Papers

Two independent attempts, separated by two decades, to encode turbulent dissipation with a fractional Laplacian both converge on the operator order as the signature of the fully developedinertial range: the additive, fixed order model, and the dynamically deforming operator of the Adaptive Fractional Navier Stokes. We show that, despite sharing this fixed point, the two constructions belongto distinct universality classes: Chen operator is a superposition of two fixed order kernels whose relative weight drifts with scale, while AFNS posits a single operator whose order itself flows continuously with the local Reynolds number. We derive a scale resolved observable, the effective spectral order, whose logarithmic anomaly term discriminates between these two mechanisms in principle, and then obtain a sharper, purely analytic verdict from the two dimensional, enstrophy conserving limit: the generative mechanism matching a stable process index to the empirical pair dispersion law has no solution once vortex stretching is kinematically switched off. Whether this dichotomy leaves a residual signature in real quasi two dimensional flows is left as an open experimental challenge.

Simulating large-scale free-surface water by coupling a localized 3D fluid solver to a cheaper 2D surface model has long faced a mismatch in wave dynamics: efficient 2D wave models used in graphics are typically either linear or non-dispersive. These models are fast, simple, and accurate for calm, small-amplitude seas, but coupling them with strongly nonlinear 3D solvers produces visible reflections and artifacts at the 2D–3D interface. We address this problem by introducing a nonlinear and dispersive 2D wave model based on the canonical Zakharov formulation. Its Hamiltonian structure, in which the surface elevation and surface potential form a canonical pair ($\eta$, $\psi$) governed by the wave energy, enables a canonically consistent two-way coupling scheme, allowing information to pass smoothly across the 2D–3D interface. Our 2D solver reduces mean wave-height error by 1.7–5$\times$ over SWE, BEM, and Airy baselines while running more than $10^3\times$ faster than BEM; it achieves greater nonlinear accuracy and coupling fidelity than SWE and Airy, with minor losses in speed and stability. Coupling it with a 3D Navier–Stokes solver yields a full system that suppresses visible seam artifacts across a range of experiments, including dispersion-matching and Kelvin-wake tests, and runs over 4$\times$ faster than a pure GPU NB-FLIP simulation on the same domain.

Deriving anomalous scaling exponents from the equations of motion remains a central problem in the statistical theory of turbulence. Here we obtain a first-principles perturbative solution for a nonlinear stochastic dyadic shell model. The model preserves the conservative cascade structure and exact scaling symmetry of the deterministic dynamics, while stochastic transfer fluctuations provide a perturbative setting in which the leading-order rescaled dynamics is Gaussian. Using the statistically restored hidden scaling symmetry of the inertial-range equations, we determine the stationary statistics of the rescaled variables. We then formulate anomalous scaling as a Perron–Frobenius eigenvalue problem for the multiplier statistics. The resulting perturbative expansion yields explicit analytical expressions for the scaling exponents of structure functions of arbitrary order in the weak-noise regime. Direct numerical simulations provide an independent verification of the theoretical predictions. The results demonstrate that the hidden-symmetry perturbation framework extends from linear random models to a genuinely nonlinear cascade system.

A compact vertical take-off and landing aircraft requires the same tilt-rotor configuration to perform two fundamentally different aerodynamic tasks: sustain hover and deliver efficient cruise. This work investigates the underlying wing-rotor interactions in both operating regimes using a validated unsteady Reynolds-averaged Navier-Stokes equations-based computational framework. For cruise, the advance ratio governs the balance between thrust production, propulsive efficiency, and wake coherence. Lower advance ratios produce a tightly wound slipstream that undergoes strong vortex interactions, leapfrogging, and early wake bifurcation. At higher advance ratios, the slipstream retains a narrower and more coherent jet-like structure, improving propulsive efficiency while reducing both thrust of the propellor and lift of the wing. The flow impingement at the wing is characterized through the approaching, interaction, and convection phases, revealing the combined influence of vortex stretching, wake bifurcation, blockage, image-induced velocity, and streamwise momentum convection on the downstream wake. In hover, the propeller's rotational speed governs the overall aerodynamic performance more strongly than the wing's placement. Although the position of the wing with respect to the propellor modifies the local wake interactions and flow impingement on its leading edge, its influence on the integrated thrust coefficient and figure of merit remains limited. We also explain the vortex and wake dynamics around the propellor and the wing responsible for governing these aerodynamic performance.

