Data from experiments or simulations enables tools to accelerate simulations and develop accurate predictions of important turbulence-chemistry interactions in turbulent combustion flows. Several methods designed to exploit this data are presented and discussed. They are motivated by and rooted in traditional paradigms in turbulent combustion that rely heavily on the existence of a low-dimensional manifold for the composition space and its coupling with turbulent transport. These methods include surrogate DNS with principal component transport, the extraction of closure models from multiscalar measurements, and deep operator networks for chemistry integration and acceleration.

This article briefly reviews recent developments in understanding and utilizing bubble dynamics in complex fluids. Bubble dynamics impart deformations and probe properties on time scales as short as the relaxation times of complex fluids containing suspended particles or macromolecules. Examples from our research group with increasing complexity are presented: from linear rheology of soft solids using ultrasound-driven bubbles, to bubble removal from yield-stress fluids, to self-assembly in colloidal gels driven by bubble dynamics. The growing synergy between the communities of cavitation and rheology will help address new challenges in characterization and manipulation of complex fluids.

We introduce the Magnetohydrodynamic Thermal Rotating Shallow Water (MTRSW) model, a novel framework for studying thin, magnetized, and stratified fluid layers in geophysical and astrophysical contexts, such as the solar tachocline. This model integrates thermal gradients and magnetic fields with rotation, revealing their coupled impact on stability. Furthermore, we incorporate Hall effects, enabling the model to capture essential small-scale physics like fast magnetic reconnection.

Knowing when turbulence reaches peak dissipation matters for theory and for adaptive simulation and measurement strategies. Using direct numerical simulations of the Taylor–Green vortex, we introduce a spectral diagnostic based on the curl-of-vorticity spectrum, equivalent to a k^4-weighted energy spectrum. Its peak wavenumber stabilizes before the dissipation maximum across resolutions. The resulting early-warning signal links spectral evolution to the emergence of filamentary vortical structures and can support adaptive meshing and output scheduling.

Phytoplankton, like dinoflagellates, produce mesmerizing displays of light when subjected to the turbulent flow in breaking waves and ship wakes. Here, we ask how bioluminescence is affected by turbulence, given that dinoflagellates flash with an intensity that increases with both the extent and rate of deformation. Introducing a light-emitting dumbbell as a minimal model, we show that intermittent fluctuations of the velocity-gradient subjects dinoflagellates to bursts of extreme straining, which in turn produces bright flashes. Comparisons with steady and Gaussian-fluctuating flows demonstrate that light emission is strongly promoted by the dissipation-scale intermittency of turbulence.

In dense suspensions, both rigid particles and deformable red blood cells (RBCs) exhibit a tendency to migrate away from the walls and towards the center of the vessel in which they flow. Here we experimentally investigate the transport of microparticles along with RBCs in bifurcating vessels, which is particularly relevant for targeted drug delivery. Via high-speed imaging and Lagrangian tracking, we observe that particles marginate and form layers adjacent to the sidewalls of bifurcation, while the deformable RBCs populate the center of the vessel. Our results show that the margination behavior of spherical particles is quantitatively controlled by the RBC-to-particle volume ratio.

Micro-scale cilia play a vital role in mucociliary clearance (MCC) in the human respiratory airways. We develop a three-dimensional model for predicting MCC with two-way coupling between the cilia and the two-phase airway surface liquid, comprising the periciliary layer (PCL) and the mucus layer (ML). Focusing on a single cilium, we systematically examine the effects of PCL thickness and the viscosity ratio between the PCL and ML, which can vary markedly under pathological conditions. The fluid transport mechanisms are clarified by identifying two competing effects, namely the balance between drag and elastic forces and the viscous diffusion of momentum, and by establishing quantitative relationships between the flow rate and the beating pattern.

This study investigates turbulence/flame/wall interaction in turbulent boundary layer combustion with varying wall surface reactivity using direct numerical simulation (DNS). The effects of combustion on the turbulent boundary layer were investigated, revealing that the hairpin vortices of the boundary layer turbulence are lifted upward, upstream of the flame, due to the combustion-induced adverse pressure gradient. The effects of wall surface reactivity on flame/wall interaction were revealed in terms of near-wall heat release rate, wall heat flux and flame quenching behavior.

