We investigate the evolution of vortex-surface fields (VSFs) in compressible Taylor-Green flows at Mach numbers (Ma) ranging from 0.5 to 2.0 using direct numerical simulation. The formulation of VSFs in incompressible flows is extended to compressible flows, and a mass-based renormalization of VSFs is used to facilitate characterizing the evolution of a particular vortex surface. The effects of the Mach number on the VSF evolution are different in three stages. In the early stage, the jumps of the compressive velocity component near shocklets generate sinks to contract surrounding vortex surfaces, which shrink vortex volume and distort vortex surfaces. The subsequent reconnection of vortex surfaces, quantified by the minimal distance between approaching vortex surfaces and the exchange of vorticity fluxes, occurs earlier and has a higher reconnection degree for larger Ma owing to the dilatational dissipation and shocklet-induced reconnection of vortex lines. In the late stage, the positive dissipation rate and negative pressure work accelerate the loss of kinetic energy and suppress vortex twisting with increasing Ma.

Aligned finger structures, with a characteristic width, emerge during the slow drainage of a liquid-granular mixture in a tilted Hele-Shaw cell. A transition from vertical to horizontal alignment of the finger structures is observed as the tilting angle and the granular density are varied. An analytical model is presented, demonstrating that the alignment properties are the result of the competition between fluctuating granular stresses and the hydrostatic pressure. The dynamics is reproduced in simulations. We also show how the system explains patterns observed in nature, created during the early stages of a dike formation.

Drag reduction capability of uniform blowing in supersonic turbulent boundary layers is investigated by means of direct numerical simulation of channel flows with uniform blowing on one side and suction on the other. The bulk Reynolds number based on the bulk density, the bulk mean velocity, the channel half-width, and the viscosity on the wall is set to ${\text{Re}}_b=3000$. The bulk Mach number is set at 0.8 and 1.5 to investigate a subsonic and a supersonic condition, respectively. The amplitude of the blowing or suction is set to be 0.1%, 0.3%, or 0.5% of the bulk mass flow rate. At both Mach numbers, modifications of the mean streamwise velocity profiles with blowing and suction are found to be similar to those in an incompressible turbulent channel flow: The skin friction is reduced on the blowing side, while it is increased on the suction side. As for the drag reducing effect of blowing, the drag reduction rate and net-energy saving rate are hardly affected by the Mach number, while the control gain is increased with the increase of Mach number due to the increased density near the wall. The compressibility effect of drag reduction and enhancement is also examined using the physical decomposition of the skin friction drag. A noticeable Mach number effect is found only for the contribution terms containing the viscosity, which is increased by the increased temperature.

The Koopman mode decomposition (KMD) is a data-analysis technique which is often used to extract the spatiotemporal patterns of complex flows. In this paper, we use KMD to study the dynamics of the lid-driven flow in a two-dimensional square cavity based on theorems related to the spectral theory of the Koopman operator. We adapt two algorithms, from the classical Fourier and power spectral analysis, to compute the discrete and continuous spectrum of the Koopman operator for the post-transient flows. Properties of the Koopman operator spectrum are linked to the sequence of flow regimes occurring between $\text{Re}=10000$ and $\text{Re}=30000$, and changing the flow nature from steady to aperiodic. The Koopman eigenfunctions for different flow regimes, including flows with mixed spectra, are constructed using the assumption of ergodicity in the state space. The associated Koopman modes show remarkable robustness even as the temporal nature of the flow is changing substantially. We observe that KMD outperforms the proper orthogonal decomposition in reconstruction of the flows with strong quasiperiodic components.

The generation of a turbulent inflow is a tricky problem. In the framework of aeroacoustics, another important constraint is that the numerical strategy used to reach a turbulent state induces a spurious noise which is lower than the acoustic field of interest. For the study of noise radiated directly by a turbulent boundary layer on a flat plate, this constraint is severe since wall turbulence is a very inefficient source. That is why a method based on a transition by modal interaction using a base flow with an inflection point is proposed to cope with that. The base flow must be a solution of the equations so we use a profile behind a backward-facing step representative of experimental trip bands. A triad of resonant waves is selected by a local stability analysis of the linearized compressible equations and is added with a weak amplitude in the inlet plane. The compressible stability calculation allows the specification of the thermodynamic quantities at the inlet, which turns out to be fundamental to ensure a quiet inflow. A smooth transition is achieved with the rapid formation of $\mathrm{\Lambda }$-shape vortices in a staggered organization as in subharmonic transition. The dominance of oblique waves promotes a rapid breakdown by the liftup mechanism of low-speed streaks. The quality of the fully turbulent state is assessed and the direct noise radiation from a turbulent boundary layer at Mach 0.5 is obtained with a very low level of spurious noise.

