The dynamics of a single vortex ring impinging on the concave hemicylindrical shell with different radii at $\mathrm{Re}=1500$ are explored experimentally. Five different ratios of hemicylindrical cavity radii to vortex ring are studied: $D_m/D_e=15,10,5,2,1$. Planar laser-induced fluorescence and two-dimensional particle image velocimetry techniques are adopted for flow measurements, and the finite-time Lyapunov exponent field based on the Lagrangian framework is employed to identify the Lagrangian coherent structures of the vortex dynamics. The experimental results indicate that for $D_m/D_e=15,10$ conditions, the impinging dynamics of the vortex ring are similar to the vortex ring interacting with a flat plate. The subvortex cluster consisting of secondary vortex rings and tertiary vortex rings, dominates the motion of the induced vortex rings after the primary vortex ring impinges with concave surfaces. For $D_m/D_e=5,2$ conditions, the collision of the vortex ring on the concave surfaces is quite different. The concave surface effectively constrains the primary vortex ring after impinging it. The concave secondary vortex ring rotates earlier than the straight-edged secondary vortex ring. Eventually, the straight-edged secondary vortex ring is lifted in the straight-edged direction, moving diagonally towards the collision axis, away from the solid wall. Subvortex rings in the final dominant flow field change from the tertiary to the secondary as the model radius decreases. As the diameter decreases to $D_m/D_e=1$, the primary vortex ring deforms farther in the straight-edged direction. After the straight-edged secondary vortex ring is formed, it moves vertically away from the wall. Finally, a dynamic model is proposed to illustrate the effects of cylindrical cavity radii on the vortex-ring impingement.

Laminar jets in crossflow are analyzed using direct numerical simulation to identify the source of vorticity leading to the formation of the counter-rotating vortex pair. A vorticity transport analysis conducted on steady cases shows that all counter-rotating vortex pair vorticity is generated in the nozzle walls for large velocity ratio jets ($R$), but that additional boundary layer vorticity is entrained at low $R$. The transport mechanisms are quantified and discussed in detail, including the influence of having a square jet cross section. The study also examines the effect of varying the velocity ratio in the range $0.25\le R\le 5$ and the jet Reynolds number in the range $100\le {\text{Re}}_{\text{jet}}\le 300$. Increasingly complex flow patterns are revealed, even in the steady regime, including the onset of bubble vortex breakdown of the counter-rotating vortex pair. Breakdown onset is quantified and analyzed in detail, revealing that it is a gradual process that depends on the jet vorticity and the adverse pressure gradient formed downstream of the jet inlet. Additionally, breakdown is discovered to precede the onset of unsteady flow for decreasing $R$ and fixed ${\text{Re}}_{\text{jet}}$ for jets with both cross sections. A newly discovered asymmetric instability is identified at ${\text{Re}}_{\text{jet}}=300$ and characterized, where each of the counter-rotating vortices undergoes breakdown while oscillating laterally at low frequency. Hairpin vortex shedding, typical of low $R$ laminar jets in crossflow, is captured in our simulations. Breakdown bubbles are identified for $R>0.4$, where the flow remains approximately steady in the near field. For $R\le 0.4$, the increasing fluctuation amplitude in the near field results in the rollup of fluid and the destruction of the breakdown bubbles in the instantaneous flow field.

High-order methods, such as the discontinuous Galerkin method, have gained increasing attention in the computational fluid dynamics community because they are expected to deliver high-accuracy results on complex flows and geometries. However, in realistic high Reynolds number flows, the significant computational cost and lack of robustness are unavoidable concerns when compared to low-order methods. The present paper develops a detached eddy simulation model based on the $k\text{−}g$ equations, where the near-wall scaling of the new transport variables suits the polynomial nature of the discontinuous Galerkin method. The hybrid modeling framework of “${\ell }^2\times \frac{1}{T}$” mimics traditional Smagorinsky and dynamic subgrid models in the eddy-resolving regions, and provides seamless hybrid modeling of the unresolved scales in coarse-mesh simulations of wall turbulence and separated flows. Robustness is achieved by both proper near-wall scaling of turbulence variables and the scale-dependent hybrid modeling of unresolved turbulence. For the latter, no extra cutoff filtering, overintegration, or additional viscosity is needed regardless of the mesh resolution. Our model can perform both traditional delayed detached eddy simulation and wall-modeled large eddy simulation for high Reynolds number turbulent flows like its predecessor, the adaptive ${\ell }^2\text{−}\omega$ model [Yin and Durbin, Int. J. Heat Fluid Flow 62, 499 (2016)]. By implementing the method in a spectral element discontinuous Galerkin solver, the proposed model is tested in a transonic airfoil with shock-turbulent boundary layer interaction.