We show that the Boltzmann-Grad (BG) limit, $N\varepsilon^{d-1}=\alpha=\text{const}$, is not a neutral scaling condition but already encodes the Second Law of Thermodynamics, resolving Loschmidt's paradox. Newton's First Law is the bridge: applying the BG condition locally to two adjacent cells at different temperatures, we decompose their evolution into a free-streaming period $\delta t_f$, governed by inertia alone, during which molecules cross the interface ballistically and still carry their cell of origin's velocity distribution; and a collisional adjustment period $\delta t_a$, governed by Newton's Second Law, during which the locally mixed, non-Gaussian population relaxes toward a new Gaussian equilibrium. Using the one-dimensional Gaussian velocity distribution, we show that isotropy alone produces non-zero net molecular and momentum flux across the interface, directed from the warmer to the cooler cell – the microscopic origin of the pressure gradient driving the system toward uniformity. Treating relaxation as a sum of random collisional increments, the Central Limit Theorem fixes the collision count $n^*$ required for convergence, giving $\delta t_a \sim n^*\,\ell/\bar v$. This decomposition resolves Loschmidt's paradox: his reversal acts on a fixed, identifiable set of molecules, while the temperature field Boltzmann's equation tracks is carried by an ever-changing local population; the step relating the two – convergence under the Central Limit Theorem – is itself a coarse-graining that discards microscopic information by construction, recoverable only at an unavoidable thermodynamic cost, by Landauer's principle. Temporal irreversibility is present from the moment the BG framework, and the coarse-graining it requires, are adopted – not generated during derivation.

We investigate the melting dynamics of an ice disk subjected to an external oscillatory flow using two-dimensional direct numerical simulations, in the absence of buoyancy, varying the flow amplitude and its oscillation frequency. We identify two distinct regimes governed by the interplay between advection and diffusion within the boundary layer. For slow oscillations, the melting process is well described by an effective steady flow, where a description based on classical forced convection is applicable. For fast oscillations the melting time increases significantly and approaches the diffusion limit regime, as a result of the oscillatory flow being unable to renew the fluid within the oscillating boundary layer, causing cold meltwater to accumulate near the interface and reducing heat transfer.

The effects of pressure on the chemical sooting structure of equi-diffusive soot formation (SF) in a counterflow diffusion flame (CDF) are explored in a combined experimental and numerical study over pressures ranging from 1 bar to 6 bar. Experiments preserve the diffusive flame structure and carbon flux at increasing pressures and utilize measurements of soot concentrations, dispersion exponents and soot production rates. Numerical simulations are completed in OpenSMOKE++ with detailed \ce{C1}-\ce{C16} chemistry, lumped PAH consideration up to \ce{C160}, sectional soot model and tracking of the C/H ratio in particulates. Network-based tools are utilized to study the organization and evolution of carbon routing pathways. Results show that for equi-diffusive flames, soot concentration increases with residence time and pressure, whereas soot production rates are influenced only by pressure. Soot C/H ratio is observed to increase with pressure using numerical and experimental methods, but numerical solutions underestimate the increase in hydrogen abstraction reactions. The soot-forming network undergoes a percolation-like organization of its pathways before soot inception. The network then continues to grow by adding connections through its influential nodes. Acetylene is identified as a highly influential node in the carbon transfer graph, with its influence increasing with pressure.

We investigate the diffusiophoretic motion of a chemically isotropic active colloid in a three-dimensional wedge formed by two distinct fluid media, in the limit of vanishing Péclet and Reynolds numbers. The concentration field is obtained using the Fourier-Kontorovich-Lebedev transform, yielding an exact representation for arbitrary wedge opening angles and interfacial contrasts. We introduce the interfacial parameter $\Gamma=(1-\lambda\ell)/(1+\lambda\ell)$, where $\lambda$ denotes the diffusivity contrast and $\ell$ the solute partition coefficient. For $\Gamma=\pm1$ and commensurate wedge angles, the solution reduces to finite image constructions, with distinct structures for even and odd commensurability. The general solution also recovers the planar-interface and semi-infinite-interface limits. The leading-order translational phoretic velocity is derived from the concentration field, revealing a strong interplay between wedge geometry and interfacial properties that governs both the magnitude and direction of particle motion. This work provides a framework for understanding and controlling phoretic transport in confined multiphase environments and offer a basis for extensions to finite-size geometries and mixed fluid–fluid and solid boundary conditions. Our results may find applications in the control of active-particle transport in confined multiphase environments, where interfacial properties and geometry can be exploited to tune phoretic motion.