The interaction of a counter-rotating vortex pair (dipole) with a flat plate in its path is studied numerically. The vortices are initially separated by a distance $D$ (dipole size) and placed far upstream of a plate of length $L$. The plate is centered on the dipole path and inclined relative to it at an incident angle ${\beta }_i$. At first, the plate is held fixed in place. The vortices approach the plate, travel around it, and then leave as a dipole with unchanged velocity but generally a different travel direction, measured by a transmitted angle ${\beta }_t$. For certain plate angles the transmitted angle is highly sensitive to changes in the incident angle. The sensitivity increases as the dipole size decreases relative to the plate length. In fact, for sufficiently small values of $D/L$, singularities appear: near critical values of ${\beta }_i$, the dipole trajectory undergoes a topological discontinuity under changes of ${\beta }_i$ or $D/L$. The discontinuity is characterized by a jump in the winding number of one vortex around the plate, and in the time that the vortices take to leave the plate. The jumps occur repeatedly in a self-similar, fractal fashion, within a region near the critical values of ${\beta }_i$, showing the existence of incident angles that trap the vortices, which never leave the plate. The number of these trapping regions increases as the parameter $D/L$ decreases, and the dependence of the motion on ${\beta }_i$ becomes increasingly complex. The simulations thus show that even in this apparently simple scenario, the inviscid dynamics of a two-point-vortex system interacting with a stationary wall is surprisingly rich. The results are then applied to separate an incoming stream of dipoles by an oscillating plate.

Orientational order in a fluid affects the swimming behavior of flagellated microorganisms. For example, bacteria tend to swim along the director in lyotropic nematic liquid crystals. To better understand how anisotropy affects propulsion, we study the problem of a sheet supporting small-amplitude traveling waves, also known as the Taylor swimmer, in a nematic liquid crystal. For the case of weak anchoring of the nematic director at the swimmer surface and in the limit of a minimally anisotropic model, we calculate the swimming speed as a function of the angle between the swimmer and the nematic director. The effect of the anisotropy can be to increase or decrease the swimming speed, depending on the angle of alignment. We also show that elastic torque dominates the viscous torque for small-amplitude waves and that the torque tends to align the swimmer along the local director.

We revisit the Wayner problem of the microregion of a contact line at rest formed by a perfectly wetting single-component liquid on an isothermal superheated flat substrate in an atmosphere of its own pure vapor. The focus is on the evaporation-induced apparent contact angles. The microregion is shaped by the effects of viscosity, Laplace and disjoining pressures (the latter in the form of an inverse-cubic law), and evaporation. The evaporation is in turn determined by heat conduction across the liquid film, kinetic resistance, and the Kelvin effect (i.e., saturation-condition dependence on the liquid-vapor pressure difference). While an asymptotic limit of large kinetic resistances was considered by Morris nearly two decades ago [J. Fluid Mech. 432, 1 (2001)], here we are concerned rather with matched asymptotic expansions in the limits of weak and strong Kelvin effects. Certain extensions are also touched upon within the asymptotic analysis. These are a more general form of the disjoining pressure and account for the Navier slip. Most notably, these also include the possibility of Wayner's extended microfilms (covering macroscopically dry parts of the substrate) actually getting truncated. A number of isolated cases encountered in the literature are thereby systematically recovered.

We study nonlinearities of inertial waves in rotating turbulence. At small Rossby numbers the kinetic energy in the system is contained in helical inertial waves with time dependence amplitudes. In this regime the amplitude variations time scales are slow compared to wave periods, and the spectrum is concentrated along the dispersion relation of the waves. A nonlinear time scale was extracted from the width of the spectrum, which reflects the intensity of nonlinear wave interactions. This nonlinear time scale is found to be proportional to ${\left(\mathit{U}·\mathit{k}\right)}^{-1}$, where $\mathit{k}$ is the wave vector and $\mathit{U}$ is the root-mean-square horizontal velocity, which is dominated by large scales. This correlation, which indicates the existence of turbulence in which inertial waves undergo weak nonlinear interactions, persists only for small Rossby numbers.

