In this work, a liquid jet in supersonic crossflow (LJSC) was simulated by solving the quasi-conservative five-equation model with surface tension and viscosity terms. The jet trajectory and deformation were detailedly validated against experimental data, showing excellent agreement. Detailed turbulent vortices were identified in the flow field, further confirming the accuracy of the numerical schemes. The influence of Mach number on jet morphologies and trajectories was investigated under constant injection velocity conditions. As the Mach number increases, the liquid jet exhibits reduced penetration and faster fragmentation. The column breakup mechanism shifts from the development of axial instability waves at lower Mach numbers to intense aerodynamic drag at higher ones. By analyzing the relationship between the bow shock wave and jet deflection, a bow shock model was proposed and validated using simulation results. Furthermore, a theoretical model was developed to describe the primary breakup process of LJSC, incorporating the effects of critical forces, jet deformation, mass stripping, and the bow shock wave. The proposed model demonstrated significantly higher accuracy in near-field trajectory prediction compared to existing empirical correlations and proved applicable across a wide range of Mach numbers.

Axisymmetric direct numerical simulations are carried out to study the hydrodynamics of a laminar, stationary, incompressible, Newtonian, single-phase flow in an Annular Plane Couette (APC) channel. This configuration is that of a Straight Plane Couette (SPC) flow but curved around itself to form an annulus. These simulations are validated by Particle Image Velocimetry measurements at different Reynolds numbers. The flow is analyzed using three dimensionless parameters: the channel aspect ratio $A_c$, which controls the effects of sidewall confinement, the channel curvature ratio $C_r$, which affects the centrifugal forces due to curvature, and the Reynolds number $\mathrm{Re}$. The rotation of the top annular plate generates a main flow in the azimuthal direction, while generating a secondary recirculation flow in the plane of the channel cross section due to the presence of a centrifugal force difference across the radius. As a result, the vertical profile of the longitudinal velocity deviates from the classical linear profile of the SPC flow, adopting an unexpected S shape similar to that observed in a turbulent SPC flow. Depending on the values of $A_c$ and $C_r$, the flow exhibits a wide range of behaviors, from a quasi-2D flow with a homogeneous shear rate at moderate $\mathrm{Re}$ with appropriate geometrical parameters ($A_c\ge 5$, $C_r\le 0.1$) to a complex 3D flow otherwise. Whereas it is laminar, the APC flow shares a strong analogy with a turbulent Taylor-Couette (TC) flow. At large Reynolds numbers, the velocity gradients concentrate near the wall and the flow reaches an asymptotic regime where the torque scales as ${\mathrm{Re}}^{\alpha }$ and the flow structure becomes independent of $\mathrm{Re}$. Such properties make the APC flow an interesting configuration for fundamental investigations as a complement of the TC flow when shear and gravity are required to be in the same plane. In particular, it can be used to investigate the rheology of a dispersed two-phase mixture similarly to previous work by Yi et al. in the TC device.

This study conducts a systematic investigation into the effects of particle shape on granular flow dynamics through discrete element method (DEM) simulations, with particular emphasis on rheological properties of superballs in plane shear with gravity. Comparative analysis reveals that superballs exhibit distinct flow characteristics relative to spherical particles, including pronounced boundary effects, increased equivalent bulk viscosity, and modified velocity profiles. A generalized rheological framework is established through the development of particle shape-dependent constitutive model that quantitatively correlates particle shape parameters with effective friction coefficient. This model incorporates a dimensionless granular temperature to account for nonlocal effects, enabling comprehensive rheological characterization across both quasistatic and inertial flow regimes. Validation through continuous simulations, achieved by implementing rheology-dependent viscosity in the Navier-Stokes equations, demonstrates excellent agreement with corresponding DEM results in predicting transient flow behavior during granular collapse. These findings establish a robust theoretical foundation for predicting flow behaviors in granular systems with complex particle geometries, providing significant advancements in the modeling and analysis of natural and industrial granular materials.

