Pushing two fluids with different density one against the other causes the development of the Rayleigh-Taylor instability at their interface, which further evolves in a complex mixing layer. In porous media, this process is influenced by the viscous resistance experienced while flowing through the pores, which is described by the Darcy's law. Here, we investigate the mixing properties of the Darcy-Rayleigh-Taylor system in the limit of large Péclet number by means of direct numerical simulations in three and two dimensions. In the mixing zone, the balance between gravity and viscous forces results in a non-self-similar growth of elongated plumes, whose length increases linearly in time while their width follows a diffusive growth. The mass-transfer Nusselt number is found to increase linearly with the Darcy-Rayleigh number supporting a universal scaling in porous convection at high Ra numbers. Finally, we find that the mixing process displays important quantitative differences between two and three dimensions.

Introducing surface corrugations to alter the boundary layer flow is a proven way to reduce the fluid drag on a surface. In this study, we examine the effect of periodic, infinitely long spanwise grooves on the laminar boundary layer over a plate for global Reynolds numbers $\left(\mathrm{R}{\mathrm{e}}_L\right)$ between 1000 and 25 000. By employing numerical simulations in two-dimensional domains, we investigate the flow and pressure evolution over surfaces containing rectangular grooves that are perpendicular to the flow and infinitely long in the spanwise direction, and compare them to a flat plate. We characterize the flow interactions near the grooves based on their width-to-depth aspect ratio (AR). Below a certain aspect ratio, a primary vortex fills the space inside each groove. These vortices allow the free stream to “slip over” the grooved regions and result in less skin friction on the wall. However, the interaction between the flow and the grooves’ vertical walls leads to a pressure drag. We study the behavior of the individual drag components over a wide range of aspect ratios (0.2 < AR < 200) and compare the total drag reduction in each case. Based on the simulation results, the transverse grooves in the laminar regime can reduce the total drag up to 10% in comparison to a flat plate, despite increasing the wetted surface area of the plate. Conversely, at some aspect ratios the grooves cause a total drag increase of more than 200%. We observe that by increasing the aspect ratio, the free stream bends more toward the grooves; ultimately at a certain aspect ratio, denoted by $\mathrm{A}{\mathrm{R}}^{*}$, the flow breaks apart the underlying circulation and reaches the bottom of the grooves. When this happens, the flow shear on the grooves’ bottom walls combined with the high-pressure drag exerted on the vertical walls can lead to a net increase in the drag. Therefore, the aspect ratio of the grooves is a critical parameter in optimizing drag reduction in transverse geometries.

Experiments on the mixing of two different fluids at low Reynolds number inside helical channels have shown that their curvature and torsion induce secondary flow at the channel cross section, which enhances mixing between liquids. While these channels are mostly of symmetric cross section, e.g., circular and rectangular, recent experiments suggest that helical channels with asymmetric cross sections can enhance mixing even further. There have, however, been few systematic studies on the coupled effect of the asymmetry of a channel cross section and its three-dimensional orientation on the mixing of fluid streams. In this regard, we have examined mixing between three differently dyed streams of cross-linkable silicone material inside triple-helical microchannels; we have also simulated the flow of liquids through such channels using fluent software. Our results show that the length of the interface that separates different liquids at any cross section varies linearly with a nondimensional parameter involving curvature, torsion, axial length, and helix radius of the channel. Moreover, mixing efficiency increases with Péclet number, the exponent of variation being dependent on the Reynolds number of flow.

Thermal convection in a rotating spherical gap is investigated using numerical simulations and compared with results of the GeoFlow ISS experiment. To induce convection, a radial buoyancy force field is established by using the dielectrophoretic effect from a high-frequency alternating electric field. Two heating sources are implemented. One source is a temperature difference across the gap and the other is the internal dielectric heating of the working fluid. To distinguish both heating sources a heating parameter, $\lambda$, is introduced that is varied together with the electric Rayleigh number, $L$, and Ekman number, Ek $\approx {10}^{-3}$. The governing thermoelectro hydrodynamic equations are analyzed via a linear stability analysis and by three-dimensional numerical simulations. The results are compared with experimental data of the GeoFlow experiment which show that the threshold of convection and the occurrence of global columnar cells agreed with the theoretical predictions. In addition the observed fluid flow showed non-Gaussian characteristics which are described by the quasinormal approximation. The overall flow phenomena are based on polar plumes and equatorial confined columnar cells and in addition are influenced by internal dielectric heating.