Rarefied gas flow in a three-dimensional enclosure induced by nonuniform temperature distribution is numerically investigated. The enclosure has a square channel-like geometry with alternatively heated closed ends and lateral walls with a linear temperature distribution. A recently proposed implicit discrete velocity method with a memory reduction technique is used to numerically simulate the problem based on the nonlinear Shakhov kinetic equation. The Knudsen number dependencies of the vortices pattern, slip velocity at the planar walls and edges, and heat transfer are investigated. The influences of the temperature ratio imposed at the ends of the enclosure and the geometric aspect ratio are also evaluated. The overall flow pattern shows similarities with those observed in two-dimensional configurations in literature. However, features due to the three-dimensionality are observed with vortices that are not identified in previous studies on similar two-dimensional enclosures at high Knudsen and small aspect ratios.

Systematic simulations of the two-fluid model of superfluid helium (He-II) encompassing the Hall-Vinen-Bekharevich-Khalatnikov (HVBK) mutual coupling have been performed in two-dimensional pipe counterflows between 1.3 and 1.96 K. The numerical scheme relies on the lattice Boltzmann method. A Boussinesq-like hypothesis is introduced to omit temperature variations along the pipe. In return, the thermomechanical forcings of the normal and superfuid components are fueled by a pressure term related to their mass-density variations under an approximation of weak compressibility. This modeling framework reproduces the essential features of a thermally driven counterflow. A generalized definition of the entrance length is introduced to suitably compare entry effects (of different nature) at opposite ends of the pipe. This definition is related to the excess of pressure loss with respect to the developed Poiseuille-flow solution. At the heated end of the pipe, it is found that the entrance length for the normal fluid follows a classical law and increases linearly with the Reynolds number. At the cooled end, the entrance length for the superfluid is enhanced as compared to the normal fluid by up to one order of magnitude. At this end, the normal fluid flows into the cooling bath of He-II and produces large-scale superfluid vortical motions in the bath that partly re-enter the pipe along its sidewalls before being damped by mutual friction. In the superfluid entry region, the resulting frictional coupling in the superfluid boundary layer distorts the velocity profiles toward tail flattening for the normal fluid and tail raising for the superfluid. Eventually, a simple analytical model of entry effects allows us to re-examine the long-debated thresholds of $T1$ and $T2$ instabilities in superfluid counterflows. Inconsistencies in the $T1$ thresholds reported since the 1960s disappear if an aspect-ratio criterion based on our modeling is used to discard data sets with the strongest entry effects. Furthermore, it is observed that entry effects can spuriously reproduce the signature of a $T2$ transition with a normal flow remaining laminar.

We study a mechanism for active aerodynamic drag reduction on morphable grooved cylinders, whose topography can be modified pneumatically. Our design is inspired by the morphology of the Saguaro cactus (Carnegiea gigantea), which possesses an array of axial grooves, thought to help reduce aerodynamic drag, thereby enhancing the structural robustness of the plant under wind loading. Our analog experimental samples comprise a spoked rigid skeleton with axial cavities, covered by a stretched elastomeric film. Decreasing the inner pressure of the sample produces axial grooves, whose depth can be accurately varied, on demand. First, we characterize the relation between groove depth and pneumatic loading through a combination of precision mechanical experiments and finite element simulations. Second, wind tunnel tests are used to measure the aerodynamic drag coefficient (as a function of Reynolds number) of the grooved samples, with different levels of periodicity and groove depths. We focus specifically on the drag crisis and systematically measure the associated minimum drag coefficient and the critical Reynolds number at which it occurs. The results are in agreement with the classic literature of rough cylinders, albeit with an unprecedented level of precision and resolution in varying topography using a single sample. Finally, we leverage the morphable nature of our system to dynamically reduce drag for varying aerodynamic loading conditions. We demonstrate that actively controlling the groove depth yields a drag coefficient that decreases monotonically with Reynolds number and is significantly lower than the fixed sample counterparts. These findings open the possibility for the drag reduction of grooved cylinders to be operated over a wide range of flow conditions.