Understanding the dynamics of gas discharges is critical for numerous technological applications. While the physics of electric breakdown in gas, such as air, has been studied for many decades, the early stages of the discharge dynamics remain to be an active subject of research. In this paper we provide a simple approach that helps us understand such early stages of dynamics and explains the structure of the discharge channel at the qualitative level. Comparison with experimental data shows a good agreement of the approach with the measured characteristics, such as discharge current, at small times after the discharge initiation.

Three-dimensional simulations of a reacting hydrogen jet in supersonic crossflow are performed using a discontinuous Galerkin (DG) method, which is appealing for its high-order accuracy and geometric flexibility. Analysis of the coupled chemistry and compressible flow shows a predominantly non-premixed combustion mode with localized premixed regions. A key result is the accurate prediction of this configuration on a fully unstructured tetrahedral mesh, demonstrating the potential of DG methods to capture complex physics in high-speed reacting flows.

Polar sea ice is a crucial component of Earth’s climate system which is generally modeled as a non-Newtonian fluid in climate simulations. To overcome the accuracy limitations of existing non-Newtonian models for sea ice, we present a framework for learning an effective shear viscosity function for sea ice from velocity data. We apply our approach to data generated from a complex sea ice discrete element method (DEM). The learned rheology is capable of reproducing the DEM velocity data accurately.

Shock–boundary layer interactions over the convex wall of a supersonic turbine vane are explored through a detailed analysis of extreme separation bubble events. By conditionally sampling expanding and contracting bubble states and using finite-time Lyapunov exponents together with a deforming control-volume framework, this study reveals how near-wall streaks and streamwise vortices influence the separation bubble unsteadiness and the mass flux along its surface.

Turbulent mixing at the interface between a convection zone and a neighboring stably stratified region in a star or planet often causes the convective region to grow. This mixing process therefore plays a key role in shaping the internal structure and long-term evolution of stars and planets, especially when compositional gradients contribute substantially to the density stratification. Our numerical simulations show, however, that when the compositional stratification is sufficiently strong, chemical diffusion can halt the expansion of the convection zone. Taken together, these results suggest that chemical diffusion sets a limit to convective penetration in strongly stratified interiors.

Rotating Rayleigh–Bénard convection is a key model for rapidly rotating planetary interiors, but direct numerical simulations are restricted by the fine spatial resolution required at small scales. We systematically assess a scale-dependent horizontal hyperdiffusion scheme as a computationally cheaper alternative, comparing 107 simulations against DNS across a wide parameter range. We show that hyperdiffusion can either weaken rotational constraints at low supercriticality or suppress small-scale energy at high supercriticality, and identify parameter choices that preserve large-scale dynamics.

If a denser solution of a solute A lies above a less dense solution of a solute B in the gravity field, a Rayleigh-Taylor instability can trigger convective motions which favor mixing of the two fluids. We show by numerical simulations that double-diffusive effects occuring when A and B diffuse at different rates can modify the scalings of the onset time and acceleration of the instability. Moreover, the difference in diffusion of the solutes can be used to optimize mixing between the two solutions.

In this work, we experimentally investigate the freezing and ice aging dynamics in saline water under natural convection. We show that the rapid formation of a mushy ice layer is followed by desalination processes that might lead to a slow asymptotic decrease of the ice thickness. Desalination of mushy ice reduces its porosity, which alters the dynamic thermal equilibrium and ice thickness by weakening buoyancy-driven convection within mushy ice. In turn, changes in brine convection and ice thickness further affect the desalination process. The long-term dynamics can be predicted by a one-dimensional model based on appropriate parameterizations of global heat and mass transfer properties.