We investigate the transition from forward to inverse energy cascade in turbulent flows in thin layers, varying the functional form of the forcing and the thickness of the layer. We show that, as the forcing function becomes more three dimensional, the inverse cascade is suppressed and the critical height $h_c$, where the transition occurs, is decreased. We study the dependence of this critical height on a parameter $r$ which measures the dimensionality of the forcing and thus construct a phase-space diagram in the parameter space $r-h$. We discuss the effect of Reynolds number and domain size.

We investigate argon bubble flow in liquid gallium within a container large enough to avoid wall effects. Flow with and without applied horizontal magnetic field is studied. We demonstrate the successful capture and quantification of the effects of applied magnetic field using dynamic neutron radiography and the previously developed and validated robust image processing pipeline, supported by the in silico reproduction of our experiment. Significant reduction of the amplitude of bubble tilt angle variations due to applied horizontal magnetic field is successfully resolved through a 30 mm thick liquid metal layer. Our results clearly show the potential of expanding the range of gas/liquid metal systems that can be studied using downscaled though representative experimental setups.

We present observations of oscillations in the shape of the temperature profile of the large-scale circulation (LSC) of turbulent Rayleigh-Bénard convection. Temperature measurements are broken down into Fourier moments as a function of $\theta -{\theta }_0$, where $\theta$ is the azimuthal angle in a horizontal plane at midheight, and ${\theta }_0$ is the LSC orientation. The oscillation structure is dominated by a third-order sine moment and third-order cosine moment in a cubic cell. In contrast, these moments are not found to oscillate in a cylindrical cell. This geometry-dependent behavior can be explained by a minimal model that assumes that the heat transported by the LSC is conducted from the thermal boundary layers, and is proportional to the pathlength of the LSC along boundary layers at the top and bottom plates. In a noncircular cross-section cell, oscillations of the LSC orientation ${\theta }_0$ result in an oscillation in the container shape in the reference frame of the LSC, resulting in an oscillation in the pathlength of the LSC at a given $\theta -{\theta }_0$. In a square-cross-section cell, this model predicts the dominant third-order sine moment and third-order cosine moment with magnitudes within 50% of measured values, when using the amplitude of the oscillation of ${\theta }_0$ as input. A cylindrical cell is special in that the pathlength is independent of ${\theta }_0$, and so these oscillating moments are not induced. In a cylindrical cell, the model reproduces the sinusoidal mean temperature profile with a sloshing oscillation dominated by the second-order sine moment, consistent with previous observations in that geometry.

We derive a discrete framework for the calculation of eigenvalue sensitivity to geometric deformations. We apply the technique to the steady compressible Navier-Stokes and Reynolds-averaged Navier-Stokes (RANS) flows. The analysis enables one to control (reduce or increase) the amplification rate or frequency associated to the least stable global mode, which is identified using stability analysis. A methodology using a discrete framework is proposed, allowing one to recover the gradients in compressible and turbulent flows. The potential of the resulting shape gradients is evaluated on the well-known circular cylinder flow problem and on a RANS turbulent flow scenario to control the buffet onset on a NACA0012 airfoil. The predicted deformations show excellent performance on the stabilization or excitation, and frequency control, of the global modes and for the two cases tested.