A solvable model for space-time correlations of passive scalars advected by turbulent flows is proposed in the present paper. The model is a combination of Taylor's frozen-flow model and Kraichnan's random-sweeping and white-noise models, namely the Taylor–Kraichnan (TK) model, in which the advection velocity is the sum of a constant mean velocity, a random-sweeping velocity and a white-noise velocity. We find the exact solution of the TK model and consequently obtain analytical expressions for the space-time correlation. These results are used to demonstrate the scale invariance of space-time correlations and the self-similarity of iso-correlation contours in the inertial-convective subrange. In particular, the elliptic approximation to space-time correlations is justified and thus used to rescale spatial and temporal separations, collapsing a family of space-time correlations into a single curve.

The gap between two solid, coaxial cylinders is filled with two ferrofluids of differing viscosity and magnetic susceptibility. Axial motion is driven by a pressure gradient and/or translation of the inner cylinder. An axial magnetic field is imposed externally, while current flowing in the inner cylinder generates an azimuthal field. It is known that the axisymmetric capillary instability of the cylindrical fluid interface may be controlled either by hydrodynamic shear or magnetic effects, but each of these can give rise to other instabilities, often nonaxisymmetric. This paper investigates the 10-dimensional parameter space to determine when combined action of shear and magnetic effects can provide overall stability, essentially using shear to stabilize the troublesome helical "tearing" mode, while magnetic stresses control the hydrodynamic instability. Stability is easier to obtain when the inner fluid is more magnetic.

This paper focuses on designing a versatile state-space representation for parallel shear flows to facilitate both modal analysis and closed-loop control. Our objective in designing a control law is to regulate shear flows around a stationary desired state—a laminar flow—despite disturbances while ensuring the physical interpretability of the decision-making process. Our closed-loop control implementation involves linearizing the Navier-Stokes equations around the desired state, spatially discretizing the resulting linear system, and computing the feedback gain using an optimal control formulation. We assume that the actuators operate at the boundaries and model their effects as a forcing term using the elimination method rather than the lifting method, the former being standard in partial differential equations solvers but less common in flow control. Furthermore, we assume that the flow state is reconstructed from image sensors. To illustrate the efficiency of our approach, we derive a state-space representation for both the 2D periodic channel flow and the 2D spatially developing mixing layer flow. Hydrodynamic stability analysis confirms the representativeness of the state matrix and identifies the primary natural modes with exponential growth. The resolvent analysis highlights forcing modes, analogous to Orr structures in 2D shear flows, that induce misaligned response modes, analogous to natural modes, with the most significant transient energy growth. These observations provide insights for designing controllers that mitigate disturbances and enhance flow stability. Balanced truncation corroborates these observations and suggests an opposing control mechanism in which the control signal is derived by projecting the flow state onto the adjoint balanced modes. This approach targets dominant dynamic features, particularly the Orr structures, for effective control. For the two flows, linear quadratic regulator controllers are deduced from the full linear state-space model and implemented within a nonlinear Navier-Stokes solver. Additionally, for the periodic channel flow case, pole placement controllers are deduced from the reduced-order state-space model obtained via balanced truncation, as this reduced model naturally lends itself to effective pole placement. All simulation results confirm that these control laws stabilize the 2D periodic channel flow, preventing the development of unstable modes. Furthermore, they delay the onset of large eddies in the 2D spatially developing mixing layer by attenuating relatively slow endogenous disturbances in the control signal.

We investigate the dynamics of small inertial particles in a two-dimensional, steady Taylor-Green vortex flow. A classic study by Taylor (1940) showed that infinitely heavy inertial point particles (having density parameter $R=1$) are trapped by the flow separatrices when the particle Stokes number $\text{St}$, which measures the particle's inertia, is less than $1/4$. Here, we consider finitely heavy particles, incorporating the previously neglected effects of added mass and the Boussinesq-Basset history force. Using linear stability analysis near fixed points, we determine the critical parametric conditions in the $\text{St}\text{−}R$ plane that lead to particle trapping within vortex cells. Including the added mass effect identifies additional fixed points beyond the traditional ones located at the vortex cell corners, and we analyze their stability. Numerical analysis of the full nonlinear system confirms the existence of distinct particle behaviors—trapped, diffusive, and ballistic—depending on initial conditions, consistent with Nath et al. [Phys. Rev. Fluids 9, 014302 (2024)], with modifications due to added mass effect. We delineate the regions in the $\text{St}\text{−}R$ plane where these behaviors dominate based on the prominent particle dynamics. However, when both the history force and added mass effect are included, all particles exhibit ballistic motion regardless of $\text{St}$ and $R$.