This study investigates the effect of the thermal conductivity of titanium dioxide (TiO${}_2$) nanoparticles suspended in water on heat transfer dynamics and the formation of convection cells. Experimental observations reveal that colloidal stability and nanoparticle sedimentation strongly influence the evolution of convection patterns and overall heat transfer. Due to the low particle concentration and small size, a thin heat-conducting sediment layer forms within the thermal boundary layer. This locally enhances the conductive heat flux in the lower boundary layer, leading to an asymmetry in the temperature profile between the top and bottom of the cavity.

The dynamics of a stratified, rotating fluid, contained in a box and subject to differential heating in the horizontal direction, is approximated by a low-order set of five nonlinear ordinary differential equations (ODEs). Its forced and damped versions reduce to well-known ODEs for convection or long-wave dynamics. In the ideal fluid limit, one integral of motion represents initial stratification and motion. The remaining equations, capturing the essence of ‘rotating horizontal convection’, are integrable in the absence of rotation or differential heating. In general, they represent a forced, complex Duffing equation that appears to be a generalized nonintegrable 2 DOF Hamiltonian system.

Understanding droplet retraction on hydrophobic surfaces is crucial for applications ranging from self-cleaning coatings to inkjet printing. While previous models relied on static wetting properties, we demonstrate that the retraction of viscous droplets is governed effectively by the dynamic receding contact angle. By incorporating this nonequilibrium parameter, we establish a unified scaling law that accurately predicts retraction rates across diverse substrates.

The singular collapse of a cavity can produce extremely fast and fine jets from the dynamics of larger systems. These jets have a wide range of applications, from printing technologies to cavitation bubbles or the formation of aerosols. We investigate the formation of extremely fast singular jets generated when a coaxial water‑in‑oil compound drop impacts a solid surface. Experiments and simulations reveal how cavity collapse, controlled by impact velocity and volumetric ratio, produces high‑speed jets and microdroplets. Two distinct collapse regimes emerge, governed by 1/2 and 2/3 self‑similar power laws.

This paper offers new insight into the nature of active matter and the design of coated microbubbles to act as microswimmers for ultrasound assisted drug delivery, by clarifying the role of shape imperfections in their dynamics. It shows that even small initial defects can significantly reduce the buckling threshold, while the symmetry of the imperfection governs the emerging post-buckling shapes. The resulting asymmetric shapes induce translational motion in the direction of concavity, with velocities that strongly depend on the acoustic frequency and shell properties.

The maximum droplet volume that a fiber can retain is a classic problem in the physics of droplet-fiber interactions, with established results for horizontal and Λ-shaped bent fibers. However, this question has remained less explored for V-shaped bent fibers, despite their relevance to fog harvesting and condensation technologies. Here, we develop a free-energy- based analytical model to predict the maximum droplet volume on V-shaped fibers and validate it experimentally using multiple liquid-fiber pairs. We reveal a non-monotonic dependence of the maximum droplet volume on the fiber opening angle, identifying a transition regime that facilitates droplet detachment.

Electro-thermoconvection (ETC) turbulence can enhance heat transfer under microgravity conditions. Using direct numerical simulation for ETC turbulence in a cavity, we find that the flow field exhibits several main modes. In contrast, the temperature and charge fields are only dominated by a specific mode in ETC turbulence. The heat transfer efficiency of ETC turbulence can be up to two orders of magnitude compared to a conduction state. It is also found that there is a potential scaling law between the Nusselt number and electric-driven parameters.

Shock-driven Richtmyer–Meshkov instability is central to astrophysical and inertial-confinement-fusion plasmas, where kinetic-scale effects invalidate single-fluid MHD descriptions. Using an ideal two-fluid plasma model, we show that a magnetic field parallel to the interface suppresses instability growth by transporting and phase-mixing interfacial vorticity on plasma wave packets, with increasing efficacy at smaller plasma length scales. In contrast, an out-of-plane magnetic field fails to suppress the instability and instead promotes Kelvin–Helmholtz–like roll-up through charge-separation-driven vorticity generation.

