The purpose of this work is to investigate whether a cascading process can be associated with the rotational motions of compressible three-dimensional turbulence. This question is examined through the lens of circulicity, a concept related to the angular momentum carried by large turbulent scales. By deriving a Monin-Yaglom relation for circulicity, we show that an “effective” cascade of this quantity exists, provided the flow is stirred with a force having a solenoidal component. This outcome is obtained independently from the expression of the equation of state. To supplement these results, a coarse-graining analysis of the flow is performed. This approach allows us to separate the contributions of the transfer and production terms of circulicity and to discuss their respective effects in the inertial range.

Nonspherical particles transported by an anisotropic turbulent flow preferentially align with the mean shear and intermittently tumble when the local strain fluctuates. Such an intricate behavior is here studied for small, inertialess, rod-shaped particles embedded in a two-dimensional turbulent flow with homogeneous shear. A Lagrangian stochastic model for the rods angular dynamics is introduced and compared to the results of direct numerical simulations. The model consists in superposing a short-correlated random component to the steady large-scale mean shear and can thereby be integrated analytically. Reproducing the single-time orientation statistics obtained numerically requires to take account of the mean shear, of anisotropic velocity gradient fluctuations, and of the presence of persistent rotating structures that combine together to bias cumulative Lagrangian statistics. The model is then used to address two-time statistics. The notion of tumbling rate is extended to diffusive dynamics by introducing the stationary probability flux of the rods unfolded angle, which provides information on the overall, cumulated rotation of the particle. The model is found to reproduce the long-term effects of an average shear on the mean and the variance of the fibers angular increment. Still, for intermediate times, the model fails catching violent fluctuations of the rods rotation that are due to trapping events in coherent, long-living eddies.

Turbulent diffusion and mixing of heat, introduced passively by a thin ribbon in grid-generated turbulence, were enhanced drastically by a small array of thin cylinders, positioned closely downstream of the ribbon. A multistructure flow region was formed behind the array and relaxed towards grid turbulence, albeit maintaining a turbulence intensity and an integral length scale that were twice as large as those in the absence of the array.

A gas or vapor bubble collapsing in the vicinity of a rigid boundary displaces toward the boundary and produces a high-speed jet directed at the boundary. This behavior has been shown to be a function of the “anisotropy” of the collapse, measured by a dimensionless representation of the Kelvin impulse known as the anisotropy parameter [Supponen et al., J. Fluid Mech. 802, 263 (2016)]. However, characterization of the anisotropy parameter in different geometries has been limited to simplified analytic solutions. In this work we develop an inexpensive numerical model, based on the boundary element method, capable of predicting the anisotropy parameter for any rigid complex geometry. We experimentally explore a robust measure of bubble displacement, showing that the bubble displacement in a range of complex geometries behaves as a single function of the predicted anisotropy parameter values.

Large eddy simulation (LES) combined with filtered density function (FDF), i.e., LES/FDF, is an effective approach for high-fidelity simulation of turbulent flames. In this work, LES/FDF simulations are performed for the turbulent piloted premixed methane-air flame F3 to investigate the impact of reaction-induced subgrid scalar mixing on the predicted flame characteristics. The effects of mixing formulation on flame characteristics, as well as the performance of the classic constant mechanical-to-scalar mixing timescale model, are investigated, illustrating that reaction-induced scalar gradient plays an important role in determining the species mixing frequency. A new closure of scalar mixing timescale (hybrid-DD) is proposed to account for the reaction-induced differential mixing among species. The model adaptively adjusts the relative contribution from turbulence and reaction and requires no ad hoc model parameters to be specified manually. It is found that the hybrid-DD model yields a reasonable prediction of the overall combustion process of the flame F3, notably better than the conventional constant mechanical-to-scalar mixing timescale model with the nonoptimal model constant. The predicted scalar mixing frequency by the hybrid-DD model is found to exhibit differences among species, resulting in more abundant thermochemical states. Considering that all the components of the hybrid-DD model are readily available in the transported FDF method, the model is a promising candidate to be employed in LES/FDF simulations of turbulent premixed flames.

A theoretical model is presented to explore how surface waves in an inviscid fluid layer are damped by the bending stresses induced in a overlying floating film of yield-stress fluid. The model applies in the long-wavelength limit, combining the shallow-water equations for the inviscid fluid with a theory for the bending of a thin viscoplastic plate described by the Herschel-Bulkley constitutive law. An exploration of the energetics captured by the model suggests that waves decay to rest in finite time, a result that is confirmed using a combination of approximate, numerical and asymptotic solutions to the model equations. In the limit that the plate behaves like a perfectly plastic material, the sloshing motions take the form of triangular waves with bending restricted to narrow viscoplastic hinges.