The breakup process of stretching liquid bridges between plates is crucial for liquid transfer in printing technology. In the present study, the liquid bridges stretched by two parallel flat plates were simulated by using many-body dissipative particle dynamics, in which the competition between slip velocity of contact lines and thinning velocity of liquid bridges was focused on, and it shows that this competition plays a key role in determining the breakup behaviors of liquid bridges and the liquid transfer ratio between the two plates. The influences of surface wettability, plate stretching velocity, and liquid Oh number on the breakup process were discussed. The simulated results show that both poorer surface wettability and larger stretching velocity help to increase slip velocity and enable the liquid bridge to slip off the surfaces. For the case with hydrophilic surface and small plate stretching velocity, thinning velocity dominates the breakup process and the pinch-off occurs approximately at the middle part of the liquid bridge. For cases with asymmetric surface wettability, the liquid transfer ratio depends only on the asymmetry of surface wettability for smaller plate stretching velocity and larger Oh number. However, this phenomenon no longer occurs if the stretching velocity is increasing, where slip of the contact line becomes important. The shift of minimal radius for liquid bridges with asymmetric stretching velocities is also investigated, and it was found that the shift moment is only related to the surface wettability, regardless of the plate stretching velocity. Moreover, it shows that the formation of satellite drops depends on the sequential order of the appearance of the liquid bridge slipping off the surface and the breakup of the filament. The present work provides some insight to better understand the rupture mechanism of stretching liquid bridges, and may help to improve printing technology.

There is a continuing effort by turbulence researchers to provide improved turbulent heat flux predictions for Reynolds-averaged Navier-Stokes (RANS) calculations of heat transfer applications. In this paper, data-driven models are developed for the turbulent heat flux prediction in wall jets with coflow using a gene expression programming (GEP)–based machine-learning technique. The training data used as input to the optimization algorithm are obtained by performing highly resolved large eddy simulations (LES) of nine cases covering various flow and geometry conditions. The study examines whether predictive RANS-based heat transfer closures can be trained that are robust to these physically very different nine LES cases. The GEP heat flux closures were developed by adopting the gradient-diffusion hypothesis with the optimization target being a nondimensional parameter representing the inverse of a nonconstant turbulent Prandtl number ($P{r}_t$), with a functional dependence on the velocity and temperature gradients. First, examination of the turbulent Prandtl number calculated from time-averaged LES data showed a significant deviation from the commonly assumed constant value of 0.9, with a more significant dependence on the lip wall thickness than the blowing ratio. Second, a posteriori testing of the developed closures by solving the RANS-based scalar transport equation using as input the LES time-averaged velocity and turbulent viscosity showed a significant improvement in the prediction of adiabatic wall effectiveness not only for the cases they were trained on, but also for the entire matrix of LES cases. Finally, our best-performing model (trained on the thickest lip wall case) was also evaluated in a full RANS context and a significant improvement for the prediction of the adiabatic wall effectiveness was achieved, in particular for the medium and the thin lip thickness cases. The lack of improvement when testing the thickest lip wall case in a full RANS context indicates that for cases with strong vortex shedding the effect of organized unsteadiness on the turbulent flow field is important. In such cases, only modifying the heat flux model without improving the RANS velocity field is not sufficient and other methodologies like deriving a model for the Reynolds stress are necessary. Collectively, the current study demonstrates the ability of the presented model-development framework in creating bespoke models that can provide accurate predictions for a wide range of operating conditions.

Recent experimental and numerical studies of surface gravity waves propagating over a sloping bottom have shown that an increase in the probability of extreme waves can be triggered by depth variations in sufficiently shallow waters. This phenomenon is studied here by means of a boundary element method with fast multipole acceleration to solve the fully nonlinear water wave equations. We focus on the case of a random, unidirectional wave field with prescribed statistical properties propagating over a submerged slope and consider different depth variations, including a step. Validation is provided by comparing with experiments by Trulsen, Zeng, and Gramstad [Phys. Fluids 24, 097101 (2012)]. Strongly non-Gaussian statistics are observed in a region localized near the depth transition, beyond which the statistics settle rapidly to the steady statistical state of finite-depth random wave fields. Using a harmonic separation technique, we show that the second-order terms are responsible for the change in the statistical properties near the depth transition. We explore in detail the effects of peak frequency, significant wave height, the inclination of the slope, and the depth of the shallower water side on the kurtosis, skewness, and the excess probability of the crest height, including their spatial distributions.

