In this paper, we conduct a numerical investigation to analyze the turbulent flow characteristics over three-dimensional wavy walls with varying amplitudes and wavelengths, with a specific focus on the transfer of momentum and kinetic energy. Detailed three-directional momentum statistics are presented to elucidate the influence of shape parameters on flow behavior. The temporal-spatial averaging at relative height is employed to highlight the impact of the wall on mean, time-averaged, and dispersive momentum flux as well as kinetic energy production. Our findings indicate that the current wall amplifies the effects of spanwise momentum flux, which is determined by the transverse flow around the crest. The dispersive shear stress (DSS) demonstrates a notable correlation with vorticity enhancement, while the near-wall vertical momentum flux is jointly governed by the counteraction of Reynolds shear stress and DSS. Through an analysis of kinetic energy conservation, we observe the transfer of kinetic energy among time-averaged, mean, dispersive, and turbulent motions. Overall, kinetic energy is transferred from dispersion to the mean flow and subsequently to turbulence downstream of the crest. On the windward side, both turbulent and dispersive energy are injected into the mean flow, suggesting the possible growth of internal boundary layer. Additionally, the exchange between dispersion and turbulence significantly contributes to turbulent kinetic energy production, particularly in cases with high amplitudes or spanwise wavelengths.

In this study, we propose a new theoretical approach to describe the spectra of kinetic energy and helicity under the influence of stratification. We introduce a scaling parameter $m$ and perform the scaling analysis, which allows us to consider the effect of stratification on the spectra. It becomes possible to categorize the spectral properties of energy, helicity, and dual cascades in stratified turbulent flows based on the energy- and helicity-dominated cascade scenarios. New scaling laws for dual cascade scenarios in flows with a strong stratification are formulated as well. The comparison of the theoretical results against atmospheric balloon-borne observations reveals that slopes of the energy cascades are typically steeper than the helicity ones. This is an indication of the energy-dominated cascade behavior at considered scale ranges and altitude segments.

Turbulence may be strongly influenced by near-wall nonuniform body forces. A widely encountered example is buoyancy acting in mixed convection flows. Here we use direct numerical simulations to present two key ideas: First we show that introducing opposing body forces whilst maintaining the pressure gradient does not cause key turbulence characteristics to change. It follows that the concept of “apparent Reynolds number” introduced by He et al. [J. Fluid Mech. 809, 31 (2016)] to explain laminarization can now be extended to explain the opposite phenomena of turbulence enhancement by opposing body forces. This new understanding has allowed turbulent shear stress and skin friction to be easily predicted simply from the nonuniform body force profile and reference data despite the nonequilibrium nature of the flow. Second, we analyze the flow in the context of turbulence regeneration cycle and provide evidence that complements the recent study from Jiménez [J. Fluid Mech. 945, R3 (2022)], which suggests that streaks are more decoupled from the regeneration cycle than previously thought.

The filtered density function (FDF) in the context of large eddy simulation (LES) has demonstrated its unique strength in predicting complex turbulent reacting flows. However, the high computational cost of FDF-LES may hinder its application in industrial configurations. The combination of FDF with the hybrid Reynolds-averaged Navier–Stokes (RANS)-LES method can potentially provide an effective means to significantly reduce computational cost while maintaining accuracy. In this work, the FDF method within the framework of self-adaptive turbulence eddy simulation (SATES), a hybrid RANS-LES approach, is formulated. The focus is on ensuring consistency in both definition and scalar-mixing modeling. The filtered density function in SATES-FDF can be interpreted as the spatial filtering density function under either RANS or LES filtering scale, depending on the local turbulence integral scale and grid resolution. The inconsistency of scalar-mixing rate modeling between RANS mode and LES mode in SATES-FDF is revealed. The general modeling criteria for modeling consistency of scalar-mixing rate are formulated in the context of SATES. A scalar-mixing rate model is then proposed through dimensional analysis, which utilizes a hybrid length scale to meet the criteria and achieve the consistency. The SATES-FDF approach is demonstrated in the simulations of standard turbulent premixed swirling burner TECFLAM, in which the $k-\omega$ shear stress transport model is adopted for the base model of SATES. With the consistency issue being resolved, it is shown that this mixing-frequency model achieves better overall agreement with experimental data than the classic models in standalone RANS or LES context in terms of reproducing the swirling flow and related flame characteristics, demonstrating its potential for practical combustor configurations. Finally, H equivalence is employed to extend SATES-FDF to more several hybrid RANS-LES frameworks, such that a unified framework for FDF in conjunction with hybrid RANS-LES method is established.

