We use the conservative phase-field lattice Boltzmann method to investigate the dynamics when a Newtonian droplet comes in contact with an immiscible viscoelastic liquid film. The dynamics of the three liquid phases are explored through numerical simulations, with a focus on illustrating the contact line dynamics and the viscoelastic effects described by the Oldroyd-B model. The droplet dynamics are contrasted with the case of a Newtonian fluid film. The simulations demonstrate that when the film is viscoelastic, the droplet dynamics become insensitive to the film thickness when the polymer viscosity and relaxation time are large. A viscoelastic ridge forms at the moving contact line, which evolves with a power-law dependence on time. By rescaling the interface profile of the ridge using its height and width, it appears to collapse onto a similar shape. Our findings reveal a strong correlation between the viscoelastic stress and the interface shape near the contact line.

This paper sets out to explore the modulational (or Benjamin-Feir) instability of a monochromatic wave propagating in the presence of damping such as that induced by sea ice on the ocean surface. The fundamental wave motion is modelled using the spatial Zakharov equation, to which either uniform or nonuniform (frequency-dependent) damping is added. By means of mode truncation the spatial analog of the classical Benjamin-Feir instability can be studied analytically using dynamical systems techniques. The formulation readily yields the free surface and its envelope, giving insight into the physical implications of damping on the modulational instability. The evolution of an initially unstable mode is also studied numerically by integrating the damped, spatial Zakharov equation, in order to complement the analytical theory. This sheds light on the effects of damping on spectral broadening arising from this instability.

We study the stability of gravity-driven viscous liquid films flowing down a vertical cylinder that is uniformly coated with a thin layer of elastic solids. Combining the gravity-driven viscous flows with the elastic deformation of the coated soft layer, we formulate a long-wave model to describe the evolution of a film flow-soft structure coupled system. Based on the model, we systematically examine the impact of the coating properties, including the elasticity and thickness on the temporal and spatiotemporal stability. Temporal stability analysis shows that the soft layer plays a dual role, namely, the elasticity acts as a destabilizing factor, leading to large deformations of both film interface and soft surface. However, due to the geometrical effect, increasing the layer thickness stabilizes the Rayleigh-Plateau instability. By contrast, the linear phase speed is always enhanced with increasing the elasticity or the thickness of the coated layer. We then analyze the spatiotemporal nature of free-surface instabilities and find that the elasticity can trigger the film flows from being absolutely unstable to convectively unstable. Transient numerical solutions of the full asymptotic model further verify the predictions from linear stability analysis, and more importantly, reveal the nonlinear effect of the softness. Compared to liquid films falling down the cylinder with rigid walls, the soft surface can enhance the coalescence of faster, larger sliding droplets with preceding slower, smaller sliding ones, thus resulting in a more unstable system. Our study highlights the potential of coating a thin layer of soft materials onto the walls of substrate to regulate the dynamics of liquid film systems, and may have implications for the emerging bioinspired applications; for instance, the large-scale collection and transport of water on flexible microfiber arrays.

High-speed videos in an optical cryostat, with frame rates up to $5\times {10}^6$ fps, are used to study the dynamics of laser-induced cavitation in helium near the critical point and in the supercritical region. The propagation of strong shock waves are observed in both regimes. The time dependence of the cavitation bubble radius as well as the acoustic pressure field outside the bubble are described by standard compressible flow models. In the temperature range $4K<T<5.2K$, a symmetric cloud of micron-scale bubbles are observed outside the main cavitation bubble as it approaches its maximum radius which is due to homogeneous nucleation and spinodal decomposition in the low-pressure fluid outside the bubble. Nucleation of secondary bubbles is also observed far below the critical point, but this requires large negative pressures that can be generated by shock waves that reflect from the primary bubble.

This work deals with the stability of two-phase stratified air-water flows in horizontal circular pipes. For this purpose, we performed a linear stability analysis, which considers all possible three-dimensional infinitesimal disturbances and takes into account deformations of the air-water interface. The main results are presented in the form of stability maps, which compare well with the available experimental data. The neutral stability curves are accompanied by the corresponding wavenumbers and wave speeds of the critical perturbations, as well as by spatial patterns of their velocity components. Accordingly, several modes of the critical perturbation are revealed. Long waves are found to be the critical perturbation over part of the stability boundary, and they are affected by the surface tension due to the confinement effect of the lateral direction. Exploring the effect of pipe diameter on the stability boundary and critical perturbations shows that for small water holdups (i.e., thin water film) the scaling of the critical gas velocity by the gas Froude number is valid for pipe diameters larger than about 0.1 m, where the surface tension effects due to the lateral confinement become negligible. Comparing results obtained in pipe, square-duct, and two-plate geometries, we show that there are cases where the simplified geometry of two parallel plates can be employed to model the realistic geometry reasonably well.

