In this work we consider the problem of constructing initial conditions for a flow model such that the resulting flow evolution leads to a self-similar energy cascade consistent with Kolmogorov's statistical theory of turbulence. As a first step in this direction, we focus on the one-dimensional viscous Burgers equation as a toy model. Its solutions exhibiting self-similar behavior, in a precisely defined sense, are found by framing this problem in terms of partial differential equation (PDE)-constrained optimization. The main physical parameters are the time window over which self-similar behavior is sought (equal to approximately one eddy turnover time), viscosity (inversely proportional to the “Reynolds number”), and an integer parameter characterizing the distance in the Fourier space over which self-similar interactions occur. Local solutions to this nonconvex PDE optimization problem are obtained with a state-of-the-art adjoint-based gradient method. Two distinct families of solutions, termed viscous and inertial, are identified and are distinguished primarily by the behavior of enstrophy which, respectively, uniformly decays and grows in the two cases. The physically meaningful and appropriately self-similar inertial solutions are found only when a sufficiently small viscosity is considered. These flows achieve the self-similar behavior by a uniform steepening of the wave fronts present in the solutions. The results obtained demonstrate that the proposed methodology may be used to search for self-similar behavior in more complex flow models, including shell models, two-dimensional turbulence, and, ultimately, three-dimensional turbulence.

The effective transport of heat and mass is crucial to both industrial applications and physiological processes. Recent research has evaluated the benefit of using flexible reeds for triggering the vortex-induced vibration to enhance mixing, as opposed to traditional rigid or static techniques. Inspired by the soft, porous, and moving fish gill lamellae, we proposed a concept of thermal dispenser that prescribes active pitching motion to the leading edge of an otherwise passively flapping perforated panel. Fundamentally, we identified different vortex creation and shedding mechanisms by the perforated panel than the conventionally studied nonperforated panel. We experimentally documented the effect of chordwise flexibility on inducing vortex transitions across a range of frequencies, primarily the change of dipole orientation and wake bifurcation. A semi-empirical simulation of thermal convection and diffusion took the experimentally obtained flow field as an input and yielded the temperature mixing results. We numerically showed that the actuation and chordwise flexibility both enhance mixing. Specifically, active pitching resulted in a 37–94% higher average temperature increment than statically deflected panels. The chordwise flexible panel achieved an overall higher mixing index and was able to maintain similar mixing performances across the entire tested kinematic range due to vortex transitions, whereas the rigid panel suffers from increasing pitching frequency. To synthesize the understanding of vortex dynamics and thermal mixing, we examined the Lagrangian coherent structures to elucidate the lateral entrainment, convective transport barriers, and mixing homogeneity. Our work provides a foundational understanding of the fluid-structure interactions of perforated bendable panels under active control, which has not been described before in the intermediate Reynolds number range. It provides insights for developing an innovative bio-inspired heat or mass dispenser potentially suitable for subtle and small-scale applications.

The growing availability of GPU-accelerated open-source solvers has boosted the capability of tackling complex single-phase and multiphase turbulent flows by means of direct and large-eddy simulations. GPU-accelerated solvers can leverage the heterogeneous computing architectures that are available in leading high-performance computing centers worldwide, taking advantage of the higher throughput and greater energy efficiency offered by GPUs as compared to CPUs. However, porting CPU-based numerical solvers to GPUs entails many outstanding challenges, such as parallelism exposure, inter-GPU communication, memory allocation constraints, and shared memory limitations. To overcome these challenges, GPU-friendly algorithms, performance portability strategies, and careful selection of computational paradigms and programming languages must be developed. Besides, adaptive mesh refinement and data compression may be integrated to mitigate I-O bottlenecks and enable simulations of more complex geometries on top of the existing requirements imposed by incompressible flows. When compressibility effects become significant, further considerations related to the adoption of high-performance preconditioners and multigrid solvers become crucial for tackling large, sparse linear systems and extending simulations to high-Mach flows. Finally, reduced-precision arithmetic can further enhance performance, energy efficiency, and scalability. In this work, we survey current applications of GPU-accelerated solvers in the broad area of fluid mechanics and turbulence simulations and discuss the main challenges and bottlenecks associated with code porting and optimization. We then conclude our analysis with an outlook on future perspectives for enabling efficient GPU-based exascale computing of turbulence.