This paper details the data-driven modelling and feedback control of vortex shedding past a circular cylinder at a Reynolds number of Re = 1000. We study the effect of varying the order of the reduced model for control design purposes and demonstrate that higher orders can lead to lower suppression of vortex shedding. We use the Bode integral theorem and a frequency-domain interpretation to show that this drop in performance is, in part, due to the classical “waterbed effect”, which increases sensitivity in frequency bands of unmodelled dynamics. Training data from 2D unsteady simulation is used to obtain linear reduced-order state-space models of the system via dynamic mode decomposition with control. Using only lift measurement, we show that at least a 4th-order model is required for an LQG controller to suppress vortex shedding, with the best performance achieved with as few as 9 modes, whilst higher-order (>14) controllers show a significant decrease in performance. We study the influence of external disturbances, noise rejection, and parameter uncertainty on controller performance. A 28.6 dB reduction in lift coefficient variance is achieved, resulting in a 26% reduction in drag. We further show that, for control design purposes with practical actuation bandwidth, the closed-loop control delivers a significant 13.7% drag reduction within 3D DDES, despite having been trained with 2D URANS and therefore argue that 2D URANS simulation is sufficient for reduced-order model generation and control design.

The Sandia one-meter methane fire plume is an established benchmark for turbulent combustion modeling of large-scale flames. This study investigates the combustion instabilities formed close to the base of the Sandia fire plume. Finite rate chemistry and differential diffusion are considered using a flamelet/progress variable (FPV) approach. The performance of the FPV approach is assessed by comparing with the eddy dissipation model (EDM) and the experimental data for the large-scale fire plume via large eddy simulations (LES). The effects of radiation modeling and mesh resolution on the predictive capability of the model are systematically investigated by comparing the axial and radical velocities against the experimental data at various locations. Although all models successfully capture the primary flow characteristics of fire plumes, the FPV model with differential diffusion yields improved predictions in the near-flame-base region. The formation mechanism of cellular flow structures near the flame base is investigated via a budget analysis of the vorticity equation, and the type of instability governing the formation of the cellular structure is clarified. Finally, the individual effects of finite rate chemistry and differential diffusion on the prediction of the thermo-chemical quantities are quantified. Overall, this study explains the underlying physics governing combustion instabilities at the base of turbulent fire plumes, provides novel insights into the performance of flamelet models for LES of gaseous pool fires, and offers reliable guidance for the high-fidelity numerical simulation of large-scale turbulent buoyancy driven flames.

Nonlinear terms present a fundamental challenge for quantum computational fluid dynamics, as their implementation on inherently linear quantum hardware typically requires resource-intensive workarounds that limit scalability to large-scale simulations. We present a hybrid quantum-classical tensor network algorithm that addresses this bottleneck by combining variational time-stepping with quantum tensor programming to efficiently compile operators and time-dependent fields into quantum circuits. Within a probabilistic framework, we replace prior state-based nonlinear implementations with tensor-based block encodings, stabilizing success probabilities that otherwise decay exponentially with system size. Benchmarking on turbulent flow fields demonstrates that the algorithm maintains high success probabilities and moderate measurement overhead across increasing Reynolds numbers and grid resolutions. Compared to fully classical tensor network solvers, our hybrid approach yields substantial reductions in both memory footprint and computational cost, establishing a scalable pathway toward practical quantum advantage in scale-resolving CFD simulations.

We propose a hybrid sharp-diffuse interface representation for modeling intermittent and isolated topological transitions during Cahn-Hilliard phase coarsening. Away from topological events, the evolution is approximated by the Mullins-Sekerka sharp-interface limit system and computed using a boundary integral formulation. When diffuse transition layers overlap, a novel interface surgery algorithm resolves topology changes through a localized Cahn-Hilliard pseudo-time evolution, after which the sharp-interface calculation is resumed. We develop the mathematical formulation underlying this decomposition, present a simple two-dimensional numerical implementation, and simulate a mass-exchange problem with interface coalescence. By localizing the diffuse evolution to topological events, the method achieves a speedup of two to three orders of magnitude over conventional diffuse-interface simulations.