We experimentally investigate the behavior of instantaneous localized releases of heavy particles falling as turbulent clouds in quiescent water, both with and without background rotation. We present the results of 514 systematic experiments for no rotation and for three rotation rates $\mathrm{\Omega }=5,10,20\mathrm{rpm}$ and for the size of particles in the range $5\mu \text{m}$ to $1\text{mm}$, exploring four decades of the Rouse number $\mathcal{R}\in [6\times {10}^{-4},4]$ which quantifies the inertia of particles. In the canonical framework of turbulent thermals described by Morton et al. [Proc. R. Soc. A: Math. Phys. Sci. 234, 1 (1956)], we compare particle clouds with salt-water thermals to highlight specificities due to the particulate nature of the turbulence forcing. In the absence of rotation, particle clouds initially behave as salty thermals with a modulation of their entrainment capacity, which is optimally enhanced for a finite inertia $\mathcal{R}\simeq 0.3$ due to particulate effects. However, this regime of turbulence is limited in time due to the inertial decoupling between turbulent eddies and particles. For the three values of $\mathrm{\Omega }$ explored here, the particulate enhancement of entrainment is inhibited. Moreover the cloud's expansion is interrupted when the Coriolis force overcomes its inertia, forcing the cloud to transform into vortical columnar flows which considerably increase the residence time of particles.

We study theoretically and numerically spatial distribution and collision rate of droplets that sediment in homogeneous isotropic Navier-Stokes turbulence. It is assumed that, as it often happens in clouds, typical turbulent accelerations of fluid particles are much smaller than gravity. This was shown to imply that the particles interact weakly with individual vortices and, as a result, form a smooth flow in most of the space. In weakly intermittent turbulence with moderate Reynolds number ${\text{Re}}_{\lambda }$, rare regions where the flow breaks down can be neglected in the calculation of space averaged rate of droplet collisions. However, increase of ${\text{Re}}_{\lambda }$ increases probability of rare, large quiescent vortices whose long coherent interaction with the particles destroys the flow. Thus, at higher ${\text{Re}}_{\lambda }$, that apparently include those in the clouds, the space averaged collision rate forms in rare regions where the assumption of smooth flow breaks down. This intermittency of collisions implies that rain initiation could be a strongly nonuniform process. We describe the transition between the regimes and provide collision kernel in the case of moderate ${\text{Re}}_{\lambda }$ describable by the flow. The distribution of pairwise distances (radial distribution function or RDF) is shown to obey a separable dependence on the magnitude and the polar angle of the separation vector. Magnitude dependence obeys a power law with a negative exponent, manifesting multifractality of the droplets' attractor in space. We provide the so far missing numerical confirmation of a relation between this exponent and the Lyapunov exponents and demonstrate that it holds beyond the theoretical range. The angular dependence of the RDF exhibits a maximum at small angles quantifying particles' formation of spatial columns. We provide typical dimensions of the columns, which belong in the inertial range. We derive the droplets' collision kernel using that in the considered limit the gradients of droplets' flow are Gaussian. We demonstrate that as ${\text{Re}}_{\lambda }$ increases the columns' aspect ratio decreases, eventually becoming one when the isotropy is restored. We propose how the theory could be constructed at higher ${\text{Re}}_{\lambda }$ of clouds by using the example of the RDF.

The evolution of nonstationary side forces acting upon an axisymmetric ogive-cylinder body with a blunt base and subjected to flows at a wide range of angles of attack is studied numerically. To analyze the results, the body surface is divided into narrow cross-section disks and for each disk the time histories of rms and the mean of the side force are calculated and used to create bifurcation diagrams for angles of attack from ${20}^{\circ }$ to ${80}^{\circ }$. These diagrams are compared with the diagrams obtained for the resultant side force acting on the entire body and those obtained for the ogive forebody and the cylindrical afterbody and its base. Results show that at low or medium angles of attack the flow is steady along the entire body except for some small oscillations near the body base. As the angle of attack increases beyond ${40}^{\circ }$, the flow about the aft of the cylindrical afterbody becomes unsteady and the side force oscillates with nonzero mean; this unsteady region extends upstream toward the nose as the angle of attack increases. When the angle of attack exceeds ${50}^{\circ }$ the side force along the far aft of the body oscillates symmetrically with zero mean, and this symmetric region extends upstream with the increasing angle of attack until at $\alpha ={80}^{\circ }$ it stretches virtually over the entire body.