The degree to which particles such as larvae, seagrass pollen, and microplastics are dispersed by waves and currents influences many ecologically important aspects of their transport and fate. Particle transport models often assume dispersion is simply a function of the local turbulence, but there are many additional parameters related to both the particle characteristics and the flow dynamics that can impact how particles disperse. Here, we perform a parametric study of solutions to the Maxey-Riley equation and Euler's equation for rigid body motion for negatively buoyant, ellipsoidal particles dispersing in a wave-current flow. We systematically examine the impact of a comprehensive set of parameters on particle dispersion: the ratio between the time scales associated with particle settling and the waves, the Archimedes number, the particle eccentricity, the wave steepness, the Keulegan-Carpenter number, and the Stokes number. Our results show that no parameters can be discounted, but that the settling-wave time scale ratio has the largest influence on particle dispersion.

Compressible turbulent mixing evolving from Richtmyer-Meshkov and Rayleigh-Taylor instabilities and Bell-Plesset effects has been investigated using high-resolution implicit large eddy simulations of fundamental spherical implosion problems. Broadband (BB) and narrowband (NB) initial perturbations consisting of multimode cosine perturbations are considered at a high Atwood number ($A_t=0.9$) corresponding to a density ratio of 20. This research examines the turbulent transport and budgets of turbulent kinetic energy, turbulent mass flux, and density self-correlation, and the balance of the terms in the transport equations is used to approximate the numerical discretization effect on the derived equations. Strong non-Boussinesq effects and asymmetries were observed in the distribution of the anisotropy terms and budgets within the mixing layer. The production and destruction terms dominate the late stages of the mixing process in all the equations compared to the other transport terms. The BB layer showed higher levels of density self-correlation compared to the NB case, which showed larger destruction levels relative to the state of the layer. Higher levels of turbulent mass flux and turbulent kinetic energy (e.g., larger potential to kinetic energy conversion rates) were observed in the BB case due to the longer-wavelength perturbations in the BB layer that dominate the growth at late times. The numerical discretization terms implicitly modeling the effect of the unresolved scales contribute to both diffusion and dissipation and the current study shows that their effect may be both examined indirectly through residuals and quantified directly through observed destruction.

We present a parametric study of the unsteady phenomena associated with the flow of elongated gas bubbles traveling through liquid-filled square capillaries under high Weber number conditions. These conditions induce the formation of an indentation at the back of the bubble that commonly gives way to a deep reentrant liquid jet penetrating the bubble. Subsequent steps include pinch-off events in the penetrating liquid to generate one or multiple encapsulated drops which may coalesce, in conjunction with the bursting of the bubble-liquid interface by either the liquid jet or the drops. Some of these interfacial instabilities have previously been reported experimentally and numerically for liquid-liquid flow in microchannels. We carry out three-dimensional direct numerical simulations based on a hybrid interface-tracking/level-set method capable of accounting for the presence and dynamic exchange of surfactants between the liquid bulk phase and the liquid-gas interface. Our results indicate that the delicate interplay among inertia, capillarity, viscosity, surfactant adsorption/desorption kinetics, and Marangoni stresses has a dramatic influence over the nonaxisymmetric morphological structures of the encapsulated drops-elongated bubble. This strong coupling also influences the pinch-off time, penetration depth of the liquid, and number, size, and velocity of the encapsulated drops across the bubble. The observed phenomena are summarized in three main morphological regimes based on surfactant-related parameters and dimensionless groups. A discussion of the flow regime maps is also provided.