Concentrated noncolloidal particles under nonuniform shear can migrate across streamlines even at low Reynolds numbers, breaking the well-known reversibility of Stokes flow. We conduct systematic experiments to study this phenomenon by oscillating a finite suspension plug comprising neutrally buoyant noncolloidal particles inside a cylindrical tube with varying strain amplitudes $\gamma$. We visualize the particles on the central axial plane of the tube via refractive index matching and track the motion of individual particles. Consistent with the previous findings, our experiments show that suspension plugs under oscillatory flows dilute to a critical volume fraction and become reversible in overall shape. However, our measurements reveal persistent particle motion even after this critical volume fraction threshold is reached, which points to a previously unreported disconnect between particle-scale and system-scale reversibility. In addition, we build a simplified two-dimensional model of particles under nonuniform shear and capture the gradual dispersion of the suspension plug, in qualitative agreement with the experiments.

Extreme wall shear stress (WSS) events, usually conditioned to the streamwise WSS, are examined with a further constraint of the azimuthal WSS through direct numerical simulation of turbulent pipe flow at a frictional Reynolds number ${\text{Re}}_{\tau }\approx 500$. In light of the segmented characteristics identified in the statistical distribution of the WSS ${\tau }_{\theta }^{+}$, both extreme positive (EP) events and backflow (BF) events are further categorized into two distinct types, with the help of the proposed local extremum intersection method. The four events each have their own unique probability of occurrence, and those with larger ${\tau }_{\theta }^{+}$ are found to be more intense through the joint probability density function of ${\tau }_x^{+}$ and ${\tau }_{\theta }^{+}$. By conducting a conditional average on the regions of these events, significant differences in their vortical structures and related characteristics have been identified, distinguishing them from previous research findings. On the one hand, the different formation mechanisms of the subdivided EP events' structures are clearly revealed, with the presence of the second vortex on the opposite side of the dominant streamwise vortex in EP leading to a weakening of the spanwise motion. On the other hand, the research on the subdivided BF events demonstrates that the flow characteristics show a close correlation with tilt angle of the dominant oblique vortex, with larger angles tending to induce stronger backflow phenomena. Moreover, a relationship between angles and azimuthal shear stress is established, which roughly follows a power-law distribution. This study highlights that introducing additional new constraints could refine or expand the currently widely accepted classification framework for extreme WSS events, enhancing current understanding of them.

In boundary-layer turbulence, when the distance to the wall is within the logarithmic regime, the streamwise velocity structure function can be divided into three regimes by the horizontal scale in the order of distance to the wall, $z$, and the boundary-layer thickness, $\delta$. In the inertial range, when the streamwise two-point distance $r$ is less than $z$, the velocity structure function satisfies a power-function dependence on $r/z$. In the logarithmic range when $z<r<\delta$, the velocity structure function has a logarithmic dependence on $r/z$. In the outer range when $r>\delta$, the function approaches a constant value. This work shows that the above three regimes for the velocity structure function also apply to the mixed third-order structure function constituted by the velocity and potential temperature differences $\langle \delta u\delta {\theta }^2\rangle$. Here, $\delta u$ and $\delta \theta$ are the streamwise differences in streamwise velocity and potential temperature, respectively. We derive the logarithmic dependence of the mixed third-order structure function from the Kármán-Howarth-Monin equation for the potential energy with the help of the attached eddy hypothesis. The inertial range and logarithmic range are identified by analyzing data from the Qingtu Lake Observation Array. The transition scale between the two ranges decreases with an increase of $z/L$ in weak stable conditions where $L$ is the Obukhov length.