In this study, we investigate the steady inhalation, steady exhalation, and oscillatory flow in a realistic airway geometry for physiologically relevant regimes ranging from quiet breathing to respiration under high frequency ventilation (HFV). We use magnetic resonance velocimetry to characterize and quantify three-dimensional (3D) velocity fields in 3D printed replicas of realistic bronchial trees. Expanding on previous studies [Jalal et al., Exp. Fluids 57, 148 (2016); Jalal et al., Phys. Rev. Fluids 3, 103101 (2018)] which focused on respiration in planar double bifurcation geometries, we compare levels of axial and lateral dispersion, and find that they exceed those found in the idealized models. Furthermore, we find that the secondary flows in realistic airways propagate deep in the bronchial tree and are stronger during exhalation as compared to inhalation, while the mean flow topology does not vary significantly between the two steady regimes. Under HFV, we note significant regions of flow reversal during the inhalation-exhalation and exhalation-inhalation transitions. This is found to be due to a difference in impedance (dominated by inertance) in the different regions of the lung and results in an asynchronous ventilation between the upper and lower lobes. This phenomenon, also known as pendulluft is demonstrated experimentally for the first time, using both Eulerian velocity fields and Lagrangian pathlines. Secondary flows are stronger in exhalation compared to inhalation and at the peak of the ventilation cycle, match the steady cases although the flow topology can be significantly different. Finally, the cycle-averaged drift velocity suggests that steady streaming, while not negligible, is not the main transport mechanism during high-frequency ventilation.

We develop a one-dimensional model for the unsteady fluid-structure interaction (FSI) between a soft-walled microchannel and viscous fluid flow within it. A beam equation, which accounts for both transverse bending rigidity and nonlinear axial tension, is coupled to a one-dimensional fluid model obtained from depth averaging the two-dimensional incompressible Navier-Stokes equations across the channel height. Specifically, the Navier-Stokes equations are scaled in the viscous lubrication limit relevant to microfluidics. The resulting set of coupled nonlinear partial differential equations is solved numerically through a segregated approach employing fully implicit time stepping and second-order finite-difference discretizations. Internal FSI iterations and under-relaxation are employed to handle the stiff nonlinear algebraic problems within each time step. Then, we explore both the static and dynamic FSI behavior of this example microchannel system by varying a reduced Reynolds number Re, which necessarily changes the Strouhal number St, while we keep the geometry and a modified dimensionless Young's modulus $\mathrm{\Sigma }$ fixed. At steady state, an order-of-magnitude analysis (balancing argument) shows that the axially averaged pressure in the flow, $\langle P\rangle$, exhibits two different scaling regimes, while the maximum deformation of the top wall of the channel, $H_{\max }$, can fall into four different regimes, depending on the magnitudes of Re and $\mathrm{\Sigma }$. These regimes are physically explained as resulting from the competition between the inertial and viscous forces in the fluid flow as well as the bending resistance and tension in the elastic wall. Finally, the linear stability of the steady inflated microchannel shape is assessed via a modal analysis, showing the existence of many highly oscillatory but stable modes, which further highlights the computational challenge of simulating unsteady FSIs.

Zero pressure-gradient (ZPG) turbulent boundary layers (TBLs) at high Reynolds numbers (Re) and TBLs with adverse pressure gradients (APGs) share some similarities such as the emergence of an outer peak in the streamwise variance profile related to the enhancement of large-scale energy. Reynolds-number and pressure-gradient effects tend to cause such an energizing of the outer-layer structures, which makes it difficult to distinguish them, mainly because both effects are usually coupled. Using two experimental data sets of ZPG and APG TBLs in which Re and pressure gradient are analyzed independently, the present paper shows that the two effects have different imprints on the flow. In particular, the analysis shows that (1) the small-scale energy in APG TBLs is, contrary to canonical ZPG TBLs, not universal, but is dependent on the APG strength, (2) the APG enhances both the small- and large-scale energy in the outer region, and (3) the outer-peak location and the amplitude of the streamwise variance scale differently for increasing Re and APG magnitude. These findings may have ramifications on the development of turbulence models since the pressure gradient has a direct influence on the near-wall dynamics.

Subcritical transition to turbulence in spatially developing boundary layer flows can be triggered efficiently by finite amplitude perturbations. In this Rapid Communication, we employ adjoint-based optimization to identify optimal initial perturbations in the Blasius boundary layer, culminating in the computation of the subcritical transition critical energy threshold and the associated fully localized critical optimum in a spatially extended configuration, the so called minimal seed. By dynamically rescaling the variables with the local boundary layer thickness, we show that the identified edge trajectory approaches the same attracting phase space region as previously reported edge trajectories, and reaches the region more efficiently.