This experimental study investigates the effects of ambient pressure and Reynolds number on the volume of a plastron in a superhydrophobic surface (SHS) due to compression and gas diffusion. The hierarchical SHS consists of nanotextured, ∼100 μm wide spanwise grooves. Microscopic observations measure the time evolution of interface height and contact angle. The water tunnel tests are performed both without flow as well as in transitional and turbulent boundary layers at several Reynolds numbers. Particle image velocimetry is used for estimating the wall shear stress and calculating the momentum thickness for the SHSs under Cassie-Baxter (CB) and Wenzel states as well as a smooth wall at the same conditions. Holographic microscopy is used for determining the wall shear stress directly for one of the CB cases. The mass diffusion rate is calculated from changes to the plastron volume when the liquid is under- or supersaturated. For stationary water, the mass diffusion is slow. With increasing pressure, the interface is initially pinned and then migrates into the groove with high advancing contact angle. Upon subsequent decrease in pressure, the interface migrates upward at a shallow angle and, after being pinned to the tip corner, becomes convex. With flow and exposure to undersaturated liquid, the diffusion-induced wetting also involves pinned and downward migration states, followed by shrinkage of the plastron until it decreases below the resolution limit. The corresponding changes to the velocity profile indicate a transition from slight drag reduction to significant drag increase. In supersaturated water starting at a Wenzel state, a bubble grows from one of the bottom corners until it reaches the other side of the groove. Subsequently, dewetting involves upward migration of the interface, pinning to the tip corners, and formation of a convex interface. The diffusion rate increases with the level of under- or supersaturation and with the Reynolds number. A power law relation, $\mathrm{S}{\mathrm{h}}_{\mathrm{\Theta }0}=0.47{{\mathrm{Re}}_{\mathrm{\Theta }0}}^{0.77}$, is obtained for the turbulent flow regime using the smooth wall momentum thickness for calculating the Sherwood ($\mathrm{S}{\mathrm{h}}_{\mathrm{\Theta }0}$) and Reynolds ($\mathrm{R}{\mathrm{e}}_{\mathrm{\Theta }0}$) numbers. This relation agrees with published diffusion rates for smooth wall turbulent boundary layers. However, the mass diffusion rate is lower than this prediction in the transitional boundary layer. When $\mathrm{S}{\mathrm{h}}_{\mathrm{\Theta }0}$ is plotted against the friction Reynolds number ($\mathrm{R}{\mathrm{e}}_{\tau 0}$) instead, both the transitional and turbulent boundary layer results collapse onto a single power law, $\mathrm{S}{\mathrm{h}}_{\mathrm{\Theta }0}=0.34{{\mathrm{Re}}_{\tau 0}}^{0.913}$. This trend suggests that turbulent diffusion and wall friction are correlated. The relation between Sherwood number and momentum thickness Reynolds number persists if length scales of the Wenzel state are used instead of those of the smooth wall. However, trends with the friction Reynolds number change slightly.

The macroscopic properties of fluid flow and transport through porous media are a direct consequence of the underlying pore structure. However, precise relations that characterize flow and transport from the statistics of pore-scale disorder have remained elusive. Here we investigate the relationship between pore structure and the resulting fluid flow and asymptotic transport behavior in two-dimensional geometries of nonoverlapping circular posts. We derive an analytical relationship between the pore throat size distribution $f_{\lambda }\sim {\lambda }^{-\beta }$ and the distribution of the low fluid velocities $f_u\sim u^{-\beta /2}$, based on a conceptual model of porelets (the flow established within each pore throat, here a Hagen-Poiseuille flow). Our model allows us to make predictions, within a continuous-time random-walk framework, for the asymptotic statistics of the spreading of fluid particles along their own trajectories. These predictions are confirmed by high-fidelity simulations of Stokes flow and advective transport. The proposed framework can be extended to other configurations which can be represented as a collection of known flow distributions.

Stochastic rotation dynamics (SRD) is a widely used method for the mesoscopic modeling of complex fluids, such as colloidal suspensions or multiphase flows. In this method, however, the underlying Cartesian grid defining the coarse-grained interaction volumes induces anisotropy. We propose an isotropic, lattice-free variant of stochastic rotation dynamics, termed iSRD. Instead of Cartesian grid cells, we employ randomly distributed spherical interaction volumes. This eliminates the requirement of a grid shift, which is essential in standard SRD to maintain Galilean invariance. We derive analytical expressions for the viscosity and the diffusion coefficient in relation to the model parameters, which show excellent agreement with the results obtained in iSRD simulations. The proposed algorithm is particularly suitable to model systems bound by walls of complex shape, where the domain cannot be meshed uniformly. The presented approach is not limited to SRD but is applicable to any other mesoscopic method, where particles interact within certain coarse-grained volumes.

