While various aerodynamic noise generation mechanisms and characteristics have been extensively studied for drone research, the noise features during the descending flight state have not been well addressed. In this work, we investigate the aerodynamics and aeroacoustics of a two-bladed drone rotor operating in descent using both experimental and numerical approaches. First, we measure the rotor thrust and torque in an anechoic wind tunnel at various rotational speeds and descent rates. The results reveal a significant loss of mean thrust and strong thrust fluctuations with the increase of descent rates due to the formation of highly unsteady vortex rings. The measured acoustic spectra show multiple humps occurring at the blade passing frequency and its harmonics. Next, we perform numerical simulations based on the delayed detached eddy simulations to gain more understanding of the noise generation mechanisms. The computed integrated aerodynamic forces and acoustic spectra agree well with the experimental results. We present nearfield flow structures that demonstrate the gradual formation process of the vortex ring and the complex turbulent wake structures. Notably, the computed aeroacoustic characteristics exhibit a similar tendency with respect to the descent rate to the experimental results. Moreover, the simulation results suggest that the additional noise has a radiation directivity in the axial direction perpendicular to the rotation plane. Finally, we conduct a noise source analysis on the blade surface based on the simulation results, revealing that the strong leading-edge sources are likely related to the blade-wake interaction process during descending flight.

We investigate the linear stability analysis of a gravity-driven three-dimensional incompressible viscous fluid flowing down a uniformly heated inclined plane under the influence of an external constant shear stress on the fluid surface. Based on a coupled system of boundary value problems involving the amplitudes of the perturbation normal velocity and perturbation temperature, the stability analysis is accomplished for infinitesimal disturbances of arbitrary wave numbers. The analytical solution of the boundary value problems in the long-wave regime reveals the existence of the H-mode, which is destabilized by both the Marangoni number and the imposed shear stress acting in the coflow direction. Furthermore, we determine the critical value of the Marangoni number below which the inertialess flow is linearly stable, but the flow may be linearly unstable in this range due to inertia. However, the numerical solution based on the Chebyshev spectral collocation method reveals the existence of additional thermocapillary S-mode and thermocapillary P-mode in the long-wave and finite streamwise wave number regimes, respectively. It is found that the H-mode and S-mode instabilities are destabilized, but the P-mode instability is stabilized if the constant shear stress is applied in the coflow direction. Interestingly, as the imposed shear stress rises, the onset of instability for the H-mode and the onset of stability for the S-mode merge with each other and produce a single onset for the primary stability. However, a completely opposite phenomenon takes place if a constant shear stress is imposed in the counterflow direction. In addition, we observe that the shear mode exists in the high Reynolds number regime, and the associated instability can be initiated at a lower Reynolds number by applying a constant shear stress in the coflow direction. Conversely, the shear mode instability can be delayed by imposing a constant shear stress in the counterflow direction. Finally, the spanwise wave number exhibits a stabilizing influence on the H-mode, S-mode, and shear mode instabilities but exhibits a destabilizing influence on the P-mode instability.

The impingement of a liquid jet onto a moving wall can lead to deposition in which fluid spreads into a steady, U-shaped lamella. Experiments are conducted by impinging a jet from a nozzle onto a rotating disk to produce jet Reynolds numbers $15\le {\mathrm{Re}}_j\le 6000$ and wall-to-jet velocity ratios $0.04\le u_w/v_j\le 14$ under conditions where the effects of surface tension and gravity are relatively minor. Although experiments were conducted over a broad range of ${\mathrm{Re}}_j$, the steady, U-shaped lamella only forms for $15\le {\mathrm{Re}}_j\le 400$; at higher ${\mathrm{Re}}_j$ the jet splashes. High-speed video is used to measure the geometry of the impinging jet. The experiments are complemented with numerical simulations, which reveal the anatomy of the lamella: The jet is diverted sideways by pressure gradients over an impact zone that has a radius of order the jet diameter. Viscous stresses play little role in the diversion of incoming fluid but act outside the impact region to turn the flow towards the direction of motion of the wall. A fraction of the viscously redirected fluid is thereby taken back underneath the jet, cushioning its impact. Eventually, the fluid enters a downstream region of almost uniform depth wherein all the fluid is conveyed with the wall. A simple model is proposed to rationalize the U shape of the lamella, fixing that footprint by arguing that this arises where the radially symmetric, viscously modified outflow from the jet matches the wall velocity. The simple model predicts the dimensions of the lamella (the length of the upstream heel and the width of the downstream lamella) and that the shape takes a universal form when scaled by one of these distances. These predictions agree well with the experiments and simulations, except when the heel becomes excessively small.