Many dense granular systems are non-monodisperse, consisting of particles of different sizes, and will segregate based on size during flow. This phenomenon is an important aspect of many industrial and geophysical processes, necessitating predictive continuum models. This paper systematically studies a key aspect of the three-dimensional nature of segregation and diffusion in flowing, dense, bidisperse granular mixtures—namely, segregation and diffusion acting along the direction perpendicular to the plane of shearing, which we refer to as the anti-plane modes of segregation and diffusion. To this end, we consider discrete-element method (DEM) simulations of flows of dense, bidisperse mixtures of frictional spheres in an idealized configuration that isolates anti-plane segregation and diffusion. We find that previously developed constitutive equations, calibrated to DEM simulation results from flows in which both the segregation and diffusion processes occur within the plane of shearing, do not capture aspects of the anti-plane segregation dynamics. Accordingly, we utilize DEM simulation results to inform and calibrate constitutive equations for the segregation and diffusion fluxes in their anti-plane modes. Predictions of the resulting continuum model for the anti-plane segregation dynamics are tested against additional DEM simulation results across different cases, while parameters such as the shear strain rate and mixture composition are varied, and we find that the calibrated model predictions match well with the DEM simulation results. Finally, we suggest a strategy for generalizing the constitutive forms for the segregation and diffusion fluxes to obtain three-dimensional constitutive equations that account for both the in-plane and the anti-plane modes of the segregation and diffusion processes.

This paper investigates the evolution of the Euler equations near a potential blow-up solution. We employ an approach where this solution exhibits second-type self-similarity, characterized by an undetermined exponent $\nu$. This exponent can be seen as a nonlinear eigenvalue, determined by the solution of a self-similar partial differential equation with appropriate boundary conditions. Specifically, we demonstrate the existence of an axisymmetric solution of the Euler equations by expanding the axial vorticity using associated Legendre polynomials as a basis. This expansion results in an infinite hierarchy of ordinary differential equations, which, when truncated up to a certain order $N^{*}$, allows for the numerical resolution of a finite set of ordinary differential equations. Through this numerical analysis, we obtain a solution that satisfies the appropriate boundary conditions for a specific value of the exponent $\nu$. By exploring various truncations, we establish a sequence in $N^{*}$ for the parameter ${\nu }_{N^{*}}$, providing evidence of the convergence of the exponent $\nu$. Our findings suggest a self-similar exponent $\nu \approx 2$, presenting a promising path for a numerical or analytical approach indicating that $\nu$ may indeed be exactly 2.

The dual-channel characteristics of large-scale helicity transfer in compressible turbulent flows, including subgrid-scale (SGS) and viscosity terms, are investigated. After selecting a suitable definition for large-scale helicity, we confirm the existence of the dual channel of SGS and viscosity terms of large-scale helicity governing equations and theoretically prove that no dual pressure term channel exists. The second channel of the SGS and viscosity terms also consists of two terms, which originate from the rotation of the SGS stress and the baroclinic of the velocity and density gradients, respectively. The identical relationship of the ensemble averages of the dual channel of SGS and viscosity terms can be theoretically and numerically confirmed, whereas their second channel which is associated with shocklets is more intermittent. For the SGS term, the compression regions are dominant in contrast to the expansion regions, and the strain regions are dominant in contrast to the rotation regions in the inertial scale range. The viscous dissipation mechanism of large-scale helicity differs from that of large-scale kinetic energy. It is dominated by the first channel on the inside of the vortex structure and by the second channel on the outside. The further decompositions of the second channel of the SGS and viscosity terms provide a possible mechanism for the inverse helicity transfer. This means that expansion motions promote inverse helicity transfer through the second terms of their second channels.