Point-particle direct numerical simulations of horizontal open-channel turbulence two-way coupled with inertial particles (${\text{St}}^{+}=1,31,100$) are performed to investigate the effects of the Saffman force (the shear-induced lift force) on particle motion and turbulence modulation. The friction Reynolds numbers of particle-free wall turbulence are ${\text{Re}}_{\tau }=180$ and 580, respectively. The results show that for ${\text{St}}^{+}=31$ and ${\text{Re}}_{\tau }=180$, the near-wall negative lift force increases the rebound velocity of particles after particle-wall collisions and prevents them from following the fluid motions. Therefore, the accumulation of the particles near the wall and the preferential concentration in the low-speed streaks are suppressed by the lift force. As a result, the turbulent velocity fluctuations are decreased below the buffer layer. The destruction of the conditional hairpin vortex is observed because particles with the lift force are easy to cross the vortex core. In the outer layer, the particle-turbulence interaction is increased by the lift force because of higher particle concentration. The significance of the lift force on turbulence modulation decreases with the increasing Reynolds number, albeit the near-wall lift force itself becomes more important at high Reynolds number. Finally, even with the shear-induced lift force, the particle-turbulence interaction is still the strongest for the moderate-inertia particle in the ${\text{St}}^{+}$ range studied in this paper.

This paper presents an experimental investigation of a three-dimensional flow driven by acoustic forcing in a closed cavity. This problem is a generic model for streaming flows due to waves attenuating in fluids and reflecting on domain boundaries (for examples acoustic streaming in industrial processes but also streaming of gravity waves in geophysical context). The purpose of this work is to go beyond the current state of knowledge that is mostly limited to individual streaming jets and to characterize the flow obtained when the waves reflect on boundaries as it may occur in more realistic problems. To this end, we set up an experiment where we fire an ultrasonic beam radiated by a planar circular source so that it undergoes multiple reflections inside a water-filled cuboid cavity. This produces a helix-shaped acoustic field that drives the flow. The velocity field of the resulting three-dimensional flow is measured by means of particle tracking velocimetry (PTV) for different forcing magnitudes. The time-averaged fields obtained in the entire fluid domain feature jets following the acoustic beam and impinging the vertical boundaries of the cavity, giving rise to large vortical structures which are favorable for stirring purposes. Such acoustic field also generates fluid flows in both up and down directions, as well as an overall rotating motion for which an analytical scaling law is derived. Time-resolved PTV measurements in the vicinity of the first jet impingement shed light on the progressive development of unsteadiness with increasing forcing. The highly three-dimensional nature of the fluid motion and its observed dynamics make this flow particularly relevant for stirring applications at large scale.

The reconstruction of incomplete information in flow fields is a pervasive challenge in numerous turbulence-related applications. This paper proposes a framework for the high-fidelity reconstruction of large-area damaged turbulent fields with high resolution based on a physically constrained generative adversarial network. The network incorporates some special designs, such as leveraging complete or sparse fields of velocity components as physical constraints, employing a ResNet-like network with a fast Fourier convolution module, and adopting a PatchGAN discriminator network. To train the network, we employ a combination of loss functions, which comprise mean absolute error, network-level loss, and feature matching loss. We validate our method on a dataset of compressible isotropic turbulent flow and investigate three distinct damaged distributions with gap ratios of $39.06\%$ and $56.25\%$. The proposed reconstruction framework has been shown to achieve excellent reconstruction performance. The reconstructed flow fields are consistent with the raw flow fields in terms of magnitude, power spectrum, and two-point correlation function. We also provide extensive ablation studies to validate our approach. The results indicate that the utilization of physical constraints significantly improves the reconstruction performance in damaged regions, particularly in cases that involve a large damaged area. Furthermore, in the proposed reconstruction framework, the size of patch in the PatchGAN discriminator network can be flexibly adjusted according to the scale of turbulence structures, and the perceptual loss function plays a crucial role in evaluating differences between feature maps of flow fields at network levels based on a pretrained network. These special designs ensure consistency across diverse scales of turbulence structures and improve the accuracy and efficiency of network training.

