We investigate the gravitational settling of a long, model elastic filament in homogeneous isotropic turbulence. We show that the flow produces a strongly fluctuating settling velocity whose mean is moderately enhanced over the still-fluid terminal velocity and whose variance has a power-law dependence on the filament's weight but is surprisingly unaffected by its elasticity. In contrast, the tumbling of the filament is shown to be closely coupled to its stretching and manifests as a Poisson process with a tumbling time that increases as a power law with the elastic relaxation time of the filament. Apart from elasticity, inertia, and gravitational acceleration, we have also considered the effect of bending stiffness and found that stiff filaments settle slower but tumble faster than fully flexible filaments.

The granular column collapse is a simplified version of granular flows such as landslides, avalanches, and other industrial processes mobilized in air or within a fluid. In this configuration, the particles collapse in an accelerating phase, reaching a state of constant spreading velocity until they decelerate and stop. Granular flows commonly involve particles of different sizes, a property termed polydispersity. Understanding the role of polydispersity remains a challenging task that is often analyzed with nearly monodisperse systems and demanding a series of simplifications when coupled with a fluid in a numerical model. Here, we study the effect of particle-size polydispersity in dry and immersed granular columns, using a finite element method-discrete element method model for fluid-particle interactions. We show that the velocity of the column collapse and runout distance decrease with an increase in the level of polydispersity in immersed conditions, and remain nearly independent of the level of polydispersity in dry conditions. Moreover, we find that the runout scales with the spreading front kinetic energy, weighted by the ratio between the particles' density and the density difference between particles and fluid. This scaling helps in identifying the governing processes in polydisperse granular columns, unifying the runout description of both dry and immersed collapses, and indicating that the column initial packing fraction is the governing parameter.

The turbulent wake behind a square-back Ahmed body in close proximity to the ground exhibits bimodal switching. This manifests as the center of the wake switching between one of two asymmetric positions, either horizontally or vertically. Switches occur over random timescales, with the wake recovering symmetry in the long time average. The present work employs wall-resolved large eddy simulations to investigate feedback control for suppressing horizontal (lateral) wake bimodality of a square-back Ahmed body at Reynolds number, ${\mathrm{Re}}_H\sim 3.3\times {10}^4$ based on the body height. Base-mounted pressure sensors are used to estimate the position of the wake as an input signal for the controller, while actuation targets the near-wake region via synthetic jets emanating from a gap around the perimeter of the Ahmed body base. A nonlinear feedback controller based on a Langevin model of the wake dynamics is synthesized. This successfully suppresses the wake lateral bimodal switching. However, this switching is replaced by a time-periodic streamwise motion of the large coherent structure occupying the near-wake region, leading to amplification of the higher frequency dynamical wake modes. The action of feedback control also leads to base pressure recovery and a reduction in pressure drag. Upon varying the controller parameters, a trade-off between the degree of bimodality suppression and drag reduction is observed. A maximum drag reduction of $7.4\%$ is achieved for a semisymmetrized wake, with a fully symmetrized wake achieving $2.5\%$ reduction. Bimodality suppression is proposed to have an indirect link to drag reduction through the effect of the wake state on the separated free shear layers and the upstream boundary layers.

Direct numerical simulations of porous-walled channel flows with computational domain size constraints were performed to clarify the role of spanwise rollers associated with the Kelvin–Helmholtz instability on turbulent flows over a porous wall. The constraints of the domain size, which effectively hindered the development of the spanwise roller sustaining the near-wall turbulent motions, were imposed to isolate the effects of the near-wall turbulent motions and spanwise rollers. For each domain case, we considered thick and thin porous walls to isolate the effects of surface roughness and vertical permeability. It is found that the surface roughness plays a principal role in the modification of near-wall turbulent motions, including streaks and longitudinal vortices, whereas vertical permeability is essential for the development of spanwise rollers with streamwise alternating low- and high-speed regions. The spanwise roller contributes to an increase in the skin friction coefficient at the porous wall, and considerably increases the turbulence intensities deep inside the porous wall. The discussion in the logarithmic region based on the extended Jackson model reveals that the von Kármán constant is increased in the presence of the spanwise rollers, which is considered to reflect an increase in the characteristic vortex size owing to the spanwise rollers. The increase in the mixing length due to the role of the spanwise roller can be reasonably predicted by the classical mixing-length model with an increased von Kármán constant.