Inertial particles (IPs) in vortical fluid flow cluster strongly, forming singular structures termed caustics for their resemblance to focal surfaces in optics. Here we show that such extreme aggregation onto low-dimensional submanifolds can arise without mechanical inertia for self-propelled particles (SPPs), through a formal correspondence between the dynamics of IPs and SPPs in a generic background flow. We establish that a singular perturbation underlies caustics formation by SPPs around a single vortex, and numerical studies of SPPs in two-dimensional Navier-Stokes turbulence reveal intense caustics in straining regions of the flow, peaking at intermediate levels of self-propulsion. Our work offers a route to singularly high local concentrations in a macroscopically dilute suspension of zero-Reynolds-number swimmers. Caustics generate burstlike encounters through large relative velocities between neighboring swimmers, with potentially significant implications for communication and sexual reproduction. An intriguing open direction is whether the active turbulence of a suspension of swimming microbes could serve to generate caustics in its own concentration.

The transient growth of disturbances made possible by the non-normality of the linearized Navier-Stokes equations plays an important role in bypass transition for many shear flows. Transient growth is typically quantified by the maximum energy growth among all possible initial disturbances, which is given by the largest squared singular value of the matrix exponential of the linearized Navier-Stokes operator. In this paper, we propose a data-driven approach to studying transient growth wherein we calculate optimal initial conditions, the resulting responses, and the corresponding energy growth directly from flow data. Mathematically, this is accomplished by optimizing the growth over linear combinations of input and output data pairs. We also introduce a regularization to mitigate the sensitivity to noisy measurements and unwanted nonlinearity. The data-driven method simplifies and broadens the application of transient growth analysis: it removes the burden of writing a new code or linearizing an existing one, alleviates the computational expense for large problems, eliminates the challenge of obtaining a well-posed spatial propagator for spatial growth analyses, and enables the direct application of transient growth analysis to experimental data. We validate the data-driven method using a linearized Ginzburg-Landau model problem and Poiseuille flow corrupted by process and measurement noise and obtain good agreement between the data-driven and the standard operator-based results. We then apply the method to study the spatial transient growth of disturbances in a transitional boundary layer using data from the Johns Hopkins Turbulence Database. Our method successfully identifies the optimal output response and provides plausible estimates of the transient spatial energy growth at various spanwise wave numbers.

The interaction mechanisms among detonation waves, shock waves, and liquid droplets play a critical role in advancing propulsion technologies such as rotating detonation engines. This study conducts a detailed comparison of wave dynamics, cavitation phenomena, and droplet deformation during the detonation wave and the shock-wave interactions with a water droplet, employing a high-resolution numerical model that integrates multicomponent compressible fluid dynamics, chemical reactions, and phase transition effects. Numerical simulations reveal distinct characteristics between detonation and shock-induced phenomena. Unlike the shock wave, detonation-induced reflected shock waves exhibit significantly higher propagation velocities while maintaining nearly identical wave configurations, a phenomenon this study mechanistically explains by the unique postwave conditions. A fundamental distinction arises in cavitation dynamics between the detonation wave and the shock wave, with the detonation-wave triggering cavitation zone collapse at significantly higher rates compared with the shock wave. This difference is attributed to the shorter persistence of low-pressure regions behind the detonation front, where rapid attenuation of postwave pressure and flow velocity occurs. Moreover, detonation-induced flow interactions create unique droplet fragmentation patterns. The rapid postwave velocity reduction prevents Rayleigh-Taylor instability-driven forward jet formation, instead causing leeward-side flattening of the droplet through the vortex in the recirculation zone.

Bicuspid valves with crescent-shaped leaflets are found in lymphatic vessels and veins, where their primary function is to prevent reflux and ensure unidirectional flow toward the heart. These valves are passive, and their functionality emerges spontaneously from a complex interplay between the properties of the valve leaflets and the flow patterns developing within the vessel sinus region surrounding the valve. The main function of the valves is to limit retrograde flow, or reflux, but the optimal valve structure has not been well characterized. Here we investigate numerically how the length of the leaflets affects the valve efficiency in preventing reflux. The valves are subjected to backward flow, akin to that imposed by gravity. We report the flux through the valve orifice as a function of key parameters: valve length, leaflet length, and leaflet rigidity. We monitor the transition in the flow regime—from reflux to complete flow blockage—by varying only the leaflet length. The transition threshold is found to depend strongly on the valve shape and stiffness. We captured these control parameters numerically to evaluate the ability of the valve to close and prevent reflux. This study allowed us to explain reflux observed experimentally in certain incompetent abnormal and immature valves, particularly those with shorter leaflets.