In this work, a localized artificial-viscosity/diffusivity method is proposed for accurately capturing discontinuities in compressible flows. There have been numerous efforts to improve the artificial diffusivity formulation in the last two decades, through appropriate localization of the artificial bulk viscosity for capturing shocks. However, for capturing contact discontinuities, either a density or internal energy variable is used as a detector. An issue with this sensor is that it not only detects contact discontinuities but also falsely detects the regions of shocks and vortical motions. Using this detector to add artificial mass/thermal diffusivity for capturing contact discontinuities is hence unnecessarily dissipative. To overcome this issue, we propose a sensor similar to the Ducros sensor (for shocks) to detect contact discontinuities and further localize artificial mass/thermal diffusivity for capturing contact discontinuities. The proposed method contains coefficients that are less sensitive to the choice of the flow problem. This is achieved by improved localization of the artificial diffusivity in the present method. A discretely consistent dissipative flux formulation is presented and is coupled with a robust low-dissipative scheme, which eliminates the need for filtering the solution variables. The proposed method also does not require filtering for the discontinuity detector/sensor functions, which is typically done to smear out the artificial fluid properties and obtain stable solutions. Hence, the challenges associated with extending the filtering procedure for unstructured grids are eliminated, thereby making the proposed method easily applicable for unstructured grids. Finally, a straightforward extension of the proposed method to two-phase flows is also presented.

The study of capillary imbibition has ramifications in many fields, such as energy, biology, process industry, and subsurface flows. Although the capillary rise of Newtonian liquids has been the subject of several studies since the seminal works of Lucas (1918) and Washburn (1921), its generalization to the case of non-Newtonian fluids is still an open question. To fill this gap, starting from first principles, we derive a transient one-dimensional model describing the rising dynamics of shear-thinning fluid, whose viscosity is described by the Ellis viscosity model. Our model identifies the scaling for the different imbibition regimes accounting for the interplay of inertial, gravity, and viscous non-Newtonian effects (i.e., the zero-shear-rate and the shear-thinning behavior). Specifically, the rising dynamics is described by the interplay of three dimensionless parameters: the Richardson number (i.e., the ratio between potential and kinetic energies), the Ellis number (i.e., the ratio between the characteristic shear-stress of the fluid and gravity), and the shear-thinning index which quantify the degree of shear-thinning of the fluid. At early times the system follows a universal inertial regime, followed by two possible limiting regimes, i.e., the classical Lucas-Washburn and the oscillatory regimes. The competition between the governing dimensionless numbers dictates the transition between the two. We show that when the viscous effect dominates over inertia, the identification of a (time-dependent) scaling law for the effective viscosity leads to a generalization of the Lucas-Washburn theory and the rescaled trajectories toward equilibrium collapse over the classical 1/2 scaling law. On the contrary, when inertia dominates the later stage of the imbibition, the filling length oscillates around the equilibrium. By means of linear control theory, we discuss the physical mechanisms that lead to such oscillating behavior and map the different regimes in terms of the governing dimensionless parameters.