Lagrangian acceleration has been investigated both experimentally and numerically in the past, and it has been shown to exhibit extreme fluctuations, which have been rationalized as events in which tracer particles get trapped into vortical structures such as vortex tubes or filaments. Here, we consider the statistics of acceleration within the multifractal framework, as in Biferale et al., Phys. Rev. Lett. 93, 064502 (2004), and investigate the statistics of Lagrangian acceleration using shell models of turbulence, as in Boffetta et al., Phys. Rev. E 66, 066307 (2002), that—by construction—do not contain vortical structures. Our analysis reveals that, despite not accounting for specific coherent vortex structures, the multifractal model accurately captures the extreme intermittent fluctuations observed in the acceleration, with predictions that remain robust across a wide range of Reynolds numbers.

We study the statistics of deformation of neutrally buoyant droplets in homogeneous isotropic turbulence (HIT), wherein the characteristic droplet size $R$ is smaller than the characteristic Kolmogorov scale $\eta$ of the turbulent flow. We systematically focus on the characterization of droplet deformation statistics obtained with various phenomenological (reduced-order) ellipsoidal models (EMs)—assuming that the droplet preserves the ellipsoidal shape at all times—with the droplet moving as a passive tracer in the turbulent flow. The predictions of the EMs are compared with ground-truth data obtained with three-dimensional fully resolved simulations without any ad hoc assumption on the droplet shape. Our work helps in elucidating the applicability of the EMs in describing droplet deformation in HIT at changing the capillary number $\text{Ca}={\tau }_{\sigma }/{\tau }_{\eta }$, weighting the relative importance of the droplet characteristic time ${\tau }_{\sigma }$ with respect to the turbulent flow characteristic time ${\tau }_{\eta }$.

This study systematically investigates the hypersonic near-continuum boundary-layer stability over a blunt cone at varying degrees of wall cooling and nose bluntness, offering insights into the rarefaction effects on linear stability mechanisms. The freestream conditions are Mach 8 at an altitude of 50 km. To accurately capture the local rarefaction effects, the slip boundary conditions and nonlinear constitutive relations are incorporated into the conventional Navier-Stokes (NS) equations and linear stability theory (LST) to compute the base flow and perform linear stability analysis. The effects of surface slip and shear nonequilibrium on the base flow and stability at varying wall-cooling degrees and nose bluntness are clarified. The results show that rarefaction effects lead to a thinning of the boundary layer in terms of base flow, primarily due to the influence of velocity-slip and shear nonequilibrium effects. Increasing the wall temperature largely enhances the slip effects at the wall, and decreasing the nose bluntness significantly intensifies the shear nonequilibrium effect in the boundary layer. As for stability, rarefaction effects stabilize the second-mode instability, and this stabilizing influence becomes more pronounced at higher wall temperatures or smaller bluntness. Detailed analyses reveal that velocity-slip plays a dominant role in stabilizing the second mode by modifying the steady base flow, whereas temperature-jump and shear nonequilibrium effects have comparatively weaker contributions. Furthermore, both bluntness and rarefaction contribute to stabilizing near-continuum boundary layer. However, the delay in second-mode critical locations induced by rarefaction effects is significantly greater than that caused by increased bluntness, particularly at lower Reynolds numbers based on bluntness in the near-continuum regime.