In one-dimensional (1D) evolution models of gas giant planets, an outer convection zone advances into the interior as the surface cools, and multiple convective layers form beneath that convective front. To study layer formation below an outer convection zone in a similar scenario, we investigate the evolution of a stably stratified fluid with a linear composition gradient that is constantly being cooled from above. We use the Boussinesq approximation in a series of two-dimensional simulations at low and high Prandtl numbers ($\mathrm{Pr}=0.5$ and 7), initialized with constant temperature everywhere, and cooled at different rates. We find that multiple convective layers form at $\mathrm{Pr}=7$, as the result of an instability in the diffusive thermal boundary layer below the outer convection zone. At low Pr, layers do not form because the temperature gradient within the boundary layer is much smaller than at large Pr and, consequently, is not large enough to overcome the stabilizing effect of the composition gradient. For the stratification used in this study, on the long-term the composition gradient is an ineffective barrier against the propagation of the outer convection zone and the entire fluid becomes fully mixed, whether layers form or not. Our results challenge 1D evolutionary models of gas giant planets, which predict that layers are long-lived and that the outer convective envelope stops advancing inwards. We discuss what is needed for future work to build more realistic models.

The transport of a passive scalar with molecular Prandtl number Pr near unity was studied using direct numerical simulations (DNS) of a fully developed channel with smooth and rough walls. The effects of roughness on the turbulent Prandtl number ${\text{Pr}}_{\mathrm{T}}$, turbulent timescale ratio and scalar-dissipation budget were investigated. For the rough-wall case, the turbulent Prandtl number was almost constant (${\text{Pr}}_{\mathrm{T}}\approx 0.9$) from the roughness centroid up to the roughness crest, matching the common assumption used in modeling. ${\text{Pr}}_{\mathrm{T}}$ changes rapidly as the base of the roughness is approached, similar to the near-wall behavior in the viscous sublayer of a smooth-wall case. Away from the wall, Townsend's similarity hypothesis holds; the curves collapse when scaled in wall units. An effective turbulent Prandtl number ${\text{Pr}}_{\mathrm{T},\mathrm{eff}}$, which also includes the dispersive terms was examined. ${\text{Pr}}_{\mathrm{T},\mathrm{eff}}$ and ${\text{Pr}}_{\mathrm{T}}$ have an overall similar behavior, suggesting that they can be interchangeable and that the ${\text{Pr}}_{\mathrm{T}}\approx 0.9$ approximation may be accurate enough when modeling rough-wall flows with constant scalar wall flux. This implies that the ad hoc adjustment of model coefficients is not necessary, and that the scalar dispersive term do not need to be modeled separately. The near-wall behavior of the ratio between turbulent scalar and momentum timescales, $\mathcal{R}$, depends strongly on the molecular Pr for a smooth-wall case; roughness significantly reduces this dependence, tends to lower $\mathcal{R}$, and results in a more uniform behavior. Only below the centroid $\mathcal{R}$ rises rapidly as the base of the roughness is approached; as Pr decreases, the location at which this rise occurs approaches the base of the roughness. Townsend's similarity hypothesis also applies to $\mathcal{R}$ away from the roughness crest. The budget of the scalar dissipation ${\varepsilon }_{\theta }$ has a complex near-wall behavior in a smooth-wall case. In a rough-wall case this behavior is significantly simpler, approximating an equilibrium in which several production-of-dissipation terms match the dissipation-of-dissipation. The leading turbulent production-of-dissipation term is only due to the gradients of velocity and scalar fluctuations, which are only indirectly affected by the roughness. Compared with the smooth-wall case, this term is enhanced due to improved alignment between the fluctuating scalar gradient and the principal compressive direction of the strain-rate tensor. The roughness also enhanced the gradient-production of scalar dissipation, which is directly affected by the roughness shape, due to the diffusive nature of the mean scalar, which results in large gradients of the time-averaged scalar field.

The combined effects of inlet turbulence and localized injection on turbulent channel flow are investigated experimentally in an air channel. A porous plate was used to locally inject air streams at the bottom wall of the channel, while an active grid at the inlet of the channel generated different inlet turbulence intensities. Six different wall boundary conditions as well as four different inlet turbulence cases were investigated with planar particle image velocimetry measurements above the injection zone and farther downstream of it. The results show that, above the injection zone, the mean velocity and all Reynolds stress components are significantly altered by the localized injection forming an affected layer (AL), while the inlet turbulence only intensifies the streamwise fluctuations. The AL is then transported away from the wall, and the results indicate that the inlet turbulence slightly facilitates this process by increasing the turbulence transport inside the channel. The measurement results at the downstream position show that the effects of the injection are still present in the flow; however, the AL is transported farther away from the wall to the outer layer. Turbulence structure analysis reveals that the inlet turbulence effects, such as amplifying intense streamwise fluctuations and increasing the contributions of different quadrant events to the total Reynolds shear stress, are more prominent in the central regions of the channel. On the other hand, above the injection zone, the localized injection was found to significantly affect the distribution of the fluctuations and quadrant contributions in the near-wall regions. The same effects, although less prominent, are still present at the downstream position yet only in the outer layer. Also, the inlet turbulence does not affect the inclined features of the internal boundary layer, while the localized injection slightly increases their inclination angle.