The accurate prediction of pressure drop across randomly packed beds is critical for the design of chemical reactors, adsorption columns, and thermal energy storage systems, yet existing semiempirical correlations often lack consistent accuracy across diverse geometric and flow regimes. This study presents a residual-driven sensitivity analysis framework that systematically evaluates the influence of key operational and geometric parameters, namely, superficial velocity $U_s$, normalized bed length $L/D$, and normalized column diameter $D/d_p$, on the prediction error of classical pressure drop models. Using an extensive experimental dataset collected in our laboratory, comprising over 3000 measurements across four column diameters (50–200 mm) and six particle sizes (2.5–42.6 mm), we integrate robust outlier detection, iterative data sanitation, and multimethod sensitivity assessment combining Pearson correlation, tree-based feature importance, and partial dependence analysis. Results show that for the raw dataset, errors are collectively influenced by all three parameters, with no single factor dominating. Through successive cleaning iterations that progressively remove data with strong wall effects ($D/d_p<4$), low length-to-diameter ratios, and extreme geometries, the analysis reveals a clear transition: Superficial velocity emerges as the overwhelmingly dominant driver of residual error, accounting for 74.6% of the normalized Gini importance in the final filtered dataset. This evolution demonstrates that after mitigating geometric confounders, the core limitation of widely used models such as the Ergun equation lies in their inability to accurately capture flow-regime-dependent behavior. The work provides a validated methodology for sensitivity analysis in packed-bed flows and offers practical guidance for model selection and experimental data-quality assurance, highlighting that future model improvements should prioritize velocity-dependent corrections rather than further refinement of geometric terms.

Capillary suspensions are commonly encountered in a wide array of applications, but their stability in flow is not fully understood. Here, we investigate the stability of a two-particle capillary cluster in extensional flow using a combination of theory and experiments. A linear stability analysis reveals the existence of a critical capillary number ${\text{Ca}}_c=(8/45)cos\theta$ that depends only on the contact angle $\theta$. For $\text{Ca}>{\text{Ca}}_c$, clusters are unconditionally unstable, regardless of initial conditions. For $\text{Ca} < {\text{Ca}}_c$, a nonlinear analysis shows the existence of a $\text{Ca}$-dependent minimum interparticle separation beyond which breakup occurs. The analytical model further supports the experimentally observed slowdown in relaxation dynamics. Theoretical predictions are supported by precise flow experiments using a Stokes trap, where active flow modulation is used to stabilize an initially unstable cluster in extensional flow. Overall, these results provide a quantitative understanding of capillary suspension stability in flow.

Stereo inhalation draws ambient fluid into a pair of spatially separated siphons. The ubiquitous mammalian nose morphology of two separated nares uses stereo inhalation to enhance respiration and olfaction. Previous studies have found that stereo inhalation improves the spatial extent of odor capture and success of source localization. However, direct quantification of the spatial extent of inhaled fluid has received less attention, which may provide context for evolutionary adaptations to sensory appendages and design of biologically inspired sniffing devices. We numerically modeled idealized stereo inhalation through a pair of round siphons and evaluated the effects of siphon separation, proximity to boundaries, and inhalation Reynolds number (Re) on the inhaled fluid structure. We find that siphons closer together have approximately three times the lateral perception of sensory information relative to pairs of single siphons. Siphons that protrude above a solid boundary inhale fluid farther away from the orifice relative to siphons flush with the boundary. Additionally, the Reynolds number alters the axial distance that fluid is inhaled from the siphon orifice. As Re decreases from 100 to 1, outward viscous diffusion of suction-driven momentum increasingly dominates its inward advection, enhancing axial biases to inhale fluid more directionally. Organisms may alter morphology (siphon separation and extraction height) and inhalation dynamics (Reynolds number) at behavioral or evolutionary timescales to adapt to their surrounding environments. Our findings can inform principles for engineering applications and provide physical mechanisms that govern sensing enhancements from stereo inhalation.