Liquid films coating vertical cylinders can form annular liquid collars which translate downwards under gravity. We investigate the dynamics of a thin viscoplastic liquid film coating the interior or exterior of a vertical cylindrical tube, quantifying how the yield stress modifies both the Rayleigh-Plateau instability leading to collar formation and the translation of collars down the tube. We use thin-film theory to derive an evolution equation for the layer thickness, which we solve numerically to examine the nonlinear dynamics. Instability and collar formation occur when gravity is sufficiently strong to make the fluid yield initially. We use matched asymptotics to derive a model describing the quasisteady translation of a slender liquid collar when the Bond number is small. The structure of the asymptotic solution for a viscoplastic collar shares some features with the Newtonian version, but there are several novel asymptotic regions that emerge at the two ends of the collar. The global force balance, which determines the collar's speed, is modified by a leading-order contribution from viscous drag in the collar when the liquid is viscoplastic. We use the asymptotic model to describe slow changes in collar volume when the film thicknesses ahead of, and behind, the collar are unequal. When the film thickness ahead of the collar is less than a critical value that we determine, viscoplastic collars adjust their volume and reach a steadily translating state. This contrasts with the Newtonian problem, where the only state in which steady translation occurs is unstable to small changes in the film thickness.

Understanding the friction forces acting on droplets moving across non-wetting surfaces is essential for advancing applications in fluid transport and microfluidics. In this study we quantify droplet friction on both superhydrophobic and superheated (Leidenfrost) substrates using two complementary experimental approaches: inclined plane dynamics and cantilever force sensing. We identify distinct friction regimes governed by contact-line pinning, viscous dissipation, and aerodynamic drag over a broad range of velocities and viscosities. A force-based scaling law captures the transition between these regimes as a function of the capillary number, integrating contact-line effects, internal dissipation, and aerodynamic contributions. Our model is further validated through white light interferometry and high-speed reflective interference contrast microscopy, which reveal the structure and evolution of the thin air or vapor layers beneath the droplets. These findings offer a comprehensive framework for predicting droplet behavior on non-wetting surfaces and inform the design of surfaces for reduced friction in engineering and microfluidic systems.

We study locomotion of a model crawler corresponding to a deforming upper boundary of finite length above a thin Newtonian fluid film whose viscosity varies spatially. We first derive a general locomotion velocity formula with fluid viscosity variations via the lubrication theory. For further analysis, the surface of the crawler is described by a combination of transverse and longitudinal traveling waves and we find that under a uniform viscosity a transverse wave results in a retrograde crawler, while a longitudinal wave leads to a direct crawler. We then analyze the time-averaged locomotion behaviors under two scenarios: (i) a sharp viscosity interface and (ii) a linear viscosity gradient. Using the asymptotic expansions of small surface deformations and the method of multiple timescale analysis, we derive an explicit form of the average velocity that captures nonlinear, accumulative interactions between the crawler and the spatially varying environment. (i) In the case of a viscosity interface, the time-averaged speed of the crawler is always slower than that in the uniform viscosity, for both the transverse and longitudinal wave cases. Notably, the speed reduction is most significant when the crawler's front enters a more viscous layer and the crawler's rear exits from the same layer. (ii) In the case of a viscosity gradient, the crawler's speed becomes slower for the transverse wave, while for the longitudinal wave, the locomotion speed does not change significantly. Our analysis illustrates the fundamental importance of interactions between a locomotor and its environment, and separating the timescale behind the locomotion.

This experimental study examines the dynamics of the shock-induced breakup of a liquid drop within the shear-strip breakup regime. The interaction of the shock wave with the interface leads to its reflection and transmission. The reflected shock wave from the windward side of the drop, combined with the merging of the Mach stem at the downstream of the leeward side, creates an uneven pressure distribution across the drop. The compression of the windward face results in the formation of a surface wave, which is intensified by the shearing of flow. This process redistributes the liquid across the drop, resulting in the formation of a dense core and a peripheral meridional zone. With increasing strength of the Mach stem, a surface wave develops on the leeward side. The evolution of the surface wave is found to be governed by a shear-dominated cascading instability mechanism, suggesting the presence of multiscale instability. The surface wave on the windward and leeward sides collides during the drop deformation, transferring its momentum in the cross-stream direction. The acceleration of flow into the azimuthal ring causes corrugations to appear in the transverse direction. These corrugations are found to be governed by the Rayleigh-Taylor instability mechanism. These corrugations are further developed into fingers. These dynamics result in the identification of two submodes: ligament and cellular. In the ligament breakup mode, the radial fingers elongate streamwise to form a ligament that breaks due to surface tension. In cellular breakdown, the fingers evolve into U-shaped structures that combine with the azimuthal ring to form cellular structures. The azimuthal ring detaches from the deforming drop as the flow accelerates through it. The coupled Rayleigh-Taylor and Rayleigh-Plateau mechanisms govern the breakup of the azimuthal ring. An additional instability in the deforming drop leads to the formation of a secondary azimuthal ring. The core deforms as the flow accelerates into it. This deformation is governed by a Rayleigh-Taylor instability mechanism.