In this investigation, the transports of kinetic energy and scalar variance in the turbulence driven by a multiscale force $\mathit{M}{\nabla }^{\beta }{s}^{\prime }$ (which is associated with scalar fluctuations $s^{\prime }$) are theoretically studied. Although the velocity and scalar fields are strongly coupled, a universal flux conservation equation has been established in wave-number space and exhibits three different solutions, including one real solution and two complex solutions. The numerical analyses show that the turbulence generated under the multiscale force can possess four different cascade processes, including inertial subrange (constant fluxes of kinetic energy and scalar variance), constant-${\mathrm{\Pi }}_u$ subrange (quasiconstant flux of kinetic energy), constant-${\mathrm{\Pi }}_s$ subrange (quasiconstant flux of scalar variance), and a new subrange with both nonconstant fluxes of kinetic energy and scalar variance in addition to the dissipation subrange. Therefore, much richer information on the cascade processes and scaling exponents can be predicted in such a turbulent system, relative to the well-known Richardson cascade in conventional hydrodynamic turbulence. $\beta$ is a key to controlling the cascade processes and the scaling exponents. In the constant-${\mathrm{\Pi }}_u$ subrange, the slope of velocity spectrum is always ${\xi }_u=-5/3$, while the slope of the scalar spectrum is ${\xi }_s=-\left(6\beta +1\right)/3$. In the constant-${\mathrm{\Pi }}_s$ subrange, ${\xi }_u=\left(4\beta -11\right)/5$ and ${\xi }_s=-\left(2\beta +7\right)/5$. Relying on $\beta$, for the real solution, the transport of kinetic energy and scalar variance can be distinguished as four cases. (1) When $\beta <3/2$ (except $\beta =2/3$), the constant-${\mathrm{\Pi }}_u$ and constant-${\mathrm{\Pi }}_s$ subranges could be coexisted, with the former located on the lower wave-number side of the latter. At $\beta =2/3$, a new inertial subrange with both ${\xi }_u$ and ${\xi }_s$ equal to −5/3 is present in the multiscale-force dominated subrange. (2) When $3/2\le \beta <2$, only the constant-${\mathrm{\Pi }}_u$ subrange is predicted. (3) At $\beta =2$, special and singular exponents of ${\xi }_u=-1$, ${\xi }_s=-3$, ${\lambda }_u=1$ (the slope of kinetic energy flux), and ${\lambda }_s=-1$ (the slope of scalar variance flux) can be found, if $MN=1$. Otherwise, a constant-${\mathrm{\Pi }}_s$ subrange is predicted. (4) When $2<\beta \le 4$, only the constant-${\mathrm{\Pi }}_s$ subrange is predicted. For the second solution (one complex solution), when $\beta <3/2$, there are no constant-${\mathrm{\Pi }}_u$ and constant-${\mathrm{\Pi }}_s$ subranges, while for $\beta \ge 3/2$, a single constant-${\mathrm{\Pi }}_u$ subrange is predicted. For the third solution (the other complex solution), there is always a constant-${\mathrm{\Pi }}_s$ subrange. Finally, a complete transport picture of both kinetic energy and scalar variance has been established for the type of forced turbulence, which may unify hydrodynamic turbulence, stratified turbulence, turbulent thermal convection and electrokinetic turbulence, etc.

The flow features in branching networks are fundamental for the understanding of transport processes in respiratory and cardiovascular systems. Specifically for tumor embolization, the ability to predict the fate of finite-size particles in bifurcating vessels is highly desirable for improving embolization efficacy. Most past studies focused on very dilute regimes in which particles are not expected to interact with each other. In the present study, we use particle tracking velocimetry to investigate the spatial distribution, velocity, acceleration, and dispersion of finite-size particles in a four-generation bifurcating model. We consider a regime especially relevant to vascular embolization: a physiologic range of bulk flow Reynolds number and a suspension of neutrally buoyant particles with a diameter about 10 times smaller than the parent vessel diameter, reaching solid volume fractions up to 2%. We investigate how particles distribute among the distal branches and the influence of the release location. In addition, the effect of particle volume fraction is studied through Lagrangian statistics of the particle trajectories. Our results show the remarkable influence of particle concentration on particle transport in several ways. The particle traveling speed, acceleration, and dispersion are inhibited by the increasing particle volume fraction due to interparticle interactions. Importantly, the particles travel preferentially to the medial branches rather than to the lateral ones despite the uniform distribution of the distal volumetric flow rate. The findings provide insights relevant to the optimization of targeted drug delivery in embolization settings.

