subspaces, respectively, and the singular values of the FI resolvent operator correspond to the actual output amplitudes. These properties ensure that the extracted modes are consistent with the actual self-sustained flow fields. Additionally, the forcing snapshots can be used to construct the linear operator, enabling a fully data-driven FI resolvent analysis. The proposed framework is validated using the Stuart-Landau oscillator and demonstrated for a two-dimensional cylinder wake and a three-dimensional transitional boundary layer. We successfully identify the gains and the corresponding pairs of forcing and response modes, even at frequencies where the nonlinear amplification mechanism is crucial. Furthermore, leveraging the balance between the time-averaged energy amplification/attenuation by the linear operator and nonlinear forcing, we introduce a nonlinear energy transfer map that identifies the spatial domains where the extracted forcing mode injects or removes fluctuation energy, thereby providing key physical insight into the self-sustaining mechanisms.

Laminar-to-turbulent transition delay is a key challenge in hypersonic boundary-layer flows. Unstable disturbances-most prominently the first and second modes-trigger the onset of turbulence and pose a fundamental technological barrier to hypersonic transport. While existing control strategies target the second mode, simultaneous mitigation of the first mode has long appeared physically impossible. A new flow-control concept is introduced in which phase relations between wall pressure and velocity fluctuations are tailored using subsurface phonon engineering to control both modes concurrently. The outcome is substantial drag reduction and alleviation of the extreme thermal loads associated with turbulence.

This experimental work explores the flow field around a three-dimensional expansion-compression geometry on a slender cone at Mach 5 and 8 using high-frequency pressure sensors, high-framerate schlieren, temperature-sensitive paint, shear-stress measurements and oil-flow visualizations. The $7^\circ$ cone geometry has a hyperbolic slice acting as an expansion corner which is then followed by a $30^\circ$ finite-span compression ramp. The freestream Reynolds number was varied so that the boundary layer approaching the expansion corner was either laminar, transitional or turbulent. At laminar or early transitional conditions, the separation shock locks onto the expansion corner and the separation region encompasses most of the slice, with the separation shear layer flapping at a preferred frequency. As Reynolds number is increased, the separation shock moves downstream onto the slice, the separation bubble shrinks, and the shear layer flapping frequency increases while its amplitude drops. In all cases, large-scale low-frequency breathing motions are observed. The strong relaminarization across the expansion corner at Mach 8 prevents the shock/boundary-layer interaction from reaching truly turbulent conditions and fundamentally changes its behavior on this non-canonical geometry.

Viscous fingering instabilities during fluid displacement in porous media can compromise the efficiency of applications such as enhanced oil recovery, CO2 sequestration, and groundwater remediation. While extensive research exists on linear stability analysis for fully immiscible and fully miscible displacements, the intermediate case of partially miscible flow with limited mass transfer between phases remains largely unexplored. This study extends linear stability analysis to a two-phase, two-component system that accounts for gravity effects, fractional flow, capillary forces, mechanical dispersion, and interphase mass transfer, focusing on the case where a partially miscible gaseous fluid displaces a liquid. We formulate an eigenvalue problem to characterize instability growth rates and cutoff wavenumbers. The resulting ordinary differential equations have discontinuous coefficients at the transition from two-phase to pure-liquid flow, resulting in discontinuous eigenfunction derivatives. We derive jump conditions for the derivatives at this transition, and solve the eigenvalue problem using the matched initial value problem method. Results demonstrate that mass transfer has a pre-dominantly stabilizing effect by reducing viscosity contrast and altering shock properties at the displacement front. This stabilizing influence is particularly pronounced for high viscosity contrasts and dampens gravity-induced instability in upward displacements. Mass transfer most significantly affects the perturbation growth rate, while its effect on the cutoff wavenumber is less pronounced. We identify a critical value for the dimensionless longitudinal dispersion coefficient where both growth rate and cutoff wavenumber are maximized, suggesting complex interactions between capillary forces and mechanical dispersion.