We investigate experimentally the instability of steady flow of fluid confined in weakly precessing spheroids. It is known that the conical-shear instability (CSI) proposed by Lin, Marti, and Noir [Phys. Fluids 27, 046601 (2015)] grows in a precessing sphere, and the elliptical and shearing instabilities [Kerswell, Geophys. Astrophys. Fluid Dyn. 72, 107 (1993)] can grow in precessing spheroids. Previous theories predict that when $\text{Re}\lesssim {\eta }^{-5}$, where $\text{Re}$ is the Reynolds number defined by the spin angular velocity and the equatorial radius of the spheroid and $\eta$ is its ellipticity, CSI dominates the other two instabilities even in a spheroid, and that, in particular, when $\eta <0.17$ the critical Poincaré number (i.e., the critical precession rate) ${\text{Po}}^{\left(c\right)}$ is proportional to ${\text{Re}}^{-3/10}$ for $200{\eta }^{-2}\ll \text{Re}\lesssim {\eta }^{-5}$. To experimentally verify these predictions, we measure a long time-series of fluid velocity to accurately estimate the power spectrum. Then, we determine ${\text{Po}}^{\left(c\right)}$ as a function of $\text{Re}$ and show the qualitative change of its scaling depending on $\eta$. Our experimental results perfectly support the theoretical predictions, implying that CSI can grow in precessing spheroids.

By performing a large number of fully resolved simulations of incompressible homogeneous and isotropic two-dimensional turbulence, we study the scaling behavior of the maximal Lyapunov exponent, the Kolmogorov-Sinai entropy, and attractor dimension. The scaling of the maximal Lyapunov exponent is found to be in good agreement with the dimensional predictions. For the cases of the Kolmogorov-Sinai entropy and attractor dimension, the simple dimensional predictions are found to be insufficient. A dependence on the system size and the forcing length scale is found, suggesting nonuniversal behavior. The applicability of these results to atmospheric predictability is also discussed.

During motion from deep to shallow water, multiple equilibria may emerge, each with identical drag—a phenomenon that can be explained by a localized amplification of the wave drag near the shallow wave speed. The implication of this is the emergence of several previously unstudied bifurcation patterns and hysteresis routes. Here, we address these nonlinear dynamics by considering the quasisteady motion of a body between deep and shallow water, where the depth is slowly varying. We survey several theoretical models for the drag, compare these against our tow-tank experimental measurements, and then use the validated theory to explore the bifurcation patterns using two parameters: the depth of motion and the forcing. In particular, using a case study of a lake with a sinusoidal depth profile, we illustrate that hysteresis effects can play a significant role on the speed of motion and journey time, presenting interesting implications for naval and racing applications.

Droplet-wall interactions are well known to generate a wide variety of outcomes such as spreading, splashing, receding, jetting, and rebounding. In this paper, we focus on the evolution of jets that form during the recoil of impinging drops on partially wetting hydrophilic substrates composed of cylindrical micropillars. The impact of the millimeter-sized drops of water-glycerol mixtures on the microstructured hydrophilic substrates is investigated by high-speed video photography. Impact velocity and fluid viscosity are varied to characterize the jets. Wetting angles are maintained in the range of $43.6^{\circ }\le \theta \le 51.4^{\circ }$. A regime map is constructed to convey the jet behavior at a glance. We find that jet speed, height, and diameter scale linearly with the Weber number. We also find that the jet originates from the inertial collapse of an air cavity formed during the recoil phase of the drop following impact on the microstructured substrate. The relationship between the size of the top jet drop and jet velocity obeys the scaling law of [Gañán-Calvo, Phys. Rev. Lett. 119, 204502 (2017)] for jets induced by capillary surface singularities. No jet is observed for sufficiently high drop viscosity.

Motivated by specific data and accuracy requirements for building numerical databases of turbulent flows, data compression using spatiotemporal subsampling and local resimulation is proposed. Numerical resimulation experiments for decaying isotropic turbulence based on subsampled data are undertaken. The results and error analyses are used to establish parameter choices for sufficiently accurate subsampling and subdomain resimulation.