Gaucher disease (GD), the most common lysosomal storage disorder, alters red blood cell (RBC) mechanics and circulation, contributing to vascular occlusions, bone infarcts, and splenomegaly. However, the individual roles of GD-RBC biophysical properties in these processes remain unclear. Here, we present a combined computational-experimental investigation to quantitatively characterize GD-RBC biophysical properties and determine how specific mechanical parameters drive abnormal RBC behavior. Informed by experimental data, we independently quantify key RBC properties, including shear modulus (mu), surface-to-volume ratio (S/V), and bending modulus (k_c). Based on these parameters, we construct three GD-RBC subtypes (GD-RBC1-3) to systematically isolate their individual contributions. At the single-cell level, optical tweezers simulations show up to ~27% reduction in axial diameter and ~42% reduction in transverse compression. Tank-treading dynamics exhibit non-monotonic behavior, with rotation frequencies increasing by up to ~70% or decreasing under elevated bending rigidity. In confined flow, traversal times through microchannel constrictions increase by more than a factor of two, while splenic slit passage times rise from ~250 ms (control) to >1200 ms for the severe GD-RBC subtype, approaching a functional no-passage threshold. At the population level, viscosity simulations demonstrate that these alterations collectively elevate blood viscosity, with small fractions (~4.0%) of highly rigid cells disproportionately increasing flow resistance. Overall, this study provides a quantitative and mechanistic framework that disentangles the contributions of key RBC parameters to abnormal behavior in GD, linking cellular-scale biophysics to hematologic dysfunction and microvascular occlusion.

A self-contained hydrodynamic theory is proposed to reconcile the discrepancy between divergent Stokesian velocity fluctuations and finite experimental measurements in sedimenting suspensions. We show that the compensating backflow induces non-negligible inertia, giving rise to an emergent screening length $\xi \sim a\phi^{-1/3}Re_p^{-1/3}$ far exceeding the mean interparticle spacing $a\phi^{-1/3}$ even at vanishingly small particle Reynolds numbers. This backflow inertial screening, together with finite-time viscous diffusion, arrests the indefinite spatiotemporal growth of large-scale velocity fluctuations. The resulting velocity fluctuations scale as $\delta u \sim \phi^{1/3}V_sRe_p^{-1/6}$, together with the viscous correlation time $\tau_c=\xi^2/\nu$, reproducing the well-known hydrodynamic self-diffusivity scaling $D_H\sim V_s a$. The theory predicts the prefactors of these scaling laws without adjustable parameters, in good quantitative agreement with experimental measurements. It also successfully captures the experimentally observed crossover from the finite-correlation regime to the finite-system regime as the screening length becomes comparable to the system size.

We extend the generalized anomalous diffusion framework established in Part I to the short-range forcing regime ($\beta > 2/3$), where the multiscale-force dominated (MFD) subrange is intercalated after the inertial subrange, competing directly with the dissipation ranges. Focusing on electrokinetic (EK) turbulence as the prototypical example with $\beta=1$, we derive the relations for the velocity and scalar dissipation wavenumbers, $k_{MD}$ and $k_{SD}$, across all four subranges of the Quad-cascade process (inertial, constant-$\Pi_u$, constant-$\Pi_s$, and variable flux). By incorporating Golestanian's predicted anomalous diffusion regimes for electrolytes, we construct comprehensive phase diagrams showing how the relative magnitudes of $k_{MD}$ and $k_{SD}$ are governed by the scale-dependent anomalous Schmidt number $Sc_Z$. We identify two new spectral subranges that emerge exclusively in this short-range forcing regime: (i) the convective-viscous subrange ($k_{MD} \ll k \ll k_{SD}$) of velocity spectrum for $Sc_Z \gg 1$, where the scalar field drives a viscous flow yielding $E_u \sim k^{-\left(\frac{3}{2} + \frac{\xi_s}{2}\right)}$ with a stretched-exponential cutoff; and (ii) the diffusive-forcing subrange ($k_{SD} \ll k \ll k_{MD}$) of scalar spectrum for $Sc_Z \ll 1$ and $\gamma \leq \alpha$, where the scalar dissipation range determines the electric forcing, leading to $E_s \sim k^{\xi_u - 2\alpha}$. These results provide a complete analytical map of EK turbulence under anomalous diffusion, revealing how external parameters such as electric field strength and ionic diffusivity determine the cascade topology.