We study the role of the wall-normal Reynolds stress in hypersonic boundary layers and consider implications for RANS modeling. In low-Mach-number, zero-pressure-gradient boundary layers, the contribution of the wall-normal Reynolds stress to the wall-normal momentum equation is negligible. As a result, the wall-normal momentum equation indicates that pressure is uniform throughout the boundary layer. However, in hypersonic boundary layers, analysis indicates that the wall-normal Reynolds stress becomes significant compared to mean pressure, and the wall-normal momentum equation indicates that pressure must balance the wall-normal Reynolds stress. We validate this hypothesis using direct numerical simulation data of supersonic and hypersonic boundary layers. The results show that the wall-normal Reynolds stress balances with pressure, resulting in non-negligible pressure deficits in the log layer. We consider implications for RANS modeling and show that errors in standard models for the wall-normal Reynolds stress have a noticeable impact (upward of $5\%$ for a Mach 14 cold-wall flow) on wall quantities of interest, such as skin friction.

We present a phase-field model to study two-phase displacement with moving contact lines in a capillary tube. We construct a diffuse-interface formulation of solid-liquid surface energy by enforcing a consistent structure of the fluid-fluid interface between the bulk fluid and the solid surface. We first show, via simulation of equilibrium liquid slugs in a capillary tube, that this formulation allows prescribing arbitrary static contact angles and leads to the correct capillary pressure. We then propose a formulation to account for out-of-equilibrium dynamics near the contact line and demonstrate the ability of this generalized formulation to simulate spontaneous imbibition as well as viscously unstable, constant-rate displacements in a capillary tube. We show that our phase-field model captures the imbibition dynamics described by a theoretical model that combines classic Lucas-Washburn theory with Cox's law of dynamic contact angle. It also predicts wetting transition, thin-film formation, and interface pinch-off that quantitatively agree with recent experiments.

In this paper, we investigate inertially forced isothermal quantum turbulence (the coflow of normal and superfluid components) at temperatures of 1.6 and 2 K. The experiments are carried out in a large optical cryostat, where quasi-isotropic, homogeneous turbulence is generated using a double oscillating grid. Turbulence intensity is tuned by varying the grid stroke and frequency. The flow is probed via two-dimensional (2D) and three-dimensional (3D) reconstructions of quasi-isodense microsphere trajectories, from which we extract the large-scale properties of the flow in the fully turbulent regime for different Reynolds numbers: the turbulent velocity fluctuations, the energy transfer rate, and the integral length scale. Additionally, we determine the mean vortex line density $\mathcal{L}$ via attenuation of a second sound standing wave across the entire measurement volume. Our results confirm with an improved accuracy that the intervortex spacing $\ell =1/\sqrt{\mathcal{L}}$ scales with the Reynolds number ${\text{Re}}_{\kappa }$ (based on the quantum of circulation $\kappa$) as $\ell \propto {\text{Re}}_{\kappa }^{-3/4}$, with a well-defined numerical prefactor and no observed temperature dependence. This scaling recalls that of the dissipative length scale in classical Kolmogorov (K41) turbulence and it lead previous authors to interpret $\ell$ as an effective dissipation length scale. However, in our temperature range, this interpretation is not consistent with the apparent temperature independence of the prefactor. Based on those arguments, we propose an alternative interpretation that suggests that the intervortex distance in coflow turbulence is the consequence of the quantum-restricted depth of the superfluid component energy cascade.

Direct numerical simulations (DNS) of microscale fluid-structure interactions (mFSI) in multicomponent multiphase flows pose many challenges, including the thermodynamic consistency of multiphysics couplings, tracking of moving interfaces, dynamics of moving triple-phase contact lines, and the coupling of multiphase hydrodynamics with phase transition dynamics. We propose and validate a generic DNS approach: diffuse-resistance-domain approach. It overcomes the above challenges by employing Onsager's variational principle to formulate dynamic models and combining traditional diffuse-interface models for fluid-fluid interfacial dynamics with a novel implementation of complex fluid-solid interfacial conditions via smooth interpolations of dynamic-resistance coefficients across interfaces. After careful validation by numerous benchmark simulations, we simulated several cutting-edge, challenging mFSI problems across diverse fields. This generic DNS approach offers a promising tool for elucidating physical mechanisms, manipulating microscale fluid dynamics, and optimizing engineering processes across diverse fields.