Base blowing is applied through a small, centrally located square aperture at the base of a flat-backed Ahmed body. In addition to the expected drag reduction effect at low momentum injection (i.e., base bleeding effect), a major result is the complete suppression of the steady asymmetry of the wake. Both the maximum drag reduction and the minimum magnitude of the base pressure gradient are achieved for the same optimal blowing coefficient of the actuator. Independent force measurements corroborate the suppression of the wake asymmetry. Different scales of base blowing reveal a similar maximum drag reduction and asymmetry suppression, where the optimal blowing coefficient is found to scale with the bleed-to-base area ratio as ${(S_j/S)}^{1/2}$.

The flow of frictionless granular particles is studied with stress-controlled discrete element modeling simulations for systems varying in size from 300 to 100 000 particles. The volume fraction and shear-stress ratio $\mu$ are relatively insensitive to system size for a wide range of inertial numbers $I$. Second-order effects in strain rate, such as normal stress differences, require large system sizes to accurately extract meaningful results, notably a nonmonotonic dependence in the first normal stress difference with strain rate. The rheological response represented by the $\mu \left(I\right)$ scalar model works well at describing the lower-order aspects of the rheology, except near the quasistatic limit of these stress-controlled flows. The pressure is varied over five decades, and a pressure dependence of the coordination number is observed, which is not captured by the inertial number. Large fluctuations observed for small systems $N\le 1000$ near the quasistatic limit can lead to the arrest of flow resulting in challenges to fitting the data to rheological relationships. The inertial number is also insufficient for capturing the pressure-dependent behavior of property fluctuations. Fluctuations in the flow and microstructural properties are measured in both the quasistatic and inertial regimes, including shear stress, pressure, strain rate, normal stress differences, volume fraction, coordination number, and contact fabric anisotropy. The fluctuations in flow properties scale self-similarly with pressure and system size. A transition in the scaling of fluctuations of stress properties and contact fabric anisotropy are measured and proposed as a quantitative identification of the transition from inertial to quasistatic flow.

The elemental equation governing heat transfer in aerodynamic flows is the internal energy equation. For a boundary layer flow, a double integration of the Reynolds-averaged form of this equation provides an expression of the wall heat flux in terms of the integrated effects, over the boundary layer, of various physical processes: turbulent dissipation, mean dissipation, turbulent heat flux, etc. Recently available direct numerical simulation data for a Mach 11 cold-wall turbulent boundary layer allows a comparison of the exact contributions of these terms in the energy equation to the wall heat flux with their counterparts modeled in the Reynolds-averaged Navier-Stokes (RANS) framework. Various approximations involved in RANS, both closure models as well as approximations involved in adapting incompressible RANS models to a compressible form, are assessed through examination of the internal energy balance. There are a number of potentially problematic assumptions and terms identified through this analysis. The effect of compressibility corrections of the dilatational dissipation type is explored, as is the role of the modeled turbulent dissipation, in the context of wall heat flux predictions. The results indicate several potential avenues for RANS model improvement for hypersonic cold-wall boundary-layer flows.

This study analyzes the effects of shocklets on sound source characteristics using direct numerical simulations. The sound sources are obtained from the source terms of the Lighthill equation. The highest initial turbulent Mach number $M_{t0}$ is set to be 1.0, and the strong effects of shocklets on sound sources are investigated. Results show that the occurrence of shocklets in high turbulent Mach numbers $M_{t0}\ge 0.7$ affects the sound generation mechanism in addition to vortical motions which are well-known sound sources in low Mach number turbulent flows. The change in mechanism influences the relationship between the Reynolds stress and entropy terms. For low turbulent Mach number flows without shocklets, the Reynolds stress and entropy terms partially show the same signs around and on vortices. However, for high turbulent Mach numbers with shocklets, the terms exhibit opposite signs across shocklets. The behaviors of the Reynolds stress and entropy terms across shocklets are explained analytically by using a one-dimensional shock relation. The change in sound source characteristics keeps velocity dependence on total sound source strength almost unchanged independent of the turbulent Mach number, though each term's sound source strength (normalized by the total sound source strength) becomes larger for the higher turbulent Mach numbers $M_{t0}\ge 0.9$ than those for low turbulent Mach numbers $M_{t0}\le 0.4$. Besides, the applicability of the present study to predict far-field acoustic wave characteristics is discussed. The source terms based on Lilley's decomposition show that the sound sources derived by shocklets have quadruple characteristics. Also, it is shown that the given knowledge in the present study, especially for the relation between the Reynolds stress and entropy terms across shocklets, can be used to improve the source modeling for a nonlinear acoustic analogy based on the Lighthill's acoustic analogy and Burgers' equation. In addition, the paper provides a possible explanation of the contributions of the shocklets for a mechanism of crackle noise that the generated acoustic waves by shocklets propagates to the acoustic field and show high-frequency spectral characteristics.