We present a theoretical model for momentum–scalar coupled turbulence in which both fields undergo anomalous diffusion, described by fractional biharmonic operators of orders $\gamma/4$ and $\alpha/4$, respectively. Focusing on the long-range external forcing or unforced turbulence, we derive analytical expressions for the kinetic energy spectrum $E_u(k)$, the scalar spectrum $E_s(k)$, and the characteristic wavenumbers $k_K = \left( \frac{\epsilon_u^{1/3}}{c_u} \right)^{1/(\gamma - 2/3)}$ (reciprocal of Kolmogorov scale) and $k_S = \left( \frac{\epsilon_u^{1/3}}{c_s} \right)^{1/(\alpha - 2/3)}$ (reciprocal of scalar dissipation scale) as functions of $\gamma$, $\alpha$, turbulent dissipation rate $\epsilon_u$, diffusivities of momentum ($c_u$) and scalar ($c_s$), respectively. An anomalous Schmidt number $Sc_Z = k_0^{\gamma - \alpha} \frac{c_u}{c_s}$ is defined to governs the cascade topology. It describes the ratio of diffusion times of scalar and momentum on the minimum wavenumber $k_0$. Superdiffusion ($\gamma<2$ or $\alpha<2$) is shown to counter-intuitively enlarge $k_K$ and $k_S$, broadening the inertial range. The theory unifies the classical Kolmogorov–Obukhov–Corrsin–Batchelor scalings as special cases when $\gamma=\alpha=2$, and provides a foundation for understanding non-Fickian transport in complex turbulent systems.

The linearity of the Stokes equations organises the hydrodynamic response of a rigid particle into a hierarchy of resistance operators, coupling successive truncations of the ambient-flow jet to moments of the surface traction. Since the work of Kelvin and Larmor, it has been known that this response does not resolve particle geometry faithfully: bodies with discrete rotational symmetry may be indistinguishable from bodies of revolution (Brenner's helicoidal symmetry) and a chiral body may respond isotropically, as in Kelvin's isotropic helicoid. We regard the resistance operators as elements of finite-dimensional O(3)-representation spaces and use character formulae to determine, at every level of the hierarchy, which point-group symmetries are hydrodynamically distinguishable and the dimension of each invariant space. This yields an explicit nested sequence of hydrodynamic symmetry-group sets, from the translation-force level to the quadratic-flow level. The framework reveals hydrodynamic classes that no shape can realise geometrically, gives helicoidal symmetry a level-dependent definition, and shows that polyhedral symmetry becomes visible in a strict order: tetrahedral symmetry in shear, octahedral symmetry through the stresslet, and icosahedral symmetry in quadratic flow. Projecting the resistance operators onto force- and torque-free motion provides symmetry-based parameter counts and a constructive route to the corresponding dynamical normal forms. We thereby complete the Jeffery-Bretherton-Ishimoto classification, characterise all hydrodynamic classes producing Jeffery dynamics, and identify chiral tetrahedral and octahedral normal forms that can generate irregular full-attitude dynamics.

Wicking in a capillary tube could happen as long as the liquid contact angle is smaller than 90 degrees, making it possible for weak hydrophilic liquids to spontaneously invade the tube. For textured surfaces, energy minimization argument predicts the same. However, wicking of weak hydrophilic liquids on textured surfaces has not been possible due to energy barriers induced by the textures. We demonstrate how these barriers could be avoided by adjusting the shape and arrangement of the pillars, thus the wettability required for wicking reaches the theoretical limit. An unprecedented wicking contact angle of 82 degrees is reported. More surprisingly, wicking coefficients of such surfaces can be larger than that of rectangular grooves at the same porosity. These findings may significantly advance biomedical and thermal management technologies.