When do mucus films plug lung airways? Using reduced-order simulations of a large ensemble of randomly perturbed films, we show that the answer is not determined by just the film's volume. While very thin films always stay open and very thick films always plug, we find a range of intermediate films for which plugging is uncertain. The fastest-growing linear mode of the Rayleigh-Plateau instability ensures that the film's volume is divided among multiple humps. However, the nonlinear growth of these humps can occur unevenly, due to spontaneous axial sliding—a hump that slides rapidly can sweep up a disproportionate share of the film's volume and so form a plug. This sliding-induced plugging is robust and prevails with or without gravitational and ciliary transport.

Soft substrates are deformed by liquid-vapor surface tension upon contact with liquid droplets, forming the well-known wetting ridge. This ridge dynamically propagates with the moving contact line and critically influences liquid spreading. Here, we experimentally investigate gravity-driven sliding dynamics of water droplets on vertically tilted silicone layers whose viscoleasticity is characterized by the Chasset-Thirion model with the exponent $m$. At low Bond numbers, the sliding velocity scales with droplet size as $V_S\sim D^{\frac{2}{m}}$. While in the thin-film limit, velocity exhibits a pronounced power-law dependence on nominal substrate thickness, $V_S\sim \mathrm{\Pi }{\left(h\right)}^{-\frac{1}{m}}$. We rationalize these observations by quantifying viscoelastic dissipation within the soft layer and balancing it against the gravitational driving force using an energy-conservation framework. Our findings offer avenues for designing advanced soft coatings, anti-fouling and self-cleaning surfaces, and biomedical devices.

We use microparticle image velocimetry and numerical simulations to study the vortex evolution in liquid-liquid plug flows in a $400\mu \mathrm{m}$ T-junction microchannel. Experiments are conducted using the $\left[\mathrm{C}4\mathrm{mim}\right]\left[{\mathrm{T}}_2\mathrm{fN}\right]$ ionic liquid as the continuous phase and a glycerol-water blend as the dispersed phase, giving a dispersed to continuous phase viscosity ratio, $\lambda$, of 0.117. The range of mixture velocities studied is $0.002-0.03$ m/s, which corresponds to a capillary number range of ${\text{Ca}}_p\sim 0.0075-0.16$. We characterize the vortical structures based on geometry, vorticity, and circulation times within the plugs. Good agreement is found between the experimental data and the numerical predictions in terms of plug length, film thickness, and circulation patterns. The plug length is found to decrease while the film thickness increases with ${\text{Ca}}_p$. Three pairs of vortices are formed within the plug in a reference frame moving with the steady plug speed. The pairs comprise a main pair that occupies the central region of the plug and two secondary pairs located at the plug front and rear. The secondary vortices diminishment with ${\text{Ca}}_p$ is quantified based on their geometry and vorticity, subsequently correlated to the critical film thickness for vortex loss based on the predictions of Balestra et al. [Microfluid. Nanofluid.22, 67 (2018)]. It is found that the front and rear secondary vortex pairs diminish at different rates depending on ${\text{Ca}}_p$. With increasing ${\text{Ca}}_p$, based on their size, the rear vortex pair is lost before the front one, while, based on vorticity, only the front vortex pair is lost.

The assimilation and prediction of phase-resolved surface gravity waves are critical challenges in ocean science and engineering. Potential flow theory (PFT) has been widely employed to develop wave models and numerical techniques for wave prediction. However, traditional wave prediction methods are often limited. For example, most simplified wave models have a limited ability to capture strong wave nonlinearity, while fully nonlinear PFT solvers often fail to meet the speed requirements of engineering applications. This computational inefficiency also hinders the development of effective data assimilation techniques, which are required to reconstruct spatial wave information from sparse measurements to initialize the wave prediction. To address these challenges, we propose a solver method that leverages physics-informed neural networks (PINNs) that parametrize PFT solutions as neural networks. This provides a computationally inexpensive way to assimilate and predict wave data. The proposed PINN framework is validated through comparisons with analytical linear PFT solutions and experimental data collected in a laboratory wave flume. The results demonstrate that our approach accurately captures and predicts irregular, nonlinear, and dispersive wave surface dynamics. Moreover, the PINN can infer the fully nonlinear velocity potential throughout the entire fluid volume solely from surface elevation measurements, enabling the calculation of fluid velocities that are difficult to measure experimentally.