We consider the buoyancy-driven rise and interaction between two initially stationary and gravity-aligned bubbles of wide radii ratio and constant volume in an elasto-visco-plastic material, extending our previous work regarding bubbles of equal radii [Kordalis et al., Phys. Rev. Fluids 8, 083301 (2023)]. Primarily we consider a 0.1% aqueous Carbopol solution and model its rheology with the Saramito-Herschel-Bulkley constitutive model. Initially, we investigate the dynamics for a specific initial separation distance in a wide range of bubble radii, and we determine the conditions leading to three distinct patterns: bubble approach, bubble separation, and establishment of a constant distance between them. Specifically, when the leading bubble (LB) is smaller than the trailing bubble (TB), the bubbles approach each other due to the smaller buoyancy of the leading bubble. Strong attraction also occurs when the ratio of buoyant over viscous force of both bubbles is considerable. On the other hand, when the size of the TB is such that this ratio is moderate or small, the pattern is dictated by the size of the LB: A significantly larger LB compared to the trailing one causes separation of the pair. On the contrary, an only slightly larger LB may result in the bubbles rising with the same terminal velocity establishing a constant distance between them, the magnitude of which is mainly determined by the elastic response of the surrounding medium. The coupling of a negative wake behind the LB with a slight modification of the stresses exerted at its rear pole generates this dynamic equilibrium. The same equilibrium may be achieved by other specific pairs of bubble sizes for different initial distances of the pair if a critical initial distance is exceeded. Below this critical value, the bubbles approach each other. Finally, we construct maps of the three patterns with trailing bubble radius versus bubble radii ratio for different initial separation distances and material properties.

In this paper, we experimentally investigate the rebound dynamics of droplets on dry ice surfaces, unveiling the mechanism behind the inverse Leidenfrost phenomenon. We demonstrated that the underlying mechanism driving the inverse Leidenfrost phenomenon is the lift force from the air film generated by the sublimation of dry ice. The air film prevents droplet condensation, facilitating the droplet rebound. However, the presence of film significantly depends on impact conditions. During the early spreading stage, bubbles nucleate at the contact line due to the sublimation, then the bubbles grow and gradually form an air film. We showed that the droplet rebound occurs only when the air film fully forms before the maximum spreading stage. Otherwise, the contact line is frozen, ultimately preventing rebound. We propose a theoretical expression of critical air film thickness that determines whether the droplet rebounds. Based on the expression, we ultimately established a theoretical criterion for droplet rebound via thermodynamic and fluid dynamics principles. To validate our developed theoretical criterion, we further investigated the inverse Leidenfrost phenomenon for different fluids, Weber numbers, and different temperatures of droplets. The results demonstrate a high consistency between the predicted results of our theoretical criterion and experimental results.

Odd viscosity is a transport coefficient that can occur when fluids experience breaking of parity and time-reversal symmetry. Previous knowledge indicates that cylinders in incompressible odd viscous fluids, under no-slip boundary conditions, do not exhibit lift force, a phenomenon that poses challenges for the experimental detection of odd viscosity. This study investigates the impact of slip in Stokes flow, employing the odd generalization of the Lorentz reciprocal theorem. Our findings reveal that, at linear order in slip length, lift does not manifest. Subsequently, we explore the scenario involving a thin sheet with momentum decay as well as that of a finite system size, demonstrating that for Stokes flow lift does occur for the second-order slip length contribution. We address cylinder flow beyond the Stokes approximation by solving the Oseen equation to obtain a fluid profile that shows an interplay between odd viscosity and inertia, and acquire an explicit expression for Oseen lift at leading order in slip length.

We study the temporal fluctuations of the flux of surface potential energy in surface quasi-geostrophic (SQG) turbulence. By means of high-resolution, direct numerical simulations of the SQG model in the regime of forced and dissipated cascade of temperature variance, we show that the instantaneous imbalance in the energy budget originates a subleading correction to the spectrum of the turbulent cascade. Using a multiple-scale approach combined with a dimensional closure we derive a theoretical prediction for the power-law behavior of the corrections, which holds for a class of turbulent transport equations known as $\alpha$ turbulence. Further, we apply a method to disentangle the equilibrium and nonequilibrium contribution in the instantaneous spectra, which can be generalized to other turbulent systems.