The wake of a rotationally oscillating cylinder in the presence of a plane wall with various gap-to-diameter ratios are studied experimentally for a Reynolds number of 250. Flow visualization study is conducted using planar laser-induced fluorescence and hydrogen bubble technique in the plane perpendicular to the cylinder and in the spanwise plane, respectively, to find the effect of gap distance on the wake structures for various forcing frequencies and amplitudes. Quantitative analysis is provided using hot-wire anemometry to find the lock-on parameter space and particle image velocimetry (PIV) revealed the strength of vortices shed perpendicular to the cylinder. Various wake structures, like single-sided shedding, double-layer vortices, and detached shear layer shedding from the wall, are observed for different gap distances and forcing parameters using laser-induced fluorescence flow visualizations. PIV data reveals that the circulation strength of the vortices shed perpendicular to the cylinder reduces with increasing downstream distance. Hot-wire analysis reveals one of the key outcomes of the study, showing that the range of frequency-amplitude parameter space for which the lock-on phenomenon occurs reduces with a decrease in wall distance. Hydrogen bubble flow visualization data reveal the presence of two spanwise three-dimensional modes and characteristics of these modes with varying forcing conditions and gap distance are found. Interestingly, it is observed that there is a lack of three-dimensionalities in the flow when the gap ratio (wall spacing-to-diameter ratio) is reduced to $G/D=0.5$.

High-fidelity large eddy simulations of the inclined Rayleigh-Taylor instability in the Tilted Rocket Rig experimental configuration [Smeeton and Youngs, AWE Report No. O 35/87 (1987)] are performed using a tenth-order compact finite difference code. These simulations are analyzed for spatial distributions of turbulent kinetic energy, turbulent mass flux velocity, species mass fraction flux, species mass fraction variance, and Favre-averaged Reynolds stresses at two time instances, $t=37\mathrm{ms}$ and $t=52\mathrm{ms}$. Additionally, the vertical distribution of the components of the unclosed budget equations over the center of the domain for these quantities are examined. The dominant terms of these budget equations are further decomposed to examine the principal contributions to these terms in each axis. Notably, the principal contribution to the horizontal turbulent mass flux velocity budget is found to be from a term which is commonly neglected in many Reynolds-averaged Navier-Stokes models.

The interaction between two passive human swimmer scale models is investigated both experimentally and numerically. The Froude number, comparing the swimming velocity to the characteristic wave velocity, is conserved in the study. The interaction is quantified for a large range of relative positions and for three speeds corresponding to cruising, average, and sprint swimming. The associated computational fluid dynamics study using OpenFoam allows us to determine the relative positions that optimize the drafting during an open-water race: just behind a lead swimmer or at the level of the hip of a neighbor, with reductions of drag of 40% and 30%, respectively.

Near-wall regions in wall-bounded turbulent flows experience intermittent ejection of slow-moving fluid packets away from the wall and sweeps of faster moving fluid towards the wall. These extreme events play a central role in regulating the energy budget of the boundary layer and are analyzed here with the help of a three-dimensional convolutional neural network (CNN). A CNN is trained on direct numerical simulation data from a periodic channel flow to deduce the intensity of such extreme events and, more importantly, to reveal contiguous three-dimensional salient structures in the flow that are determined autonomously by the network to be critical to the formation and evolution of ejection events. These salient regions, reconstructed using a multilayer gradient-weighted class activation mapping technique proposed here, correlate well with bursting streaks and coherent fluid packets being ejected away from the wall. The focus on explainable interpretation of the network's learned associations also reveals that ejections are not associated with regions where turbulent kinetic energy (TKE) production reaches a maximum, but instead with regions that entail extremely low dissipation and a significantly higher tendency for positive TKE production than negative production. This is a key finding of the study and indicates that CNNs can help reveal dynamically important three-dimensional salient regions using a single scalar-valued metric provided as the quantity of interest, which in the present case is the ejection intensity. While the current work presents an alternate means of analyzing nonlinear spatial correlations associated with near-wall bursts, the framework presented is sufficiently general so as to be extendable to other scenarios where the underlying spatial dynamics are not known a priori.