Microorganisms' undulatory swimming in anisotropic fluids near a flat wall has emerged as a key area of interest, driven by the potential to inform the design and fabrication of microdevices through a deeper understanding of their complex behaviors. However, the swimming mechanism has not yet been clarified. To address this gap, we employ asymptotic analysis and numerical study to investigate the dynamics of microswimmers swimming near a wall in lyotropic liquidcrystal polymers at low Reynolds numbers using Doi's Q-tensor model. Our study reveals that infinitely long sheets (i.e., Taylor's swimming sheet model) speed up as they are next to the wall, accompanied by a notable increase in swimming efficiency, surpassing those observed during the free swimming scenario. We demonstrate that stiff finite-length swimmers can gradually reorient themselves and be trapped when close enough to the wall, due to a net hydrodynamic torque induced by the asymmetric distribution of the flow field around the body. These findings suggest that the wall effect is pivotal in microorganisms' swimming performance.

This study investigates the stability of a liquid film containing colloidal particles flowing along the exterior surface of a vertical cylinder due to gravity. The governing equation for the location of the liquid-gas interface is derived by simplifying the mass and momentum balance equations within the lubrication approximation. The evolution of bulk concentration is modeled by simplifying the advection-diffusion equation assuming dominant radial diffusion. Following the Krieger-Dougherty and Stokes-Einstein equations, the suspension viscosity and colloidal diffusion coefficients are considered functions of bulk concentration. These coupled film and concentration evolution equations are subsequently perturbed using a normal mode analysis to obtain the eigenvalue problem. The resulting dispersion relation is analyzed to study the influence of bulk concentration, surface concentration, particle diffusion, and the solutal Marangoni number on the stability of the system. The presence of bulk colloids leads to an increase in the viscosity and stabilizes the flow. The Marangoni stress due to concentration gradient at the liquid-gas interface stabilizes the curvature pressure-driven instability at moderate Marangoni numbers while introducing another unstable mode driven by surfactant at larger Marangoni numbers. The nonlinear analysis recovers the growth rates predicted by the linear analysis. The pattern for the first mode indicates in-phase evolving waves for film thickness and surface concentration, while a phase lag is observed between the two waves for the second mode. The mechanisms for the two modes are highlighted by using a flux analysis. At larger values of the Bond number, the film behavior asymptotically approaches that of the flow over a planar substrate. A rigid interface limit is attained at large values of the Marangoni number and the predicted growth rate is found to be independent of the concentration profile.

This work characterizes and classifies the geometric configurations that can arise in the relative equilibria of four point vortices on the unbounded plane. The problem is approached through a two-dimensional parametric formulation, enabling the identification of fourth vortex locations that yield relative equilibria for a given triangular arrangement of the first three vortices. Building on the configuration matrix approach, a bivariate polynomial is derived from the matrix minors such that its roots determine the admissible positions of the fourth vortex. In addition, a detailed analytical description of how the root structure of this polynomial varies with the two parameters defining the vortex triangle is also presented. The results show that the fourth vortex locations generally form a one-dimensional continuum, consisting of a disconnected pair of bounded and unbounded curves. Several important families of relative equilibria are identified by tracing how the two curves evolve across the parameter space. The analytical results, supported by numerical examples, offer a comprehensive geometric description of the configuration space and its bifurcation structures.