Ultrasound-driven microbubbles are increasingly being investigated for both molecular imaging and therapeutic applications. To be effective, these bubbles must be brought into close proximity or direct contact with the target site. Leveraging the acoustic radiation force provides a powerful strategy to direct their movement. In this study, we examine the translational dynamics of a microbubble with unprecedented accuracy by simultaneously time-resolving both its radial and translational responses and by using optical tweezers to study the bubble in free space. Our experimental results show excellent agreement with theoretical predictions for the bubble sizes considered, provided the history drag force is included in the force balance. For the Reynolds numbers considered (up to $\text{Re}\approx 2$), the zero-Reynolds-number history force performs as well as its finite-Reynolds-number extension. Although nonspherical modes may arise at larger bubble expansions, they do not appear to significantly influence the bubble translational motion. A major finding is that the normalized transport distance of the bubble scales linearly with the normalized volumetric expansion during its oscillation, greatly simplifying the design and analysis of transport strategies. We also investigated bubble stability during transport and observed a marked increase in dissolution rate once a threshold in bubble expansion is exceeded. These insights can be leveraged to develop optimal transport strategies that balance both transport speed and bubble stability for targeted delivery applications.

The single droplet under shear is a foundational problem in fluid mechanics. In computational fluid dynamics (CFD), the two-dimensional (2D) problem offers advantages in both computational efficiency and relevance, yet it lacks a comprehensive theoretical treatment equivalent to that of the three-dimensional (3D) case. In this brief note, we present an analytical treatment of this problem beginning with a derivation of the Lamb solution for 2D Stokes flows and then applying it to obtain the flow field around a droplet in a purely extensional flow. Using these flow fields, expressions are obtained for the apparent viscosity, ${\mu }^{*}$, of a dilute 2D emulsion as well as a small deformation theory. We show that in the limit of both zero Reynolds number ($\text{Re}\to 0$) in which inertia is negligible and zero capillary number ($\text{Ca}\to 0$) in which surface tension prevents any droplet deformations, ${\mu }^{*}=\mu (1+f\left(\lambda \right)\varphi )+\mathcal{O}\left({\varphi }^2\right)$ with $f\left(\lambda \right)=(2\lambda +1)/(\lambda +1)$ where $\lambda$ is the ratio of the droplet viscosity to the matrix viscosity and $\varphi$ is the area fraction covered by the suspended phase. In addition, we show that in the capillarity-dominated regime ($\text{Ca}\ll 1$), the steady-state value, $D_T^{\infty }$, of the Taylor deformation parameter obeys $D_T^{\infty }=g\left(\lambda \right)\text{Ca}$, where Ca is the capillary number and $g\left(\lambda \right)=1$. This contrasts with the 3D case, where $g\left(\lambda \right)$ depends on $\lambda$. These results are then validated through direct numerical simulations (DNSs) of a single droplet at the center of a periodic square box undergoing simple shear. The DNS and theory are compared across a wide range of viscosity ratios ($0.01\le \lambda \le 100$) and area fractions ($0.002\le \varphi \le 0.125$) and they are found to agree asymptotically in the limit $\varphi \to 0$ for $\text{Ca}\ll 1/(\lambda +1)$. Our results provide a basic theoretical framework for interpreting 2D droplet simulations and provide clear benchmarks for CFD codes in 2D.

In this paper, we investigate the dynamics of Hele-Shaw flow in a multiply connected domain. We consider multiple fluid domains enclosed by a moving outer interface in a radial Hele-Shaw cell, with several inner interfaces separating these fluid regions. To compute the long-time evolution of interface morphologies, we develop a spectral-accurate boundary integral method and a nonstiff time updating scheme, together with a time adaptive scheme to speed up the computation. Our numerical results reveal that interface instabilities are strongly influenced by the initial configuration of fluid domains and physical parameters such as fluid viscosities. Notably, at early times, the fingering instability observed on the outer interface—triggered by the presence of inner interfaces—differs fundamentally from the classical perturbation-initiated growth in single-interface scenarios. Depending on their configuration, the inner interfaces can either promote or suppress the development of fingering on the outer boundary, offering a potential strategy for morphological control in practical applications. Motivated by the self-similar theory and the shape-control concept introduced in Li et al. [Phys. Rev. Lett. 102, 174501 (2009)], where self-similarity is only realized at large interface sizes under time-dependent flux, we demonstrate that one can preselect a self-similar limiting morphology and promote its formation at significantly smaller scales. This is achieved through a carefully designed multi-interface setup that promotes the desired symmetry while suppressing other unfavorable instabilities.