This paper examines the theoretical modeling of a steady horizontal gravity current involving miscible fluids. The main objective is to determine the longitudinal evolution of the current characteristic quantities: its mean velocity $U$, its height $h$, its mean density $\rho$, and the local Richardson number $\text{Ri}=g\mathrm{\Delta }\rho h/\rho U^2$, which characterizes the flow regime. The theory developed by Ellison and Turner [J. Fluid Mech. 6, 423 (1959)] for Boussinesq gravity currents is first extended to the general non-Boussinesq case. In this theoretical approach, the differential equations derived from the conservation equations reveal a mathematical singularity which no longer allows them to be solved when the current passes from a supercritical to a subcritical regime, i.e., when the Richardson number reaches unity. To circumvent this problem, we propose to introduce a jump condition into the model which leads to a sudden transition from a supercritical to a subcritical regime when needed. The jump location is set to satisfy the boundary condition at the exit. Numerical simulations are carried out using a large-eddy simulation code in order to obtain reference results. These results are first used to select a suitable entrainment model among those proposed in the literature. The simulations are then compared with the theoretical model. In the case of a supercritical current without regime change, the agreement between simulation and theory is good. In the case of a supercritical current turning subcritical before the exit, the discontinuity imposed in the model by the jump is clearly abrupt in comparison with the physical reality, but it allows us to reproduce the nonmonotonic evolution of the velocity, height, and Richardson number of the current and to obtain an acceptable estimation of these quantities.

The spreading of complex fluids is not only a part of our everyday life but also a central process in industry to produce functional thin films or protective coatings. Here we consider the spreading of polymer solutions with an elastic blade that deforms during the coating (similarly to a brush or a finger). By using complex fluids with well-chosen rheological properties, we disentangle the effects of shear viscosity, shear thinning, and normal stresses. We reveal two counterintuitive results: First, the mechanical work needed to spread a given volume of a shear-thinning fluid is higher than for the same volume of an equivalent Newtonian fluid at constant spreading velocity. Second, the first normal stress difference, which usually leads to remarkable behaviors such as the swelling of jets or the rise of the fluid on a rotating rod, has strikingly negligible effect here.

The development of turbulence closure models, parametrizing the influence of small nonresolved scales on the dynamics of large resolved ones, is an outstanding theoretical challenge with vast applicative relevance. We present a closure, based on deep recurrent neural networks, that quantitatively reproduces, within statistical errors, Eulerian and Lagrangian structure functions and the intermittent statistics of the energy cascade, including those of subgrid fluxes. To achieve high-order statistical accuracy, and thus a stringent statistical test, we employ shell models of turbulence. Our results encourage the development of similar approaches for three-dimensional Navier-Stokes turbulence.

We study the dynamics of a dilute solution of rigid rodlike polymers in a viscous fluid at low Reynolds numbers by means of numerical simulations of a simple rheological model. We show that the rotational dynamics of polymers destabilizes the laminar flow and causes the emergence of a turbulent-like chaotic flow with a wide range of active scales. This regime displays an increased flow resistance, corresponding to a reduced mean flow at fixed external forcing, as well as an increased mixing efficiency. The latter effect is quantified by measuring the decay of the variance of a scalar field transported by the flow. By comparing the results of numerical simulations of the model in two and three dimensions, we show that the phenomena observed are qualitatively independent on the dimensionality of the system, but the effects of polymer are, in general, stronger in two dimensions. This dimensional effect is explained in terms of the different rotational degrees of freedom of the rods.