This chapter reviews recent advances in Scientific Machine Learning (SciML) for modeling coupled fluid flow and transport phenomena governed by the incompressible Navier-Stokes and scalar transport equations. Such systems, found in applications like turbidity currents and thermal convection, feature strong nonlinear coupling and multiscale behavior that make high-fidelity simulations computationally expensive. To address this, the chapter surveys state-of-the-art SciML methods for building efficient surrogate models, including linear reduced-order techniques based on Singular Value Decomposition (such as Dynamic Mode Decomposition) and nonlinear neural network approaches like Physics-Informed Neural Networks (PINNs) and $β$-Variational Autoencoders ($β$-VAEs). It first covers the authors' work combining these models with High Performance Computing strategies, including Adaptive Mesh Refinement/Coarsening (AMR/C) and scientific floating-point data compression. It then presents two new contributions: surrogate modeling of turbidity currents via PINNs, and the extraction of disentangled nonlinear modes from thermal flows using $β$-VAEs. Governing equations and representative benchmarks, including lock-exchange flows and Rayleigh-Bénard convection, illustrate these methodologies. The chapter is intentionally long, covering both the mathematical and physical foundations of coupled fluid flow and the computational aspects of state-of-the-art modeling. Overall, it demonstrates how SciML enables fast, accurate approximations of complex coupled systems within the specific data regimes and modeling assumptions considered, while substantially reducing computational cost relative to full-order simulations. Broader capabilities such as real-time prediction and uncertainty quantification remain active research directions whose feasibility depends strongly on the problem at hand.

Increased upper-ocean stratification is an unavoidable consequence of global warming and will strongly impact the structure of ocean currents. Using a high-resolution ocean model, we show that intensification of stratification leads to the loss of coherence of the Gulf Stream Extension, replacing its steady eastward path with vigorous, chaotic meanders. This regime shift persists independently of changes in the Atlantic Meridional Overturning Circulation and surface wind forcing. Enhanced meandering under intensified stratification also proves to be a robust feature across both idealized and realistic ocean models that resolve mesoscale eddies, but is not captured by coarse-resolution models that parameterize eddies. The presented findings therefore highlight the need for improved representations of oceanic turbulence in climate projections.

Recent experiments combining electrophoresis with pressure-driven flows in microchannels have revealed that microparticles undergo lateral migration perpendicular to the applied electric field. Although fluid inertia has been proposed as a possible explanation, inertial effects are negligibly small in these regimes, leaving the underlying physical mechanism an open question. In this study, we address these observations by extending previous theoretical work on concentration polarization,i.e., the external-field-induced modification of the ionic concentration field surrounding a dielectric object. We consider a dielectric particle with surface conductance subjected simultaneously to an external electric field and a shear flow. We show that the shear flow breaks the symmetry of the ionic concentration around the particle in the direction perpendicular to the applied field, thereby driving lateral migration. We demonstrate that the resulting migration velocity comprises two distinct contributions: an electrophoretic and a diffusiophoretic component. Our theory yields an explicit expression for the velocity magnitude as a function of the zeta potential and the Dukhin number, predicting typical speeds on the order of $\mathrmμ$m/s for representative experimental parameters. Notably, the model also predicts a reversal in the migration direction for Dukhin numbers of order unity.

Cellular automata are discrete dynamical systems defined on a lattice, in which each site carries a finite set of states that evolve in time according to local deterministic rules. An important application of cellular automata is in lattice gas models of fluids, where the cellular automaton framework provides a particle-based microscopic description of hydrodynamic behavior. The macroscopic fluid equations emerge after coarse-graining over many lattice sites and time steps, offering a bottom-up route to hydrodynamics. A celebrated example is the Frisch-Hasslacher-Pomeau (FHP) model, an automaton defined on a two-dimensional triangular lattice that yields the two-dimensional Navier-Stokes equations upon coarse-graining. In this work, we construct a parity-breaking generalization of the FHP model through two modifications: introducing chiral two-body collision rules and systematically rotating particle velocities to mimic the effect of a background magnetic field. We show that this automaton yields a hydrodynamic model with odd viscosity, a transverse transport coefficient that is a hallmark of odd fluids. We verify the analytical transport coefficients using Poiseuille-flow simulations of the chiral FHP automaton. Our results demonstrate that the chiral automaton introduced here provides a bridge between microscopic parity-breaking scattering processes and macroscopic odd-fluid hydrodynamics.