Townsend's attached-eddy model (AEM) is one of the most widely used models in explaining and predicting the logarithmic region of wall turbulence. Townsend pioneered the postulate that wall-attached eddies exhibit self-similar velocity distributions. This premise has led to the derivation of velocity variance scalings in the logarithmic region. In particular, the attached eddies have been extracted at moderate scales and have been illustrated to contain the most kinetic energies in the logarithmic region. In the present contribution, we derive analytically the scalings of the moments of velocity gradients of attached eddies by using the AEM. The direct numerical simulation data with the moderate-scale extraction of attached eddies show good agreement with the derived scalings. Moreover, the contributions of different-scale structures to the moments of velocity gradients are compared, showing that the wall scalings of all-scale velocity gradients are interestingly half of moderate-scale attached eddies. This also indicates the non-negligible influence of the small-scale eddies on the velocity gradients in the logarithmic region. In addition, there are departures in the moments of velocity Hessian, inspiring future improvement in the extraction method of attached eddies.

Steady-state interfacial waves exhibiting class-III triad resonance are investigated in a two-layer liquid with a free surface. Two independent linear dispersion relationships related to surface and internal modes exist in the idealized model. One-dimensional class-III triad resonance requires the presence of two short surface wave modes and one long internal wave mode in a copropagating wave system. Convergent series solutions are achieved by the homotopy analysis method (HAM) for steady-state interfacial wave groups involving resonant triads and quartets. Unlike conventional progressive interfacial waves that have small surface amplitude and large interface amplitude, the free surface wave height is far larger than that of the internal interface waves because the resonance interactions comprise multiple surface wave modes and a single internal wave mode. As the upper layer thickness increases, energy from the interface is transported to the free surface, and energy in the whole wave system shifts from shorter to longer resonant triads and quartets. Our results indicate that steady-state interfacial waves with class-III exact and near-resonance interactions among surface and internal wave modes could occur in cases representative of the real ocean.

It is well known that the scale-similarity class of subgrid models have a high correlation with the actual subgrid stresses in a priori tests. However, these models are typically underdissipative and not robust enough to be practically useful for large-eddy simulation. On the other hand, the dynamic Smagorinsky model (DSM), which is a popular subgrid model, is sufficiently dissipative and robust, but has a lower correlation with actual subgrid stresses in a priori tests. There have been many successful attempts to combine the two models into a “mixed” subgrid model that have typically retained the favorable properties of both. However, most dynamic mixed models require two or more levels of test filtering beyond the (often implicit) grid filtered quantities that are solved, in contrast to a single test filtering operation for the dynamic Smagorinsky model. The additional cost involved in test filtering has likely hindered the widespread use of dynamic mixed models in production codes. We propose an efficient dynamic mixed model that is constrained to have the same subgrid dissipation as the DSM model, and only requires a single level of test filtering. Thus, the additional computational cost is negligible compared to the DSM model. A posteriori simulations of the turbulent channel flow reveal that the proposed mixed model is as robust as the DSM model, and more accurate on coarser grids. Notably, smooth-body turbulent separation is better captured by the new model when combined with a standard wall model.

We report on the melting dynamics of ice suspended in fresh water and subject to natural convective flows. Using direct numerical simulations we investigate the melt rate of ellipsoidal objects for $2.32\times {10}^4\le \text{Ra}\le 7.61\times {10}^8$, where Ra is the Rayleigh number defined with the temperature difference between the ice and the surrounding water. We reveal that the system exhibits nonmonotonic behavior in three control parameters. As a function of the aspect ratio of the ellipsoid, the melting time shows a distinct minimum that is different from a disk which has the minimum perimeter. Furthermore, also with Ra the system shows a nonmonotonic trend, since for large Ra and large aspect ratio the flow separates, leading to distinctly different dynamics. Lastly, since the density of water is nonmonotonic with temperature, the melt rate depends nonmonotonically also on the ambient temperature, as for intermediate temperatures $(4{}^{\circ }\mathrm{C} – 7{}^{\circ }\mathrm{C})$ the flow is (partially) reversed. In general, the shape which melts the slowest is quite distinct from that of a disk.