This article presents a topological data analysis of the Lagrangian orbits occurring in natural convection flows inside cylindrical containers heated from below. The fluid motions are calculated via the numerical integration of the mass, momentum, and energy conservation equations using the Fourier-Chebyshev pseudospectral method. The study focuses on steady-state flows, and their qualitative properties are described in terms of the Rayleigh number. The Lagrangian orbits are calculated using the Eulerian velocity fields and their features are analyzed with Poincaré maps placed at the horizontal central plane of the cylinder. The qualitative features of the Lagrangian orbits calculated are closely related to those predicted by Hamiltonian theory, with the phase space being the real space in our case and considering the Rayleigh number as the driving parameter. The orbits are embedded in nested tori surfaces for low Rayleigh numbers ($\mathrm{Ra}=8\times {10}^3$). Some orbits seem to be dense in the tori and others form sets of points divided into segments in the Poincaré maps. At larger Rayleigh numbers ($\mathrm{Ra}={10}^4$, $2\times {10}^5$) the orbits form increasingly complicated structures, including loop islands in the Poincaré maps. Also, large areas in the maps show irregular or chaotic distributions of points. Topological data analysis (TDA) was used to define parameters that quantify the geometrical properties of the points distributions in the Poincaré maps. The number of segments in the sets of points and the occurrence of holes were determined with the 0- and 1-persistent homologies, respectively. Pairs of relatively prime numbers are used to characterize quasiperiodic orbits; the pairs are naturally identified with torus knots. It is found that the ratio of toroidal to the poloidal number of turns follows a simple rule for each Rayleigh number explored. The most important advantage of using TDA is the quantification and accurate identification of topological features found in the Poincaré maps.

The transitional flow which initiates within the junction (anastomosis) of an arteriovenous fistula (AVF) is known to be a contributing factor in the onset of vascular disease. A novel treatment method involving the implantation of a flexible stent across the anastomosis has enabled the retention of a large proportion of functioning AVFs, despite the propensity for stent malapposition to occur at the sharp inner curve of the anastomosis. Large eddy simulations of a single patient-specific AVF with and without the presence of a stent captured oscillatory flow behavior emanating from the interface of the two inlet flows in the stent-absent case, however, these oscillatory features were subdued in the stented case. The stent-absent case generally had higher turbulent kinetic energy (TKE) in the anastomosis which led to larger cycle-to-cycle variations in wall shear stress (WSS). The significantly lower TKE generated at the heel of the stented AVF was contained within the malapposed stent, thereby resulting in lower WSS fluctuations. However, a slight increase in turbulence downstream of the malapposed stent edge was noted. This detailed study reveals a significant decrease in turbulence within the AVF in the presence of the stent, thereby providing a level of understanding underpinning the success of the treatment strategy (in this patient case) from a fluid dynamic perspective.

In this article we present a comparative atomic level study analyzing the vibrational excitation and dissociation of molecular nitrogen due to ${\mathrm{N}}_2{(}^1{\mathrm{\Sigma }}_g{}^{+})+\text{N}{(}^4{S}_u)$ and ${\mathrm{N}}_2{(}^1{\mathrm{\Sigma }}_g{}^{+})+{\mathrm{N}}_2{(}^1{\mathrm{\Sigma }}_g{}^{+})$ interactions governed by independently developed potential energy surfaces at the University of Minnesota and NASA Ames Research Center. Vibrational excitation was studied for ${\mathrm{N}}_2+{\mathrm{N}}_2$ interactions from $T=10000$ to $25000$ K and for ${\mathrm{N}}_2+\text{N}$ from $T=5000$ to $30000$ K. Nonequilibrium dissociation is studied from $T=10000$ to $30000$ K under the quasi-steady-state condition for ${\mathrm{N}}_2+{\mathrm{N}}_2$ and ${\mathrm{N}}_2+\text{N}$ interactions. Finally, an inviscid Mach 20 dissociating nitrogen flow over a cylinder with a Knudsen number of 0.015 is carried out to study the impact of molecular interactions predicted by independently developed potential energy surfaces on a canonical hypersonic flow.