Peritrichous bacteria swim in viscous fluids by rotating multiple helical flagellar filaments. As the bacterium swims forward, all its flagella rotate in synchrony behind the cell in a tight helical bundle. When the bacterium changes its direction, the flagellar filaments unbundle and randomly reorient the cell for a short period of time before returning to their bundled state and resuming swimming. This rapid bundling and unbundling is, at its heart, a mechanical process whereby hydrodynamic interactions balance with elasticity to determine the time-varying deformation of the filaments. Inspired by this biophysical problem, we present in this paper what is perhaps the simplest model of bundling whereby two or more straight elastic filaments immersed in a viscous fluid rotate about their centerline, inducing rotational flows which tend to bend the filaments around each other. We derive an integrodifferential equation governing the shape of the filaments resulting from mechanical balance in a viscous fluid at low Reynolds number. We show that such equation may be evaluated asymptotically analytically in the long-wavelength limit, leading to a local partial differential equation governed by a single dimensionless bundling number. A numerical study of the dynamics predicted by the model reveals the presence of two configuration instabilities with increasing bundling numbers: first to a crossing state where filaments touch at one point and then to a bundled state where filaments wrap along each other in a helical fashion. We also consider the case of multiple filaments and the unbundling dynamics. We next provide an intuitive physical model for the crossing instability and show that it may be used to predict analytically its threshold and adapted to address the transition to a bundling state. We then use a macroscale experimental implementation of the two-filament configuration in order to validate our theoretical predictions and obtain excellent agreement. This long-wavelength model of bundling will be applicable to other problems in biological physics and provides the groundwork for further, more realistic, models of flagellar bundling.

A numerical method is presented that conveniently computes upper bounds on heat transport and poloidal energy in plane layer convection for infinite and finite Prandtl numbers. The bounds obtained for the heat transport coincide with earlier results. These bounds imply upper bounds for the poloidal energy, which follow directly from the definitions of dissipation and energy. The same constraints used for computing upper bounds on the heat transport lead to improved bounds for the poloidal energy.

It is well known that charged analytes in the presence of nonuniform electric fields concentrate at locations where the relevant driving forces balance, and a wide range of ionic stacking and focusing methods are commonly employed to leverage these physical mechanisms in order to improve signal levels in biosensing applications. In particular, nanofluidic channels with spatially varying conductivity distributions have been shown to provide increased preconcentration of charged analytes due to the existence of a finite electric double layer (EDL), in which electrostatic attraction and repulsion from charged surfaces produce nonuniform transverse ion distributions. In this work, we use numerical simulations to show that one can achieve greater levels of sample accumulation by using field-effect control via wall-embedded electrodes to tailor the surface potential heterogeneity in a nanochannel with overlapped EDLs. In addition to previously demonstrated stacking and focusing mechanisms, we find that the coupling between two-dimensional ion distributions and the axial electric field under overlapped EDL conditions can generate an ion concentration polarization interface in the middle of the channel. Under an applied electric field, this interface can be used to concentrate sample ions between two stationary regions of different surface potential and charge density. Our numerical model uses the Poisson-Nernst-Planck system of equations coupled with the Stokes equation to demonstrate the phenomenon, and we discuss in detail the driving forces behind the predicted sample enhancement. The numerical velocity and salt concentration profiles exhibit good agreement with analytical results from a simplified one-dimensional area-averaged model for several limiting cases, and we show predicted amplification ratios of up to ${10}^5$.

We study the dynamical state of the one-dimensional noisy generalized Kuramoto-Sivashinsky (gKS) equation by making use of time-series techniques based on symbolic dynamics and complex networks. We focus on analyzing temporal signals of global measure in the spatiotemporal patterns as the dispersion parameter of the gKS equation and the strength of the noise are varied, observing that a rich variety of different regimes, from high-dimensional chaos to pure stochastic behavior, emerge. Permutation entropy, permutation spectrum, and network entropy allow us to fully classify the dynamical state exposed to additive noise.