Upon rupture, a planar liquid sheet retracts under capillary forces at its free edge. We develop an asymptotic model for slender and highly viscous sheets, showing that the dynamics are governed by a remote region where viscous and inertial effects balance. There, a conserved quantity reduces the problem to a one-dimensional diffusion equation for the thickness, subject to effective boundary conditions. From this reduced description, we identify and analyze distinct retraction regimes characterized by the time elapsed since rupture and the relative magnitude of the aspect ratio to the Ohnesorge number.

The interface crossing behavior of a microswimmer is strongly dependent upon the capillary number (Ca), which is defined as the ratio of swimming to interfacial forces. When the interfacial forces dominate, the swimmer gets trapped. We propose a model, where the swimmers are trapped due to a wetting-induced thermodynamic potential. The translational motion of a prolate swimmer is accompanied by reorientation driven by the combined action of hydrodynamic and thermodynamic torques.

Droplets walking on a vibrating liquid bath have provided a platform for exploring the boundary between classical and quantum physics. The system is typically considered with monochromatic bath forcing, in a parameter regime in which the droplets bounce either in-phase or out-of-phase with respect to each other. We demonstrate here that the application of an additional subharmonic forcing allows for control of the droplets’ relative phase. The figure shows (a) an irregular array of bouncing drops in which the leftmost drop (blue) is out-of-phase with its neighbours (red) transforming into (b) an array in which all droplets bounce in synchrony in response to the subharmonic forcing.

Droplet impact on liquid pools has long been analyzed using energy-balance models dominated by inertial and gravitational effects. In the low-Froude-number regime relevant to immiscible droplet encapsulation and interfacial processing, however, the partitioning of impact energy remains poorly understood. Here we show experimentally that, alongside gravitational potential energy, surface energy and viscous dissipation make significant contributions to cavity dynamics. By incorporating cavity shape deviations and viscous losses into a revised energy framework, we establish an improved scaling description for cavity penetration in immiscible liquid impacts.

Partially miscible viscous fingering differs from the classical Saffman–Taylor instability by producing droplets through flow-induced phase separation. Experiments in a PEG–Na${}_2$SO${}_4$–water system reveal how Hele–Shaw gap confinement and flow rate control droplet formation and interfacial complexity. The total interfacial length collapses onto a universal scaling with the flow-rate-to-gap ratio, with an exponent consistent with a balance between inertial and capillary stresses. These findings identify an inertia-modified capillary regime and offer predictive insight into pattern selection in partially miscible displacement flows.

Although thermal fields are known to influence liquid jet instability, prior studies have focused primarily on axisymmetric disturbances. This work reveals that a temperature field can excite a dominant non-axisymmetric helical mode, driven by azimuthal Marangoni stresses. We show that enhancing the Marangoni effect or suppressing thermal diffusivity promotes this helical instability, triggering a fundamental transition from Rayleigh-Plateau to azimuthal Marangoni-driven destabilization. Phase diagrams provide criteria for predicting this mode transition, offering new insights into controlling jet stability in applications such as ink printing and fiber production.

The exponential decay due to Landau damping, unlike unstable modes, corresponds to no eigenmode - it lacks an eigenfunction, being a continuous superposition of singular van Kampen modes with real eigenfrequencies. Introducing arbitrarily small dissipation qualitatively transforms this: an exponentially decaying eigenfunction emerges, while the eigenvalue remains nearly identical to the Landau damping rate. Using hyperbolic tangent flow, we trace the vorticity transition in plane-parallel shear flows from nearly inviscid to purely inviscid conditions and study corresponding eigenfunction structure. Local vorticity disturbances in initial-value problems quickly assume this eigenfunction form.

Building on a fluctuating Darcy framework, this work shows that porosity fluctuations can strongly and nontrivially reshape the hydrodynamic permeability of a porous matrix or membrane. The permeability is expressed in terms of the matrix fluctuation spectrum, revealing a “frequency‑matching” regime where solid and fluid modes resonate. Exploring different excitation scenarios – breathing matrices, phonon‑like modes and active forcing – unveils new strategies to optimize membrane separation processes and potentially bypass the usual permeability–selectivity trade‑off.