In hydrodynamic (HD) and magnetohydrodynamic (MHD) turbulence an energy cascade can occur when there is a substantial range of scales—the inertial range (IR)—over which the energy transfer process is self-similar. An elementary question is the following: What are the minimum Reynolds numbers needed for a turbulent flow to have a substantial IR, that is, one of a given bandwidth. The effect of finite Reynolds numbers on the IR has been well studied in HD turbulence, which provides a roadmap for analogous study in MHD turbulence. To help identify the minimum Reynolds number associated with a substantial IR, we conduct a series of incompressible MHD turbulence simulations with Taylor Reynolds numbers ${\mathrm{Re}}_{\lambda }\approx 200\text{–}400$. These are analyzed in terms of the MHD third-order law, one of the few rigorous results concerning MHD turbulence energy transfer within a well-defined IR. Specifically, we use simulations and modelled structure functions to estimate the IR boundaries as a function of ${\mathrm{Re}}_{\lambda }$. Following studies in HD turbulence, a semiempirical power-law model is applied to structure function behavior, which allows us to extrapolate to ${\mathrm{Re}}_{\lambda }$ that are much higher than those accessible with experiments or simulations. The present results estimate the minimum Reynolds number needed to establish an IR spanning a specified number of decades. For MHD flows whose Reynolds numbers satisfy the criteria, this provides a justification for the use of the energy cascade scenario and the third-order law.

We present direct numerical simulations (DNS) of particle deposition in a turbulent channel flow, incorporating a viscoelastic soft-sphere collision model with van der Waals adhesion. Particle-wall contact is governed by an adhesion number that varies with temperature, enabling exploration of a wide range of deposition behaviors. Deposition is strongly heterogeneous, especially for inertial particles, where rolling and sliding enhance nonuniformity. Spanwise radial distribution functions reveal that deposited particles form streaks with characteristic spacing set by near-wall two-point velocity correlations. A clustering metric confirms that high-inertia, low-adhesion particles deposit in elongated, anisotropic patterns due to spanwise particle creep driven by velocity fluctuations. Finally, it is shown that this heterogeneity in deposition leads to localized wall wear rates exceeding 10 times the mean, with the most severe wear associated with particles that are carried to the wall in clusters by sweep events.

Immiscible liquid jets are crucial in various physical and chemical processes. This study explores the dynamics of a buoyant immiscible liquid-in-liquid jet in the laminar regime using simultaneous particle image velocimetry and planar laser-induced fluorescence. A refractive index-matched fluid pair—silicone oil and a sugar water mixture—was employed to overcome optical distortions. Analytical solutions for both inviscid and viscous models were developed and compared with experimental data across a range of nondimensional parameters. The viscous model accurately predicts both the jet radius and centerline velocity, although some discrepancies appear in the continuous phase velocity distribution. Furthermore, experimental data reveal that boundary layer growth at the jet interface follows classical boundary layer scaling. The flow field was divided into two broad regions: a near-field region near the inlet and a far-field region several diameters away. Distinct scaling behaviors for the jet radius were observed in these two regions, guided by the relative significance of nondimensional parameters. Among these parameters, the buoyancy parameter, $N_j$, and the Reynolds number, $\text{Re}$, were found to play dominant roles in governing jet behavior. In contrast, the Weber number, $\text{We}$, was found to affect jet dynamics when its value was significantly lower than unity, while the viscosity of the continuous phase affected jet dynamics only in the far field.