In this paper we propose a Boltzmann collision operator in the continuous internal energy setting that describes polyatomic gases with temperature-dependent specific heats or thermally perfect (nonpolytropic) gases. We adopt the assumption, already presented in the Bhatnagar-Gross-Krook setup, of letting molecular internal degrees of freedom be temperature dependent and provide a method to determine its explicit dependence upon temperature from the given experimental data. We then focus on a macroscopic system of 14 moments in the nonpolytropic setting. Computation of production terms allows us to express the transport coefficients—bulk and shear viscosities and thermal conductivity—in terms of parameters from the collisional cross section. The values of these parameters are fitted to match the experimental data for Prandtl number in a certain temperature range. This led to improvement of the estimate obtained by the Eucken formula and allowed computation of the dynamic pressure relaxation time or equivalently the bulk viscosity and comparison with its estimates in the literature.

The Arctic Ocean's main thermocline may be characterized by a series of fine-scale thermohaline staircase structures that are present in a wide range of regions, the formation mechanism of which remains unclear. Recent analysis has led to the proposal of a theoretical model which suggested that these staircase structures form spontaneously in the ocean when the turbulent intensity determined by the buoyancy Reynolds number ${\text{Re}}_b$ is sufficiently weak. In the current work, we have designed a series of ${\text{Re}}_b$ controlled direct numerical simulations of turbulence in the Arctic Ocean thermocline to test the effectiveness of this theory. In these simulations, the staircases form naturally when ${\text{Re}}_b$ falls in the range predicted by the instability criterion. The exponential growth rate of the layering mode matches well with the prediction of the theoretical model. The staircases formed in our simulations are further compared with the classical diffusive interface model, which argues that stable staircase structures can only form when the density ratio $R_{\rho }$ is smaller than the critical value of $R_{\rho }^{cr}={\tau }^{-1/2}$. Here $\tau$ is the ratio of haline diffusivity over thermal diffusivity. We show that the staircase structure can stably persist in our model regardless of whether or not $R_{\rho }<R_{\rho }^{cr}$ is satisfied.

How fast ice melts in turbulent flows is key to many natural and industrial processes, most notably the melting of ice in the polar regions. To get a better quantitative understanding of the physical mechanics at play, as a model system we pick vertical convection, consisting of ice and fresh water, and examine the lateral melting behavior through numerical simulations and theory. We find that the melting rate of ice as a function of an increasing heating temperature undergoes an abrupt transition from a slow- to a fast-melting state, contrary to the intuition of a gradual transition. The abrupt transition of the ice melting rate is due to the emergence of a reversed buoyant flow, due to the density anomaly of water near the melting point. A theoretical model based on energy conservation gives rise to a universal expression to relate the global heat fluxes and the ice melting rate which is consistent with our data. Besides their fundamental significance, our findings improve our understanding of how phase transitions couple to adjacent turbulent flow.

To identify and characterize very-large-scale motions (VLSM) in turbulent channel flows, direct numerical simulations are performed at ${\text{Re}}_{\tau }=906$ and 3216. The turbulence structure is then analyzed by proper orthogonal decomposition (POD) and multiscale POD (mPOD). Unlike POD, mPOD is able to distinguish the most energetic modes at selected scales (or frequencies) by imposing spectral cutoffs to separate VLSM, large-scale motions (LSM), and small-scale motions. The VLSM can be clearly visualized from the most energetic spatial modes of the mPOD analysis at both Reynolds numbers. The mPOD results identify a new energetic mode that is aligned in the streamwise direction with a characteristic length covering the whole domain length. This new mode (called eVLSM mode) contains substantial energy, making it an important component of the VLSM in the flow field. The other energetic modes typically appear in pairs with specific streamwise phase shifts. The large-scale structures (apart from eVLSM) are inclined to the streamwise direction and appear to be responsible for the typical meandering behavior or even for the breakup of VLSM.

The deformation of a dense carpet of hair due to Stokes flow in a channel can be described by a nonlinear integrodifferential equation for the shape of a single hair, which possesses several solutions for a given choice of parameters. Although it was posed in a previous study and it bears a resemblance to the pendulum problem from mechanics, this equation has not been analytically solved until now. Despite the presence on an integral with a nonlinear functional dependence on the dependent variable, the system is integrable. We compare the analytically obtained solution to a finite-difference numerical approach, identify the physically realizable solution branch, and briefly study the solution structure through a conserved energylike quantity. Time-dependent fluid-structure interactions are a rich and complex subject to investigate, and we argue that the solution discussed herein can be used as a basis for understanding these systems.