The search for solutions to the theory of weakly nonlinear internal gravity wave turbulence is an active research topic. It is notably stimulated by the fact that this regime could drive fine-scale ocean dynamics for which the identification of a physical model could yield improved parametrizations in global oceanic models. In this context, analytical works lead to diverse predictions and the experimental observation of a regime of developed weakly nonlinear internal wave turbulence constitutes a major, still unachieved, objective of experimentalists in the field. In this study, building on recent experimental developments, we present laboratory observations of internal gravity wave turbulence in a linearly stratified fluid, performed in a large-scale three-dimensional facility allowing the forcing of long-wavelength internal waves. Our setup allows us to access large Reynolds numbers favoring the development of turbulent power-law spectra while keeping the Froude number relatively low in order to remain weakly nonlinear. As the forcing amplitude increases, the flow seems to approach a wave turbulence regime: We indeed observe the progressive construction of a continuous distribution of energy in both the frequency and wave number spaces, whereas the spatiotemporal spectra indicate that the energy remains almost exclusively carried by internal gravity waves, verifying the dispersion relation. We finally show that, as the transition to turbulence proceeds, the bicoherence spectrum of the velocity field becomes smooth over the internal wave frequency domain, taking values of the order of the Froude number. While these observations are in line with the phenomenology of weakly nonlinear wave turbulence, the power laws in $k^{-3}$ we report over about a decade for the horizontal and vertical spatial energy spectra agree with the prediction that can be made from raw dimensional arguments for a strongly nonlinear so-called saturated wave turbulence. Whether these power laws could alternatively be compatible with a weakly nonlinear wave turbulence regime remains to be explored theoretically.

This study aims to elucidate the turbulent energy cascade and changes in vortex topology resulting from the oblique collision of a vortex ring with a vortex tube, governed by their initial circulations (CR = ${\mathrm{\Gamma }}_t/{\mathrm{\Gamma }}_r$, where ${\mathrm{\Gamma }}_t$ and ${\mathrm{\Gamma }}_r$ are the initial circulations of the tube and ring, respectively), at a Reynolds number (${\text{Re}}_{{\mathrm{\Gamma }}_r}$) of 12 000. The passing-through phenomenon is observed for CR = 0.1, where the vortex ring moves through the vortex tube without its deformation and generation of the small-scale vortices. At CR = 0.2, the stronger vortex ring entrains the weaker vortex tube in many rounds, leading to the breakdown of the entrained vortex tube parts into small-scale vortices, creating a turbulent flow with its energy cascade's slope nearly fitting to the Kolmogorov $k^{-5/3}$ slope. For higher CR = 0.5, the vortex reconnection partially occurs, where the vortex tube links with half of the vortex ring and wraps around another half of the ring, inducing a strong twisting of large-scale vortices and the formation of numerous small-scale vortices. For CR = 0.75, 1.0, and 1.5, the first reconnection creates a distorted vortex tube, and then this vortex reconnects itself to establish a new vortex ring and a new vortex tube. The turbulent flow at CR = 0.75 and 1.5 induced during the second reconnection is characterized by the $k^{-5/3}$ slope for the energy cascade, while not observed in the first reconnection. The change in the topology of the vortex structures, which later leads to the reconnection, is caused by the stretching and twisting of large-scale vortices. The induced small-scale vortices associated with turbulent flow development are observed in regions of high helicity, accompanied by the twisting of large-scale vortex structures. Furthermore, we observe that increasing ${\text{Re}}_{{\mathrm{\Gamma }}_r}$ promotes the formation of small-scale vortices and amplifies the deformation and instability of vortex cores.

This study investigates the two- and three-dimensional convective and absolute instability characteristics of planar viscoelastic jet flows using the Oldroyd-B and Giesekus models. Analyzing instability in different types of flows is fundamental for understanding their behavior in various natural and industrial applications. Convective instability refers to disturbances that propagate and grow downstream, while absolute instability involves disturbances that grow over time regardless of their position in the flow. Understanding these phenomena can help optimize industrial processes and predict complex flow behaviors, for example. Results indicate that concerning convective instability, the Giesekus model exhibits a larger unstable region compared to the Oldroyd-B and Newtonian models. On the other hand, the Oldroyd-B model is more susceptible to absolute instability than the Giesekus model. Notably, in the Giesekus model, the mobility parameter ${\alpha }_G$ significantly influences the occurrence of absolute instability, which only occurs for small values of ${\alpha }_G$, for which the fluid tends to the Oldroyd-B behavior. For the tested parameters, only low values of ${\alpha }_G$ (close to the Oldroyd-B model, which corresponds to ${\alpha }_G=0$) led to the emergence of absolute instability, while larger values did not. These observations apply to both two-dimensional and three-dimensional disturbances.