Pressure measurement has many implications in fluid mechanics and many advances have been made in terms of reconstructing the pressure field by directly integrating the pressure gradient fields originating from time-resolved particle image velocimetry measurements. The majority of the current direct integration algorithms initiate the integration at the domain boundaries where the pressure gradient measurement is often unreliable. In this work, we introduce the boundary-independent shortest path integration algorithm that initiates the integration at the inner measurement domain and grows outwards towards the boundaries. The algorithm calculates a new undeveloped grid point by averaging over millions of line integrations of shortest paths originating from nearby developed grid points. The process iterates until all points in a map are determined. Multiple maps calculated from distributed reference points are averaged to improve calculation accuracy. Using the JHU DNS database, we optimize and validate the proposed integration method. We demonstrate that this integration algorithm can be directly applied to pressure gradient fields containing inner boundaries of different sizes and shapes with no decrease in performance and accuracy. We further show that this method resulted in errors comparable to existing integration methods. Overall, this method represents a simple algorithm for reconstructing the pressure field independent of the boundary conditions and reduces the propagation of errors from the boundaries substantially.

Accurate modeling of ice accretion is important for the safe and efficient design of aircraft and wind turbine systems. Heat transfer predictions obtained from the fluid flow solvers are used as input in ice accretion codes. In glaze ice conditions, the freezing rates and resulting ice shapes are highly sensitive to the input values of the heat transfer coefficient. Hence, an accurate prediction of heat transfer on iced airfoils is crucial for correctly predicting the ice accretion process. In this study, we perform conjugate heat transfer (CHT) simulations using wall-modeled large-eddy simulation (WMLES) over surfaces characterized by ice roughness. The results show that WMLES with CHT accurately captures surface temperature distributions and heat fluxes across a range of roughness geometries. For the cases considered, large roughness-to-boundary-layer thickness ratios disrupt outer-layer similarity, leading to substantial errors in estimating equivalent sandgrain roughness when applying traditional empirical models based on surface statistics. The simulations further show that local heat fluxes vary significantly across roughness elements due to the low thermal conductivity of the solid; in particular, roughness crests exhibit reduced fluxes in contrast to slopes and valleys. Notably, as roughness height increases, the wall heat flux at the crest diminishes, even leading to heat flux reversal in some cases, where thermal energy is transferred from the fluid to the solid. These effects are not captured in isothermal wall simulations, which overestimate the Stanton number, especially at roughness peaks. By enabling the calculation of the Stanton number using heat flux distributions, not directly available in the experiments, the present simulations augment experimental results and highlight the importance of including solid conduction effects for accurately modeling heat transfer over rough, low-conductivity surfaces such as ice.

Experimental study on the instability at a V-shaped interface accelerated by a strong shock wave with a Mach number exceeding 3.0 is performed in a shock-tube facility. To highlight the effect of initial amplitude on flow evolution, five V-shaped interfaces with various initial amplitudes are considered. Several interface evolution features differing significantly from those under weak shock conditions are observed, such as the secondary vortices on the spike stem and reverse jets at the spike root. For the linear evolution period, existing models exhibit limited predictive capability because they cannot effectively describe the strong flow compressibility and the intricate coupling between interface-geometry, shock-proximity, and secondary-compression effects. To overcome this limitation, we propose a modified model that combines a compressible linear theory to cover strong compressibility and a reduction factor to describe the coupling of the three effects. This model is applicable under both weak and strong shock conditions. In the nonlinear period, the amplitude evolution law is positively correlated with the initial amplitude due to the enhanced Mach-reflection effect under higher initial-amplitude conditions. None of the nonlinear models is effective under all initial-amplitude conditions, as they fail to account for the coupling influences of the Mach-reflection effect, geometric effect, shock-proximity effect, secondary-compression effect, and Kelvin-Helmholtz instability on nonlinear evolution. To bridge this gap, we propose parametrizing the composite mechanism through correction factors explicitly expressed as functions of initial amplitude and Mach number and develop an empirical nonlinear model that achieves favorable predictive performance across a broad range of initial-amplitude conditions.