The dynamics of particles attached to an interface separating two immiscible fluids are encountered in a wide variety of applications. Here we present a combined asymptotic and numerical investigation of the fluid motion past spherical particles attached to a deformable interface undergoing uniform creeping flows in the limit of small Capillary number and small deviation of the contact angle from ${90}^{\circ }$. Under the assumption of a constant three-phase contact angle, we calculate the interfacial deformation around an isolated particle and a particle pair. Applying the Lorentz reciprocal theorem to the zeroth-order approximation corresponding to spherical particles at a flat interface and the first correction in Capillary number and correction contact angle allows us to obtain explicit analytical expressions for the hydrodynamic drag in terms of the zeroth-order approximations and the correction deformations. The drag coefficients are computed as a function of the three-phase contact angle, the viscosity ratio of the two fluids, the Bond number, and the separation distance between the particles. In addition, the capillary force acting on the particles due to the interfacial deformation is calculated.

With a streamwise magnetic field, the evolution of wake structure in a flow around an impulsively stopped sphere in an incompressible viscous fluid is investigated. The research parameter range is $60\le \mathrm{Re}\le 300$ and $0\le N\le 10$, where $\mathrm{Re}$ and $N$ are the Reynolds number and the interaction parameter, respectively. For present cases, the flow is fully developed before the sphere stopped and its symmetrical feature of the wake will be preserved after the sphere stopped. A complicated vortex structure system including a primary vortex ring, a fragmented secondary vortex, and an accompanying vortex is formed, which is summarized in a {$N,\mathrm{Re}$} phase diagram. A scaling law of the drag force is found after the sphere stopped. It decays as $t^{*-2/3}$ at a small timescale and $t^{*-1}$ or $t^{*-7/6}$ for different Reynolds numbers at a large timescale in the absence of a magnetic field, where $t^{*}$ is the dimensionless time after abruptly stopping the sphere. When the magnetic field is applied, the decay rate of drag force is slower at a small timescale but faster at a large timescale. Meanwhile, peak azimuthal vorticity at the primary vortex ring core is shown to decay as $t^{*-4/3}$ at a large timescale when the flow is axisymmetric. It will decay faster under the influence of a streamwise magnetic field.

In this paper, we present an experimental investigation on gas entrainment and gas leakage mechanisms of different ventilated cavity flow patterns around a conical axisymmetric body, by high-speed video and theoretical analysis. The ventilated cavity is generated around a conical axisymmetric body and studied in the closed-loop water tunnel at Lab of Fluid Machinery and Engineering, Beijing Institute of Technology. The experimental studies revealed three distinct cavity patterns, namely, the foamy cavity (FC), the intermittent and transitional cavity (ITC), and the continuous and transparent cavity (CTC) under different Froude and $C_Q$ values. All patterns contain the transparent region at the cavity rear (except FC) and the recirculating vortex that generates foam shedding at the cavity rear. The qualitative gas entrainment and leakage process are then explained based on the schematics of internal gas flow and surrounding water flow. As the flow pattern varies from FC to CTC with increasing ventilation rate, it is observed that the size of shedding foam grows larger while the shedding frequency gradually reduces, leading to balanced gas injection and leakage. Moreover, the mechanism controlling the hysteresis of the ITC-to-CTC transition is quantitatively explained using a gas leakage model of ITC cavities, which assumes the foam is periodically shed in the form of a vortex ring. After extensive validation by both current measurements and previous research, the model can accurately predict the ventilation rate required for the ITC-to-CTC transition. Finally, the mechanism causing closure discrepancy between CTC cavities in this paper and free-standing supercavities (without cavitator body) in past studies are investigated. Due to the impact of stagnation points on the cavitator body, the adverse pressure gradient (APG) in the streamwise direction of CTC cavities is estimated to be 6.8 times that of free-standing supercavities under the same flow conditions, leading to water flow separation at the cavity rear. As a result, after the ventilation hysteresis, the recirculating vortex closure is still observed in CTC cavities under the impact of large APG, different from free-standing supercavities that form vortex tube closure.

The oscillation instability of sessile drops is ubiquitous in surface acoustic wave (SAW) -powered digital microfluidics. Yet the physics underlying these phenomena has not been elucidated owing to the complex interplay between hydrodynamics, acoustics, and capillarity. We decipher the instability by combining high-speed imaging of the droplet surface vibration with inner acoustic pressure measurements. We rationalize the observed behavior with a model inspired from optomechanics, which couples an intracavity acoustic mode excited by the SAW to a surface deformation eigenmode through amplitude modulation and delayed radiation pressure feedback.