Separation of low-abundance biological objects requires high throughput for practical use of an acoustofluidic system. Increasing the flow rate helps in achieving high-throughput if the acoustic energy density can be increased proportionally, and this may be possible with an efficient coupling of the transducer to the device. In particular, antisymmetric actuation using two electrodes with opposite phases is theoretically proven to enhance the acoustic energy density of the device. In this work, we study the symmetric and antisymmetric actuation mechanisms of an acoustofluidic system using both experiments and three-dimensional numerical simulations. The acoustic focusability experiments show that under the same electrical input power, the antisymmetric actuation mode performs better than the symmetric actuation, quantified in terms of the normalized width of the band formed by the focused particles. Numerical simulations of this particle bandwidth are performed for both actuation modes, and the results suggest that the antisymmetric actuation mode is more robust than the symmetric one, being weakly dependent of the geometric symmetry properties of the system. The simulation results corroborate the experimental findings, which indicate that the antisymmetric actuation increases the acoustophoretic efficiency and robustness for high-throughput applications.

A salient feature of fully turbulent flows far from onset is the intermittent occurrence of extreme fluctuations at small spatial and temporal scales. These have a qualitative and quantitative effect on the instantaneous curvature of a tracer particle trajectory as an intrinsically multi-scale observable. Here, we provide a complete statistical description of the curvature of tracer particle trajectories in turbulent flows that includes and quantifies intermittency effects. We derive an exact expression and a closed-form approximation for the curvature probability density function, both agree well with data obtained from laboratory experiments of different types of turbulent flows, and quantify the generic behavior of the system. The method can be extended to more complex systems such as plasma turbulence.

Simulations of surface-tension-dominated incompressible two-phase flows are computationally expensive due to the severe capillary time-step constraint. Although many studies have proposed time-implicit discretizations of surface tension to allow larger time-step sizes and accelerate simulations, these methods suffer from either artificial dissipation or complex implementation. Here, we propose a simple and novel approach: an incompressible solver with weakly compressible subcycling. The proposed approach relaxes the capillary time-step constraint, thereby accelerating simulations by more than $8.6\times$ without relying on artificially dissipative stabilization or requiring complex implementation. The key idea is to introduce lightweight substeps using a weakly compressible solver to assist the main incompressible solver. These substeps enable the main incompressible solver to use accurately computed fluxes and surface tension force, even with large time-step sizes. Numerical tests demonstrate the effectiveness of the proposed approach for practical problems, including the Rayleigh–Plateau instability and two-phase flows in porous media. This study paves the way for a new paradigm in which a weakly compressible solver serves as an assistant to an incompressible solver.

We analytically analyse the dynamics of an internally actuated particle, modelled as a compressible elastic sphere embedded with a magnetic bead at its undeformed centre, translating in a plane Poiseuille flow in the Stokes limit. The particle is constrained to translate with a prescribed velocity while remaining at an arbitrary position within the flow by applying an external point force and external point torque at its undeformed centre. The governing equations for the fluid and particle are the Stokes and Navier elasticity equations, respectively. We use the series solutions to the governing equations and the domain perturbation method to capture the deformed shape of the particle, assuming $\alpha \ll 1$. Here, $\alpha$ quantifies the elastic strain induced in the particle due to the viscous stress from the fluid. The external force and external torque are obtained until O($\alpha^2$). The particle translating along the channel length experiences an elastic-induced hydrodynamic lift as well as hydrodynamic torque both at O($\alpha$) and O($\alpha^2$). The leading-order lift depends linearly on the local shear rate and on the combined effects of slip velocity and flow curvature, where the slip velocity is defined as the particle velocity relative to the local ambient flow. The particle reaches a stable equilibrium position away from the centreline, where the net lift vanishes. We show that the direction of deformation-induced lateral migration of the internally actuated particle is qualitatively distinct from that of drops, capsules, and vesicles in the Stokes limit and from that of rigid spheres undergoing inertial migration.

Odd viscosity, the nondissipative part of the viscous response of a time-reversal-broken fluid, is notoriously difficult to measure precisely because it does no work. Here we show that parity-time ($\mathscr{PT}$) symmetry, familiar from non-Hermitian optics, converts this elusiveness into a measurement principle. The odd Navier-Stokes equations, that include the nonlinear inertial terms, are $\mathscr{PT}$-symmetric, follow from a Lagrangian, and linearize to a Schrödinger equation in which the odd viscosity plays the role of Planck's constant; potential vorticity obeys a generalized Ertel conservation law. A probe trapped in an odd liquid realizes a pair of oscillators coupled by odd friction, and supplying balanced loss and gain drives a twofold $\mathscr{PT}$ transition whose exceptional point and Rabi sidebands locate the odd viscosity with square-root-enhanced sensitivity. Upon quantization the spectrum is of Fock-Darwin form, and the dissipative pair exhibits a Liouvillian exceptional point separating linear from exponential heating. These results furnish mechanical, stochastic, and spectroscopic protocols for measuring odd transport coefficients in classical and quantum fluids.