We examine flow and transport through an orifice in a flat wall separating semi-infinite atmospheres of two dissimilar gases. The analysis assumes steady conditions and order-unity values of the Schmidt number $\mathit{\text{Sc}}$ and Péclet number $\mathit{\text{Pe}}$, such that advection and diffusion contribute comparably to mass and momentum transport. Mixing between the two gases induces order-unity variations in viscosity and density, resulting in coupled concentration and velocity fields. The solution yields the mass transfer rates of both gases, expressed in terms of an appropriately defined Sherwood number, as well as the overpressure required to sustain the flow, all as functions of $\mathit{\text{Sc}}$ and $\mathit{\text{Pe}}$. An explicit analytical solution is obtained in the limit of small $\mathit{\text{Pe}}$, while numerical integration is used to describe flows with $\mathit{\text{Pe}}=O\left(1\right)$. The mixing of hydrogen and air is used as an illustrative example that serves to highlight the influence of large gas-molecular-weight differences on the flow structure and associated mixing rate, with additional selected results given for the case of hydrogen and water vapor.

In this work, we propose a phase-field-lattice-Boltzmann-based interfacial mass transfer model to better demonstrate the species transfer across the two-phase interface. In the model, the two-phase dynamics is governed by the Allen-Cahn equation, and the interfacial mass transfer behavior is described by a self-derived convection-diffusion equation, which shows a standard form with no source term compared with the available models. Then, we devise a multiple-relaxation-times (MRT) lattice Boltzmann scheme for their numerical solving. The simulations on typical interfacial mass transfer benchmarks indicate that the proposed phase-field-lattice-Boltzmann model shows superior interfacial mass transfer prediction performance when compared with the available models, particularly in the vicinity of the two-phase interface. The predicted concentration profile across the interface appears independent of the interface width. This model also shows the capability of predicting the interfacial mass transfer in large-density-ratio two-phase flows.

We investigate the mechanisms underlying the generation of broadband trailing-edge noise from an airfoil, focusing on the role of hydrodynamic structures with nonzero spanwise wavenumbers and the development of a corresponding reduced-order model. A wall-resolved compressible large-eddy simulation (LES) of a NACA0012 airfoil at 3° angle of attack, Reynolds number $\mathrm{Re}$ = 200 000, and Mach number $\mathrm{M}$ = 0.3 is performed. The simulation replicates the experimental setup of Demange et al. [AIAA Aviation Forum (2023)], including the tripping elements ensuring turbulent boundary layer development. The numerical domain has a large spanwise extent (43.75% of the chord) to allow for the investigation of large spanwise coherent structures. Validation against experimental data shows good agreement. The simulation results show that acoustic radiation from the trailing edge follows the scattering condition, whereby only hydrodynamic waves with spanwise wavenumbers lower than the acoustic wavenumber can generate propagative sound. Notably, the contribution from nonzero spanwise wavenumber modes becomes significant beyond the cut-on frequency at which the first nonzero spanwise acoustic mode becomes propagative. Through spectral proper orthogonal decomposition (SPOD), the associated flow structures are identified as streamwise-travelling wave packets convecting obliquely across the trailing edge. Reduced-order models based on acoustic-domain extended SPOD accurately reproduce the LES sound pressure levels within 2 dB, using only two modes per frequency–wavenumber pair. This compact representation paves the way for targeted noise-reduction strategies based on the control of the identified coherent structures.