The present study investigates the non-Oberbeck-Boussinesq (NOB) effects which arise due to the temperature dependence of material properties in cryogenic helium experiments of turbulent Rayleigh-Bénard convection. Here we quantify these effects solely by the difference of the measured mean temperature at the center of the closed cell, $T_c$, from the arithmetic mean temperature obtained from the prescribed fixed and uniform temperatures at the top and bottom copper plates of the apparatus, $T_m=(T_{\mathrm{bot}}+T_{\mathrm{top}})/2$. To this end, the material properties such as specific heat at constant pressure, dynamic viscosity, thermal conductivity, the isobaric expansivity, and the mass density are expanded into power series with respect to temperature up to the quadratic order with coefficients obtained from the software package HEPAK. A subsequent nonlinear regression that uses deep convolutional networks delivers a dependence of the strength of non-Oberbeck-Boussinesq effects in the pressure-temperature parameter plane. Strength of the NOB effects is evaluated via the deviation of the mean temperature profile ${\xi }_{\mathrm{NOB}}\equiv T_m-T_c$ from the top-bottom-symmetric Oberbeck-Boussinesq case ${\xi }_{\mathrm{NOB}}=0$. Training data for the regression task are obtained from 236 individual long-term laboratory measurements at different Rayleigh numbers which span eight orders of magnitude.

A net force can arise on objects which lie in systems with complex energy partitions, even if the system is on average stationary. These forces are usually called fluctuation forces, as they arise due to the objects modifying the character of the fluctuations within the system. We continue the investigation of Spandan et al. [Sci. Adv. 6, eaba0461 (2020)], who found an attractive fluctuation force between two parallel square plates in homogeneous isotropic turbulence (HIT). We conduct simulations which systematically vary the plate size and Reynolds number. At ${\mathrm{Re}}_{\lambda }=100$ small plates show a monotonic force dependence, with a maximum force for the smallest plate separations, while medium and large plates show a nonmonotonic behavior of the force with maximum attractive force at intermediate separations. We find that energy-related statistics cannot explain the dependence on plate separation of the force, but that statistics related to vorticity do show qualitative variations around the plate separation corresponding to the maximum force. This suggests that the role of plates in affecting intense vorticity structures is critical to the behavior of the force. By decreasing ${\mathrm{Re}}_{\lambda }$, we show that removing vortex stretching decreases the attractive force, but does not completely eliminate it, and find that the local maximum at intermediate distances becomes a local minimum. This confirms that the attractive force is related to vorticity, while suggesting that a second mechanism is present, supporting the proposal for a twofold origin from earlier work: the plates both restrict the presence of energy structures in the slit and pack intense vortical structures which stretch each other causing the pressure to drop.

We study the dynamics of the perceived velocity gradient tensor $\mathbf{M}$ constructed from four tracer particles that initially form a regular tetrad of size $r_0$. The exact evolution equation of $\mathbf{M}$, derived in our previous work [Yang et al., J. Fluid Mech. 897, A9 (2020)], contains several unclosed terms. Using numerical data, we compare the exact dynamics of $\mathbf{M}$ with the tetrad model [Chertkov et al., Phys. Fluids 11, 2394 (1999)]. In particular, we project the motion onto the $(R,Q)$ plane, where $R$ and $Q$ are the third- and second-order invariants of $\mathbf{M}$. When $r_0$ is in the inertial range of scales of the turbulent cascade, we find that at very short times the tetrad model correctly describes the main features of the dynamics of $\mathbf{M}$ on the $(R,Q)$ invariants plane. This suggests that at any instant of time, the unclosed pressure and viscous contributions to the Eulerian dynamics of $\mathbf{M}$ could be described by the nonlinear and the damping terms, respectively, in the tetrad model. However, after a time of order $\sim 2{\tau }_K$, where ${\tau }_K$ is the Kolmogorov timescale, the action of the unclosed pressure contribution to the dynamics changes very dramatically to become a strong damping term on the $(R,Q)$ plane. This qualitative change in the dynamics occurs on a timescale that differs from $T_0$, the turnover time at scale $r_0$. In addition, the fluctuations around the mean are found to deviate from the short-correlated-white-noise assumption in the tetrad model, as the timescale of the fluctuation is closer to $T_0$ than ${\tau }_K$.