We investigate the effects of horizontal oscillations on the drafting–kissing–tumbling (DKT) dynamics of two monodisperse spherical particles settling under gravity in a viscous fluid. Applying particle-resolved direct numerical simulations, we systematically vary the oscillation frequency and amplitude to assess their impact on the behavior of individual particles, their mutual interaction, and the orientation of the particle arrangement. The results demonstrate that the oscillatory effects on DKT become significant only when the particle Reynolds number $Re_p$, defined as the ratio of oscillation-induced inertial to viscous forces, exceeds unity. In this regime, oscillations alter the temporal characteristics of the DKT process, with moderate amplitudes tending to prolong and larger amplitudes to reduce the kissing phase. Moreover, oscillations affect particle reorientation. At low $Re_p$, the particles maintain their initial orientation throughout the interaction, whereas an increasing $Re_p$ promotes a preferential alignment perpendicular to the direction of oscillation. We explain these findings by analyzing the oscillation-induced pressure fields surrounding the individual particles, which develop increasingly pronounced lateral anisotropy with increasing $Re_p$. The corresponding lateral hydrodynamic forcing likewise becomes increasingly anisotropic, providing a consistent physical basis for the observed modification of particle interactions and reorientation. These findings provide a physical framework for understanding how horizontal oscillations govern binary particle–particle interactions and orientation during gravitational settling.

Travelling-wave-like wall blowing and suction is an effective approach for enhancing heat transfer with a minimal pressure drag penalty. However, achieving such a dissimilar heat transfer enhancement effect in a passive manner remains a challenge. In the present study, we propose introducing parallel perforated plates to induce travelling-wave-like disturbances passively. Pore-resolving simulations of a spatially developing laminar flow between parallel perforated plates are performed across a wide range of Reynolds numbers of $Re = 500-1500$ and pore-to-solid length ratios of $L_\mathrm{p}/L_\mathrm{s} = 0-10$. Dissimilar heat transfer enhancement is confirmed for $9 \leq L_\mathrm{p}/L_\mathrm{s} \leq 10$ at $Re = 1000$ and $4 \leq L_\mathrm{p}/L_\mathrm{s} \leq 7$ at $Re = 1500$. The highest analogy factor, i.e., the ratio of the Stanton number to the friction coefficient is obtained at $Re = 1500$ and $L_\mathrm{p}/L_\mathrm{s} = 6$, yielding an increase of more than $30$% compared to that of an impermeable solid plate. Analysis of the fluctuating fields shows that, in the travelling-wave flow regime, a pressure-induced wall-normal velocity fluctuation transports temperature fluctuations away from the perforated plate, while breaking the correlation between the streamwise and wall-normal velocity fluctuations. This enhances the turbulent heat flux relative to the Reynolds shear stress near the perforated plate. The present results indicate that introducing a perforated plate with a suitable porosity induces travelling-wave velocity disturbances and also achieves a considerable dissimilar heat transfer effect even at low Reynolds numbers where a standard impermeable flat wall yields a steady laminar flow.

Our recently published papers reporting results of Direct Numerical Simulation (DNS) of forced convection flows in porous media suggest that in a porous medium the size of turbulent structures is restricted by the pore scale. Since the turbulent kinetic energy is predominantly contained within large eddies, this suggests that turbulent flow in a porous medium may carry less energy that its counterpart in a clear fluid domain. We use this insight to develop a practical model of turbulent flow in composite porous/fluid domains. In such domains, most of the flow is expected to occur in the clear fluid region; therefore, in most cases the flow in the porous region either remains laminar or starts its transition to turbulence even if the flow in the clear fluid region is fully turbulent. This conclusion is confirmed by comparing appropriate Reynolds numbers with their critical values. Therefore, for most cases, using the Forchheimer term in the momentum equation and the thermal dispersion term in the energy equation may result in a sufficiently good model for the porous region. However, what may really affect turbulent convection in composite domains is the roughness of the porous/fluid interface. If particles or fibers that constitute the porous medium (and the pores) are relatively large, the impact of the roughness on convection heat transfer in composite porous/fluid domains may be much more significant than the impact of possible turbulence in the porous region. We use the above considerations to develop a practical model of turbulent flow in a composite porous/fluid domain, concentrating on the effect of interface roughness on turbulence.