Bursting of tip vortex cavities is commonly observed behind marine propellers and is accompanied by a sharp rise in broadband noise, yet its underlying mechanisms remain poorly understood. This work introduces an Euler-Lagrange hybrid simulation to capture the dynamics of tip vortex cavity bursting. The results reveal that bubble-type vortex bursting is the dominant instability mode and that its intensity is strongly correlated with blade-load variations induced by the hull wake.

Using the stiffened-gas equation of state (SG-EOS), we extend the classical shock dynamics theory to underwater scenarios. The Chester-Chisnell-Whitham (CCW) relation and its two-dimensional characteristic relations are systematically modified. We further propose a method of designing a shock tube that transforms planar underwater shock waves into cylindrical ones with pre-set intensity and curvature. Numerical tests demonstrate that the shock intensity and curvature can be accurately controlled to match predicted values. This work provides a theoretical framework for geometric control of shock waves in compressible liquids.

The dynamics of unconfined, low-inertia, fluidized beds is investigated. The fluidization velocity is well described by a universal function of the volume fraction involving a prefactor that depends on particle inertia, confinement, Reynolds number and inlet flow disturbances. Bed surface oscillations are used to probe concentration fluctuations within the suspension, revealing the role of vertical concentration waves upon the transition toward the heterogeneous regime at low concentrations.

A superhydrophobic sphere entering a quiescent water pool entrains an air cavity whose evolution governs its subsequent dynamics. The cavity remains axisymmetric up to the primary pinch-off, after which multiple pinch-off events occur. For lighter spheres, the entrained air volume can trigger a transition from downward penetration to upward motion due to enhanced buoyancy. Both primary and secondary pinch-offs induce abrupt buoyancy changes and force rebalancing, captured using orthogonal high-speed imaging. The coupling between cavity evolution, pinch-off dynamics, and trajectory reversal depends on impact conditions and sphere density.

Sheared polydisperse granular materials exhibit a subtle balance between size segregation and diffusion that governs their transverse dynamics. Combining annular shear cell experiments with discrete numerical simulations, we investigate how confinement, shear localization, granular temperature, and mixture composition control segregation in nonuniform flows. Beyond the classical gravity-driven mechanism, we identify inverse and horizontal segregation modes that emerge from flow kinematics and geometry. These mechanisms hinder complete segregation, explaining the persistence of mixing in steady-state granular systems.

The multistability and bifurcation in thermal vibrational convection have been systematically studied via direct numerical simulations. Two distinct states are clarified: a periodic one with single-roll dominance and higher mean heat/momentum transport, and a chaotic one with multimode interplay. Bifurcations occur primarily near St=1, where resonant sensitivity to initial conditions leads to hysteresis across varying vibrational Rayleigh number and aspect ratio. This work elucidates the underlying mechanisms of flow state transitions, providing a framework for understanding multistability and flow control in unsteady regimes.

In stably stratified turbulence, vertical transport is typically suppressed by buoyancy; however, intense vertical drafts can intermittently develop. Using direct numerical simulations and a Lagrangian approach based on particle pair dispersion, we show that these extreme events play a crucial role in vertical mixing, leading to strong departures from classical dispersion behavior. Our results demonstrate that a small fraction of particles experiencing extreme vertical drafts contributes disproportionately to vertical transport and mixing, highlighting the central role of large-scale intermittency in stratified turbulent flows.

We used a high-fidelity simulation framework to study the fluid and mixing dynamics inside two turbulent mixers: the multi-inlet vortex mixer (MIVM) and the confined impinging jets mixer, operating under various conditions. We identify differences in turbulence onset, total energy, and mixing performance of two MIVM configurations. This study demonstrates the importance of a high-accuracy numerical scheme for simulating turbulent mixers and understanding performance differences among them.

This work introduces an extra input, the near-wall wall-normal velocity fluctuation, to the spectral linear stochastic estimation between inner and outer signals to compensate for the impact of near-wall universal signals while extracting the attached-eddy contribution. Subsequently, the logarithmic decay rate of the streamwise turbulence intensity is revisited. It becomes, overall, much larger after the compensation, which reduces its dependence on the Reynolds number. These results cannot exclude the likelihood of a constant decay rate by a qualitative analysis of linear coherence functions among near-wall streamwise, near-wall wall-normal, and outer streamwise velocity fluctuations.