In this study, we numerically investigate hysteretic behaviors of secondary bifurcations in the Taylor-Couette flow of a semidilute, neutrally buoyant, and noncolloidal suspension. We consider a suspension with a bulk particle volume fraction ${\varphi }_b=0.1$, radius ratio $\eta (=r_i/r_o)=0.877$, and particle size $\epsilon (=d/a)=60$, where $d$ is the gap width between two cylinders, $a$ is the radius of the suspended particles, and $r_i$ and $r_o$ are the radii of the inner and outer cylinders, respectively. The suspension balance model is introduced for numerical simulations to model the dynamics of particles undergoing shear-induced particle migration with rheological constitutive laws. The suspension flow transitions from circular Couette flow via ribbons (RIB), spiral vortex flow (SVF), and wavy spiral vortex flow (WSVF) to wavy vortex flow (WVF) with the increase of suspension Reynolds number (${\mathrm{Re}}_s$). The primary transition arises very slowly with an oscillatory critical mode and appears through a supercritical (or nonhysteretic) bifurcation. However, we find hysteretic behaviors in subsequent bifurcations [spiral vortex flow (SVF) ↔ wavy spiral vortex flow (WSVF) and WSVF ↔ wavy vortex flow (WVF)] during increasing-Re and decreasing-Re procedures with a rapid step change near the transition boundaries. The WSVF and WVF states are more sustained below the transition boundaries, when the Reynolds number is rapidly decreased in stages. However, the SVF and WSVF become WSVF and WVF more sharply with increasing Re, respectively. To conclude this study, we also examine in detail a standing wave of weak counter-rotating vortices that occurs as the primary instability and analyze the wave that oscillates in time but is stationary in space in the RIB state.

We generate quantum turbulence in spherically symmetric thermal counterflow of superfluid ${}^4\mathrm{He}$ driven by a central heater and probe it by second sound attenuation. We show that normal fluid turbulence forms above a certain critical threshold and, in the absence of shear flow, draws energy from a preexisting random tangle of quantized vortices corresponding to Vinen-type turbulence. This experiment can serve as a model flow for cosmological phenomena relating cosmic strings to quantized vortices, for processes occurring in neutron stars, or cosmological structure formation within superfluid models of dark matter.

A theoretical analysis is presented for the flow of a Herschel-Bulkley fluid around the inside surface of a rotating cylinder, at rotation speeds for which the fluid largely collects in a prominent pool in the lower part of the cylinder. The analysis, based on lubrication theory, predicts the steady states typically reached after a small number of rotations. The analysis is also modified to consider the drainage of the film around a stationary cylinder, which allows an exploration of the dynamics when a rotating drum is suddenly stopped. The predictions of the theory are compared with experiments in which a Carbopol suspension is rotated inside an acrylic drum.

Multiphase volume-fraction-dependent quasisteady force models have recently been developed. These models account for the mean force on a particle in the presence of neighboring particles. Additionally, in shock-particle interaction, there is an unsteady effect to the perturbation flow induced by the neighbors and their arrival to a particle. Namely, there is an unsteady component to the volume fraction effect. The present work advances a simple model to capture this time-dependent perturbative influence of neighbors in the context of a shock propagating through a cloud of particles. This model makes use of existing quasisteady force correlations that account for volume fraction within the framework of the compressible Maxey-Riley-Gatignol equation. This new unsteady neighbor force is applied via a time history kernel. The problem is examined in the context of a shock propagating outward in cylindrical geometry. It is observed that for the radii of curvatures examined, the model prediction is accurate in recovering the time history of force and time-integrated impulse on the particles. By comparing with a classical model, we also highlight the importance of volume fraction correction in accurately extracting the long-time force and the importance of unsteady contribution in accurately predicting the peak shock-induced force.

Statistical moments and power spectra of velocity fluctuations and their temporal derivative were measured behind four square-mesh grids at very small bulk Reynolds numbers. Three distinct states of such flows were identified: (1) in cases with insufficiently small Reynolds number, the flow was characterized as conventional grid turbulence, in which the turbulent kinetic energy was scaled with the mean velocity; (2) when the Reynolds number dropped below a threshold, which was specific for each grid, the flow was characterized as approximately steady; and (3) for Reynolds numbers that were between the two previous bounds (“intermediate state”), the flow structure exhibited peculiarities, the details of which depended on the grid geometry and the Reynolds number. The Reynolds stress anisotropy increased drastically in the intermediate state. Moreover, power spectra in the intermediate state differed strongly, when normalized by Kolmogorov scales based on the measured dissipation rate, but nearly collapsed in their large wave number ranges, when normalized by a dissipation rate that was fitted to a universal normalized spectrum. The flow state could not be characterized accurately by the Reynolds number based on mesh size, but the change of state from the conventional to the intermediate one occurred at ${\mathrm{Re}}_{\lambda }\approx 10$ for all grids. Finally, measurements quantified the dependence of the skewness and flatness factors of the streamwise velocity derivative, the ratio of production, and dissipation of vorticity fluctuations and the dissipation parameter upon ${\mathrm{Re}}_{\lambda }$.