A thin volatile film carrying N particle species of different sizes evaporates on a deep immiscible liquid subphase. The spreading coefficient is positive, so nothing pins. The film ends at a receding front whose motion falls out of the film equations; no contact-line law is imposed. We solve the lubrication problem with a conservative depth-integrated treatment of species transport, and the front turns out to be a chromatograph. Every species piles into a concentration spike at the front, each held there in proportion to its Péclet number. The smaller, more diffusive species leaks continuously into the fluid that survives the front's passage; the larger species is laid down along the sweep path. The dried deposit is the time-integrated record of that sweep, and it is sorted by size: small-rich centre, large-rich mid-annulus. Pinned bidisperse droplets sort the other way. Depinned droplets on solids sort this way, but by a force balance; here, diffusivity contrast alone picks the direction. Size enters the transport problem only through the Péclet number, so diffusivity contrast is the only symmetry-breaking available to choose a direction: Marangoni stresses, colloidal interactions and wetting effects act on the magnitude and, by the symmetry of the transport operator, cannot set the direction. Adjacent-species band separations scale with the difference in inverse effective Péclet number, a law derived and measured here: the resolution of the chromatograph. That scaling points to a route to size fractionation of polydisperse nanoparticles in the few-nanometre regime, exactly where standard methods struggle.

We derive an exact and novel expression for an averaged two-point correlation function in the statistically stationary, forced-dissipative two-dimensional Navier-Stokes equations subject to the Coriolis force under the beta-plane approximation. This identity is related to the so-called geostrophic balance: it connects the effect of the Coriolis force to the pressure gradient through a two-point correlation function. Additionally, we provide sufficient conditions under which the asymptotics of the averaged third-order structure function at large spatial scales follow the universal third-order law of two-dimensional turbulence in the absence of the Coriolis force. This complements our previous results on small spatial scales. Together, our results provide a clear picture of the role of the Coriolis force in beta-plane turbulence. On the one hand, the spherically averaged rates of enstrophy and energy transfer are not affected by the Coriolis force. On the other hand, the Coriolis force contributes to anisotropic large-scale organization by altering the spatial distribution of energy and promoting the formation of zonal structures. The proof relies on a new formulation of the Karman-Howarth-Monin relation. For the geostrophic balance, we use a novel antisymmetric projection of the KHM relation under which only the pressure and Coriolis terms survive. For the cascade laws, we show that the Coriolis contribution to the averaged classical KHM relation vanishes identically at any scale.

We consider turbulent flow in a half-space along an infinite plane. We regard it as the limit to which the motion in the viscous sublayer of turbulent near-wall flows tends as Reynolds number increases indefinitely. In addition to the no-slip condition, an averaged shear stress value is specified on the streamlined surface. A numerical solution algorithm is proposed, based on the well-known spectral method, which demonstrates that the boundary conditions on the wall along with the physically justified constraint that the velocity components do not grow exponentially at infinity uniquely determine the turbulent flow under consideration. The implementation of the algorithm will allow us to draw conclusions about the validity of the idea that the flow in the viscous and logarithmic sublayers is independent of the external parameters of turbulent near-wall flows.

In an ignited design of inertial confinement fusion, the role of mid-to-high-mode hydrodynamic instabilities in degrading hot-spot performance, beyond reducing temperature, remains unclear. To address this, we propose an isobaric criterion to assess the isobaric assumption that forms the theoretical basis of the hot spot. The most dangerous mode l = 12 is determined through a balance between perturbation growth and ablation stabilization induced by thermal conduction. Thermal conduction outperforms convection when the Peclet number is much less than 1. Therefore, for mid-to-high modes, thermal conduction makes the hot spot isobaric before the outer mass inflow restores the lost heat. Consequently, neglecting thermal conduction overestimates pressure and underestimates volume. These results enhance our understanding of mid-to-high modes in degrading hot-spot performance, and suggest that thermal conduction losses may reduce performance even if perturbations are nearly stabilized by ablation.