Data-driven subgrid-scale modeling in the large-eddy simulations (LES) suffers from the inconsistency between the a priori tests and the $a$ $posteriori$ tests. We study the difference in filtered high-fidelity data and LES to identify the numerical deviation between the two cases, which is a combined impact of commutation error, numerical errors, and error coupling. By incorporating numerical deviations into model training, we enhance consistency, stabilize simulations, and improve predictions of the $a$ $posteriori$ tests. Our findings highlight that data-driven methods introduce significant nonlinearity and equation coupling, exacerbating inconsistencies compared to non-data-driven approaches.

Smooth and rough wall turbulent boundary layers often occur with external pressure gradients, which affect their development. This work presents an experimental investigation of high Reynolds number boundary layers, focusing on the effect of pressure gradient history on turbulence characteristics. Taking the turbulent spectra, we isolate both the effect of pressure gradient history and how the surface affects the response to a given pressure gradient history. The final part of this work looks at whether it’s possible to capture some of the effects on the turbulence spectra, particularly the peaks present within the spectra.

The complexity of wall-bounded turbulent flows has given rise to a variety of models that capture the essence of this physical problem. Townsend’s Attached Eddy Model (AEM) utilizes eddies that exhibit geometric scaling with their distance from the wall. In contrast, the One-Dimensional Turbulence (ODT) model is built on a completely different set of modeling assumptions. We re-write the ODT formulation as a Markov process and simplify some modeling assumptions, which allows us to recast the equations into a form analogous to AEM. By distilling and simplifying ODT, we highlight the implicit similarities with the modeling assumptions found in AEM.

A comprehensive dataset resulting from DNS of bypass transition in the narrow sense with inlet freestream turbulent intensity (FSTI) levels 0.75%, 1.5%, 2.25%, 3.0%, and 6.0% is reported. It is found that boundary-layer freestream scales evolve similarly to their spatially developing isotropic turbulence flow counterparts. Further, at an intermediate FSTI of 2.25%, two turbulent spot inception mechanisms coexist: the long low-speed streak primary and secondary instabilities (low FSTI) and the self-amplifying process of oblique vortex filaments interacting with a Delta-shaped low-speed patch underneath (high FSTI).

Effect of endcaps are of fundamental interest in Taylor-Couette (TC) experiments, including magnetorotational instability (MRI)-experiments. Understanding their influence on the TC flow dynamics is essential for the interpretation of experimental results. In this work, we studied the endcap effects in a Rayleigh-stable TC flow at high, experimentally relevant Reynolds numbers. The main result is that split-endcaps reduce Ekman pumping in the bulk flow and induce turbulence, which however remains localized in their vicinity. Endcaps modify the mean azimuthal velocity profile that in turn results in the lower threshold of the MRI onset, potentially facilitating its experimental detection.

Existing large eddy simulation models suffer from a lack of physical justification. In this paper, the links between two-point equations derived from the Navier-Stokes equation and Large Eddy Simulation (LES) are examined and an approximation of an exact equation is used to design a new subgrid-scale model. This new model is tested both $a$ $priori$ and $a$ $posteriori$ and is found to capture the correct physical energy transfer between filtered scales and residual subfilter scales. This is a proof of concept that two-point equations can be used to develop new LES models and this strategy may be the right one for developing more efficient models.

We experimentally investigate the impact of different inflow conditions on the breakdown of wind turbine tip vortices in a high Reynolds number wind tunnel. The data in this paper is obtained through hot wire spectral analysis. While downstream evolution of the spectra exhibits a complex scale dependent behavior, here we focus on the decay of the signature of the tip vortices for which we identify three distinct regimes. These regimes are linked to an initial advection phase, vortex breakdown, and turbulence decay. Variations in the tip speed ratio have a significant impact on the breakdown rate in the second regime, while effects of mean shear and turbulence intensity are less pronounced.