We investigate the influence of expansion geometry on the flow field and turbulence structure in axisymmetric pipe flows through comparative analysis of abrupt (${90}^{\circ }$) and gradual (${45}^{\circ }$) area expansions with an area ratio of 2.56 at step-height Reynolds numbers of 25 000 and 35 000. Using refractive-index-matched stereo particle image velocimetry, we extract turbulence statistics with high spatial resolution. The gradual expansion consistently yields elevated turbulence levels, broader shear layers, enhanced Reynolds stress anisotropy, and stronger out-of-plane fluctuations. In contrast, the abrupt expansion generates a secondary vortex that disrupts the return flow, reducing shear layer interaction and turbulent kinetic energy (TKE) production. The governing mechanism is attributed to the geometry-induced modulation of the return flow. In the gradual case, the return flow is aligned with the sloped surface and impinges obliquely on the free-stream, generating a distributed region of high shear and sustained turbulence production leading to intensified TKE and anisotropy in the near-expansion region. These findings reconcile prior observations of increased pressure loss in sloped expansions and reveal the fundamental role of expansion slope in controlling turbulence generation and energy redistribution in separated flows. The observed trends suggest a generalizable mechanism relevant to a broader range of expansion angles and flow conditions.

A rotating stall occurring in the reversible pump turbine operating within the S-shaped region significantly impairs hydrodynamic stability, leading to severe torque oscillations and pressure pulsations. Currently, theoretical frameworks and quantitative predictions for stall inception are still lacking. This study develops a theoretical model for rotating stall based on small-disturbance theory. The model analyzes the resonance conditions and stability characteristics of disturbance waves by coupling internal flow perturbation dynamics with the external characteristics of the pump-turbine system. Key stall parameters, including the onset point, rotational speed, and the number of stall cells, are predicted based on the finite-difference-based numerical implementation. The results show that single-cell stall patterns are more dominant than two-cell patterns, with the former exhibiting a clear critical stability threshold. Complementarily, an unsteady flow simulation approach is adopted to capture transient flow behavior from runaway to low-flow conditions under four guide-vane openings. Pressure fluctuations in the vaneless area are analyzed using wavelet transform to identify the onset of rotating stall. Comparison between the numerical simulation and theoretical predictions confirms the model's accuracy and utility in predicting stall onset.

This study presents a spectral-fundamental solution (SFS) method which enables efficient simulation of large-scale nonlinear wave-body interactions. The SFS method combines spectral basis functions and fundamental solutions to achieve both global efficiency and local accuracy. Based on the linearity of the Laplace equation, it decomposes large-scale boundary-value problems into independent subproblems, enabling efficient full-domain computation. Numerical validations show that SFS achieves higher accuracy than the high-order spectral method for short, steep waves and outperforms the method of fundamental solutions in long-wave conditions. Applications to nonlinear ship waves in large-scale domains yield results in good agreement with experimental data, successfully capturing higher-order nonlinear effects. The simulations reveal the physical origins of distinct energy bands in the wave spectrogram and demonstrate how ship acceleration influences the ship-generated wake field. Furthermore, the simulations explain why high-speed ships exhibit wake angles that are narrower than classical predictions. Beyond ship waves, this efficient SFS framework can be extended to a wide range of unsteady wave-structure interaction problems in ocean engineering.

We show that floating ice blocks with asymmetric shapes can self-propel with significant speeds due to buoyancy-driven currents caused by melting. In water baths with temperatures between $10{}^{\circ }\mathrm{C}$ and $30{}^{\circ }\mathrm{C}$, model right-angle ice wedges are found to move in the direction opposite to the gravity current which descends along the longest inclined side. We describe the measured speed as a function of the length and angle of the inclined side, and the temperature of the bath in terms of a propulsion model which incorporates the cooling of the surrounding fluid by the melting of ice. The heat pulled from the surrounding liquid by the melting ice block generates a thermal convection flow, leading to momentum exchange and a net propulsion force. The translation velocity is explained by balancing the propulsion force by drag. We further show that the ice block moves robustly in a saltwater bath with ocean-like salinity and maintains the same direction of motion as in freshwater. A simplified model is further developed to describe the propulsion of asymmetric ice blocks in saltwater, incorporating the effects of rising meltwater and the sinking of the surrounding bath water due to cooling. For sufficiently large temperature, we find that the cooling-induced sinking flow generates a stronger force than the upward flow from the meltwater. Consequently, the net propulsion force is in the same direction and nearly the same magnitude as that observed in freshwater. These findings suggest that melting-driven propulsion may be relevant to the motion of icebergs in sufficiently warm oceanic environments.