A flexible body interacting with a fluid flow deforms in a complex and frequently unforeseen manner. Understanding and predicting the morphologies of such flexible thin structures under hydrodynamic loadings is central in fluid mechanics. Herein, a simple physical system that enables the systematic investigation of a driven elastic rod at a high Reynolds number is proposed. A straight rod with a spherical sponge attached at one end and rotationally driven at the other is considered. In this setup, the air drag virtually concentrates at the tip of the rod. This enables controlling and quantifying the role of the aerodynamic effects by specifying the parameters of only the sponge. A shape transition, whereby a whirling rod transforms abruptly into a vertically straight, rapidly rotating configuration at a certain critical frequency, is observed. The scaling law for the rod behavior is established by combining experiment, numerical simulation, and analytical theory, which is verified by our experimental and numerical data. Further, a simple analytical model based on forced oscillation with nonlinear damping is presented to capture the physics underlying the observed transition.

We observed the zigzag motion of small Leidenfrost water droplets (radii less than 0.6 mm) on a hot, flat substrate. To understand this motion, we conducted an experiment using a glass capillary to fix a droplet at its edge and control the droplet height. Thermographic and interferometric observations reveal that the droplets rotated both vertically and azimuthally. Based on the characteristic frequency of the azimuthal rotation depending on the substrate temperature and droplet height, we developed a semiempirical model considering unsteady Marangoni convection and its relaxation. We confirmed that our model can predict the characteristic time of the zigzag motion of unfixed Leidenfrost droplets.

In the present study, the momentum and heat fluxes (MF and HF) in subsonic or supersonic channel flows are studied and compared via resorting to the established analysis tools developed for incompressible flows, such as the conditional sampling and the spectral linear stochastic estimation, by leveraging the newly built database. Particular attention is paid to clarifying the effects of the inner-outer scale interactions on the statistical characteristics of MF and HF in the near-wall and logarithmic regions. To this end, by employing the spectral linear stochastic estimation, the near-wall fluxes are decomposed into large- and small-scale components, and the logarithmic-region fluxes are decomposed into active and inactive parts, respectively. For the near-wall region, the large-scale component is found to be the footprints of large-scale eddies and rather uniform in physical space, whereas the remaining small-scale component is uneven in space and includes the strong transports of momentum and heat in the near-wall region. For the logarithmic region, both the inactive and active components of MF and HF are found to contribute to their mean flux. In the outer region, the ejections of HF are remarkably stronger than those of the MF, and the former is more sparse in the physical space. Reynolds number is shown to have a minor effect on the statistical characteristics of the two fluxes, and the enlargement of the Mach number only appears to lessen the linkages between the inner and outer region fluxes, adjust the proportions of the inactive and active components in the logarithmic region, and rarely alter the overall properties of them. The findings of the present study may contribute to the development of the modeling approach in compressible wall turbulence.

Breaking dynamics of bubbles in turbulence produce a wide range of bubble sizes, which mediates gas transfer, in particular, at the ocean/atmosphere interface. At the scales close to the stability limit of bubbles torn away by inertial forces, a typical geometry that induces bubble breakup is the uniaxial straining flow. In this configuration, the bubble shapes and their limit of stability have been studied theoretically and numerically near their equilibrium. Using numerical simulations, we investigate the bubble dynamics and breakup in such flows, starting from initial shapes far from equilibrium. We show that the breakup threshold is significantly smaller than the previous linear predictions and evidence that the breakup threshold depends on both the Reynolds number at the bubble size, and the initial bubble shape (ellipsoids). To rationalize the bubble dynamics and the observed thresholds, we propose a reduced model for the oblate/prolate oscillations (second Rayleigh mode) based on an effective potential that depends on the control parameters and the initial bubble shape. Our model successfully reproduces bubble oscillations, the maximal deformation below the threshold, and the bubble lifetime above the threshold.