Turbulence in supercritical fluids differs from its low-pressure counterpart due to strong thermodynamic coupling and pseudoboiling effects, yet their influence on velocity and thermodynamic fluctuations remains unclear. Using direct numerical simulations of isotropic turbulence in supercritical fluids, small-scale statistics are examined. Temperature-related quantities are particularly sensitive, exhibiting increased intermittency of temperature variance dissipation rate and reduced production of mean-square temperature gradients. Topological analysis also shows that regions of intense pseudoboiling activity suppress strain-dominated structures while enhancing vortical motions.

In this paper, the volumetric velocimetry measurement technique Shake-the-Box is applied to the near wake of a model wind turbine to investigate the vortex dynamics present in the wake. The interaction and breakdown of the tip vortices is visualized using three-dimensional iso-surfaces of Lamb vector magnitude, a technique and physical quantity only accessible using volumetric techniques. The paper describes the influence of the tip vortex interaction process on properties of the tip vortex, such as circulation and the circularity and inclination of the tip vortex contour itself.

Small air vehicles that operate in urban canyons, around mountainous terrains, and in the wakes of marine vessels could encounter highly unsteady atmospheric conditions with relatively strong gusts. The gust ratio can exceed 1 in these extreme flight environments, making stable flight difficult, if not currently impossible. We refer to the study of aerodynamics for gust ratios over 1 as extreme aerodynamics and identify major challenges that require breakthroughs, particularly with data-driven approaches.

This study examines transient energy growth in a high-Reynolds and high-swirl numbers heavy q-vortex. Through nonmodal stability analysis, we identify optimal perturbations that produce energy amplifications far exceeding adjoint mode predictions over finite time horizons. The analysis reveals a robust three-stage transient mechanism combining pressure-induced energy transfers and a self-sustaining Rayleigh-Taylor feedback loop between radial velocity and density perturbations. This core-centered destabilization mechanism, absent in constant-density vortices, provides new physical insights into short-term energy amplification relevant to aircraft wake dispersion, mixing, and flow control.

A flexible body can interact with an incident water wave passively and extract wave energy to generate a thrust force. In this paper, direct numerical simulation is performed to investigate the wave energy extraction mechanism in the passive propulsion of a flexible foil. Kinematics studies show that the passive flapping motion is up–down asymmetric, with a direct impact on propulsive performance under unsteady motion. At high Strouhal numbers, a passing-over leading-edge vortex is observed, which is responsible for the enhanced thrust force.

The main challenge behind simulating incompressible flows is projecting the dynamics on the space of divergence-free fields. This projection is typically achieved by solving the Poisson equation in pressure at every time step. Here, we use the Principle of Minimum Pressure Gradient to formulate this projection as a minimization problem. The flow evolves from one instant to another in a way that minimizes the L2 norm of the pressure force required to satisfy the continuity constraint. We showed that the minimization problem is a convex quadratic programming problem and derived its closed-form solution. Hence, we obtained an explicit form for the projected dynamics of Navier-Stokes.

The widespread adoption of Lagrangian particle tracking (LPT) and Particle Tracking Velocimetry (PTV) methods motivate the reconstruction of continuous velocity fields from sparse, noisy particle tracking data. This work introduces a physics-informed Gaussian process regression (GPR) framework that incorporates mass conservation, boundary conditions, and statistical symmetries directly into the assimilation process. The method provides optimal interpolation, quantifies prediction uncertainty and estimates two-point velocity covariances. Validated across canonical turbulent flows, GPR significantly outperforms the industry standard, offering improved resolution and predictive accuracy.

Assimilating planar experimental data using standard two-dimensional constraints often distorts the momentum balance, as the model artificially compensates for the lack of divergence in the measurements. We demonstrate that enforcing three-dimensional constraints (3DVar) resolves this ambiguity in deep stall flows. By enabling spanwise flow development, 3DVar balances experimental divergence errors with physical gradients rather than artificial forcing. This isolates measurement inconsistencies from turbulence model deficits, yielding physically consistent reconstructions of unmeasured quantities like pressure and eddy viscosity.