In this paper, we study the artificially thickened boundary layer flows downstream of the tripping configuration that consists of a set of trip wires of varying diameters. Single-point hot-wire measurements are executed at a fixed streamwise location in the adaptation region, where the boundary layer is in conditions ranging from understimulation to overstimulation. Comparisons of the mean flow, Reynolds stress, energy spectra, and higher-order turbulence statistics demonstrate that the tripping effects are significant in the outer region, by introducing the enhanced energetic large scales with increasing the trip-wire diameter. The emergence of large scales manifests the scale separation in the overstimulated conditions, implying that the boundary layer has the potential to simulate high-Reynolds-number flows in the current tripping configurations. Then we attempt to identify the effect of the emergent large scales by examining the scale interactions. Under the overstimulated conditions, the generated large-scale structures penetrate down to the wall and superimpose energy in the near-wall region. The cross-term of the scale-decomposed skewness factor reveals that the amplitude modulation (AM) of the large scales on small scales is enhanced in the near-wall region. On the other hand, the frequency modulation (FM) is discussed by the zero-crossings-based evidence. Both the AM and FM effects become more significant with increasing the trip-wire diameter and the free-stream velocity. Far away from the wall, a reversal mechanism occurs and becomes more noticeable due to the tripping influence on the external intermittency. Moreover, it is found that the intermittent geometry of the turbulent/nonturbulent interface exhibits a fractallike self-similar convolution behavior in the current artificially thickened wall turbulence.

The transition from a free vortex superflow to a dissipative vortex flow in a superfluid remains an open problem, in particular because in real experiments, microscopic asperities on the walls play a major role since the relevant scales in a superfluid motion are basically of atomic scale. Here we model a superflow using the Gross-Pitaevskii mean-field equation in a domain with a rigid sinusoidal boundary. We demonstrate, analytically and numerically, the existence of a well-defined critical velocity for vortex nucleation. Additionally, we discuss the intrinsic mechanism of vortex nucleation by the appearance of a solitary wave characterized by a depletion of the wave function near the boundary.

The coupling between ion transport, fluid flow, and electrostatics may give rise to electroconvection, a physical phenomenon in which the buildup of charge near selective surfaces leads to hydrodynamic instability, eventually transitioning to an unsteady and chaotic flow. Though electroconvection contains a wide range of spatiotemporal scales, averaging of the ion concentration, velocity, and electric potential fields may produce a lower-dimensional and smoother representation while still capturing the essential performance metrics: ion current density and mean applied voltage, for example. The Poisson–Nernst–Planck–Stokes equations are known to capture the chaotic dynamics of electroconvection accurately. However, there is as of yet no way to directly compute the mean fields, since the application of the well-known Reynolds-averaging procedure leads to a closure problem. In this work, we combine the macroscopic forcing method, a numerical technique for measurement of closure operators in Reynolds-averaged equations, with high-fidelity experimental data to close the equations for the mean fields in chaotic electroconvection. We show that the unclosed fluxes in the Reynolds-averaged equations may be represented to the leading order as a gradient-diffusion term, with a spatially varying eddy diffusivity that we directly measure from experimental velocity fields. As a result, we are able to directly solve for the mean ion concentration and electric potential fields by supplementing the 1D Poisson–Nernst–Planck equations with an eddy diffusivity that captures the averaged effects of mixing due to chaotic, 3D electroconvection. The resulting current-voltage curve exhibits strong agreement with experiments. Our method allows for the study of electroconvection with orders-of-magnitude cost savings by obviating the need for expensive direct numerical simulations. Additionally, our measured eddy diffusivity profiles provide a benchmark for the development of stand-alone reduced-order models of electroconvection.