Inertial particles in turbulence form clusters, which strongly affect particle collisions and transport properties. Clustering models based on statistically stationary turbulence implicitly assume the instantaneous-equilibrium approximation when applied to time-varying non-equilibrium turbulence. However, the validity of this approximation remains unclear. In this study, the temporal response of inertial particle clustering in non-equilibrium turbulence was investigated using direct numerical simulation of homogeneous isotropic turbulence with unsteady forcing. Periodic responses of the flow and clustering intensity were evaluated by varying the forcing period. The flow showed non-equilibrium scaling for all forcing periods. The relationship between instantaneous energy dissipation rate and clustering intensity showed hysteresis exceeding statistically stationary fluctuations when the forcing period exceeded several large-eddy turnover times. For the particles with the largest inertia, clustering intensity took values of 0.80 and 1.56 times the reference value at the same instantaneous energy dissipation rate. This shows that the instantaneous-equilibrium approximation is not appropriate under such conditions. A linear relaxation model was constructed from transient responses, in which clustering intensity approaches the instantaneous-equilibrium value with a finite relaxation time. The relaxation time scaling was identified as $τ_g = 1.0 T_\mathrm{e}(t)\,\mathrm{St}(t)^{0.40}$, where $T_\mathrm{e}(t)$ and $\mathrm{St}(t)$ are the instantaneous large-eddy turnover time and Stokes number. The model reduced the maximum relative error from 49% to 10% for the particles with the largest inertia and from 76% to 22% in an independent validation case. These results demonstrate that finite-time relaxation improves prediction accuracy for clustering intensity in non-equilibrium turbulence.

While proper orthogonal decomposition (POD)-based surrogates are widely explored for hydrodynamic applications, the use of Koopman autoencoders for real-world coastal-ocean modelling remains relatively limited. This paper introduces a flexible Koopman autoencoder formulation that incorporates meteorological forcings and boundary conditions, and systematically compares its performance against POD-based surrogates. The Koopman autoencoder employs a learned linear temporal operator in latent space, enabling eigenvalue regularization to promote temporal stability. This strategy is evaluated alongside temporal unrolling techniques for achieving stable and accurate long-term predictions. The models are assessed on three test cases spanning distinct dynamical regimes, with prediction horizons up to one year at 30-minute temporal resolution. Across all cases, the reduced order surrogates with temporal unrolling achieve high accuracy with relative root-mean-squared-errors of 0.0068-0.14 and $R^2$-values of 0.61-0.995, where prediction errors are largest for current velocities, and smallest for water surface elevations. In two of the three cases, the Koopman Autoencoder have higher accuracy than the POD-based surrogates. Comparing to in-situ observations, the surrogate yields -0.64% to 12% increase in water surface elevation prediction error when compared to prediction errors of the physics-based model. These error levels, corresponding to a few centimeters, are acceptable for many practical applications, while inference speed-ups of 300-1400x enables workflows such as ensemble forecasting and long climate simulations for coastal-ocean modelling.

The accurate characterisation of the 3D deformations of slender fibres and thin sheets in flow, is a key experimental challenge in the study of particle-laden flows. We propose a high-resolution, single-camera method to visualise non-intrusively the shape of a transparent crumpled sheet, as it translates, rotates and deforms. We perform periodic scans of the crumpled shape by illuminating it with a sequence of stacked light sheets at a rate much faster than its deformation and image the scattered light signal in a plane near-orthogonal to the plane of lighting. Processing of the data using a pinhole camera model yields a noisy spatio-temporal dataset of the strongly deformed time-evolving surface of the sheet, which we reconstruct in 3D using a neural autoencoder. We validate the robustness of the shape reconstruction algorithm to noise using synthetic data sets, and demonstrate the accurate reconstruction of laboratory sedimentation experiments with elastic disks. We find that the inclusion of isometricity-enforcing penalties into the cost function of the autoencoder enables us to robustly reconstruct highly folded shapes, where different regions of the sheet overlap.

The Kolmogorov-Zakharov stationary states for weak wave turbulence involve solving a leading-order kinetic equation. Recent calculations of higher-order corrections to this kinetic equation using the Martin-Siggia-Rose path integral are reconsidered in terms of stationary states of a Fokker-Planck Hamiltonian. A non-perturbative relation closely related to the quantum mechanical Ehrenfest theorem is introduced and used to express the kinetic equation in terms of divergences of two-point expectation values in the limit of zero dissipation. Similar equations are associated to divergences in higher-order cumulants. It is additionally shown that the ordinary thermal equilibrium state is not actually a stationary state of the Fokker-Planck Hamiltonian, and a non-linear modification of dissipation is considered to remedy this.