Electroconvection (EC) turbulence is an important branch of electrohydrodynamics (EHD). Because the turbulence model for EHD has not been well studied, in this work we apply the large eddy simulation (LES) to electrohydrodynamic turbulence based on the lattice Boltzmann method (LBM). The eddy-viscosity methods (the Smagorinsky and wall-adapting local eddy-viscosity models) are used to model the momentum equation, and the charge transport equation is modeled with the help of the turbulent Schmidt number. Three EC cases are chosen to test the reliability of the LBM-LES models, including two-dimensional (2D) EC turbulence in square and rectangular cells, and three-dimensional (3D) EC turbulence between two parallel plates. For 2D cases, the LES results are compared to the results of different numerical methods, including direct numerical simulation and LES. The long-time statistics of maximum velocity, charge current and its probability distribution, and flow evolution are used to validate the 2D EC turbulence. We also analyze the flow patterns and average characteristics for 3D cases. The LES results could capture the main flow features of EC turbulence for all cases, and demonstrate a good agreement when compared with references. The mentioned LBM-LES models have demonstrated reliability and high computational speed, making them suitable for further simulations of electrohydrodynamic turbulence.

It is known that, beyond a critical speed, the straight contact line of a partially -wetting liquid destabilizes into a corner. One of the earliest theoretical works exploring this phenomenon [Limat and Stone, Europhys. Lett. 65, 365 (2004)] elicited a self-similar conical structure of the interface in the viscous regime. However, noting that inertia is not expected to be negligible at contact line speeds close to and beyond the critical value for many common liquids, we provide the leading-order inertial correction to their solution. In particular, we find the self-similar corrections to the interface shape as well as the flow field, and also determine their scaling with the capillary number. We find that inertia invariably modifies the interface into a cusplike shape with an increased film thickness. Furthermore, when incorporating contact line dynamics into the model, resulting in a narrowing of the corner as the contact line speed increases, we still observe an overall increase in the inertial contribution with speed despite the increased confinement.

Carotid artery atherosclerosis is a significant contributor to mortality in the United States. While it is recognized that low wall-shear stresses trigger plaque formation, there is a limited comprehension of the internal vortical structures that impact these stresses and how they differ between a healthy and a disease-prone, high-risk patient cohort. Our objective is to determine which driving factors, such as anatomical features (artery geometry) and mass-flow split, govern vortex behavior. Physiological pulsatile flow computational fluid dynamics simulations were performed on a “healthy” and a “disease-prone” carotid artery bifurcation model. Geometry and flow effects are investigated separately by simulating a third hybrid model having a healthy geometry with outlet boundary conditions imposing disease-prone flow conditions. This “unhealthy $\mathrm{\Delta }\mathrm{P}$” model recreated disease-prone mass-flow split and internal carotid artery sinus axial pressure gradient conditions in a healthy carotid artery bifurcation geometry. The results of our study revealed that the main vortex's time of formation is primarily dictated by carotid artery bifurcation geometry, whereas its lifespan is determined by the flow conditions. The main vortex's spatial expansion, as well as its circulation decay rate, are dictated by the geometry, not the flow conditions. We conclude that a high internal carotid artery mass flow rate and a higher favorable pressure gradient maximum magnitude occurring near peak systole are strong indicators of a high predisposition towards atherogenesis.

One mechanistic interpretation of baroclinic instability is that of mutual constructive interference of Rossby edge waves. The suppression of baroclinic instability over slopes has been widely established, where previous research argues that a sloping boundary modifies the properties of these Rossby edge waves, but does not provide a mechanistic explanation for the suppression that is valid over all parameter space. In the context of an Eady problem modified by the presence of a sloping boundary, we provide a mechanistic rationalization for baroclinic instability in the presence of slopes that is valid over all parameter space, via an equivalent formulation explicitly in terms of Rossby edge waves. We also highlight the differences between edge-wave phase shifts and normal-mode phase tilts, showing that the edge-wave phase shifts should be the ones that are mechanistically relevant, and normal-mode phase tilt is a potentially misleading quantity to use. Further, we present evidence that the edge-wave phase shifts but not normal-mode phase tilts are well correlated with geometric quantities diagnosed from an analysis framework based on eddy variance ellipses. The result is noteworthy in that the geometric framework makes no explicit reference to the edge-wave structures in its construction, and the correlation suggests the geometric framework can be used in problems where edge-wave structures are not so well defined or readily available. Some implications for parametrization of baroclinic instability and relevant eddy-mean feedbacks are discussed. For completeness, we also provide an explicit demonstration that the linear instability problem of the present modified Eady problem is parity-time symmetric, and speculate about some suggestive links between parity-time symmetry, shear instability, and the edge-wave interaction mechanism.