A circular Hele-Shaw cell bounded by a volumetrically confined elastic solid can act as a fluidic fuse: during radially outward fluid flow, the solid deforms in response to the viscous pressure field such that the gap expands near the inlet (at the center) and contracts near the outlet (around the rim). If the flow rate exceeds a critical value, then the gap at the outlet can close completely, interrupting/choking the flow. Here, we consider the injection of gas into such a soft-walled Hele-Shaw cell filled with viscous liquid. Our theoretical model and numerical simulations for axisymmetric flow driven by the injection of an expanding gas bubble show that the bubble increases the critical flow rate of choking via two mechanisms. First, as the interface approaches the rim, it reduces the length over which the viscous pressure gradient deforms the solid, which increases the critical flow rate above which choking occurs. Second, compression of the gas reduces the outlet flow rate relative to the inlet flow rate. As a consequence, for large injection rates, a near-choking regime is established in which the outlet flow rate becomes independent of the injection rate and instead depends only on the instantaneous position of the interface. Our traveling-wave model for the advancement of the bubble front will enable future reduced-order modeling of nonaxisymmetric problems, such as viscous fingering.

It is shown that laminar vortex rings can be generated by impulsive body forces having particular spatial and temporal characteristics. The method produces vortex rings in a fluid initially at rest, and once generated, the flow field automatically satisfies the boundary conditions and is divergence-free. Numerical simulations and analytical models show that the strength of these rings can be accurately predicted by considering diffusion alone, despite the nonlinear nature of the generation process. A particularly simple model, which approximates the source of vorticity within vertical slabs, is proposed. This model predicts the ring circulation almost as accurately as a model that uses the exact geometry of the source of vorticity. It is found that when the duration of the force is less than a timescale based on the force radius and fluid viscosity, the ring circulation can be predicted accurately using an inviscid model.

Wedge water entry can be used to study slamming on high-speed craft, seaplane landing, and biological flows such as birds diving into the water. The focus of this paper is on experimental measurements and simulations for the primary application of slamming of small craft, where the wedge boundary conditions are closed on all edges. The simulation is comprised of a one-way coupled nonlinear hydrodynamic code developed for water entry with an Euler-Bernoulli beam finite element solver. In this paper, the dynamic surface pressures on the bottom of the wedge are measured along with structural deflection, water contact line (or spray root), and rigid body motions of the vertically constrained wedge. Five different panel types with large variations in flexural rigidity were tested at impact speeds ranging from 1.2 m/s to 3.0 m/s. Comparisons of one set of experiments are compared with the simulation predictions. For the experimental results, it was found that the nondimensionalized spray root position versus time is self-similar despite the three orders of magnitude difference in the panel flexural rigidity values. When the time for the pressure wave to reach each pressure sensor on the bottom of the panel is normalized and compared with the hydroelasticity factor (the ratio of the structural period to the wetting time for the panel), the nondimensional times of arrival are approximately constant for each nondimensional location along the panel.

Drop breakup is often associated with violent impacts onto targets or fast inner bubble growth consecutive to phase change. We report on a well-controlled drop breakup experiment where bubble growth is triggered by the decrease of the ambient pressure. The drop initially sits on a textured hydrophobic surface at controlled temperature, and a bubble grows from the center of the liquid-solid interface. We find a transition from top-breakup to triple-line breakup depending on the initial contact angle of the drop. A minimal model based on inertial dynamics and constant bubble pressure is proposed. It quantitatively captures the growth of the bubble and the distinction between top or triple-line breakup. However, the model only provides an upper bound for the breakup time.

We report pore-scale statistical properties of temperature and thermal energy dissipation rate in a two-dimensional porous Rayleigh-Bénard (RB) cell. High-resolution direct numerical simulations were carried out for the fixed Rayleigh number (Ra) of ${10}^9$ and the Prandtl numbers (Pr) of 5.3 and 0.7. We consider sparse porous media where the solid porous matrix is impermeable to both fluid and heat flux. The porosity $\left(\varphi \right)$ range $0.86\le \varphi \le 0.98$, the corresponding Darcy number (Da) range ${10}^{-4}<\mathrm{Da}<{10}^{-2}$ and the porous Rayleigh number $({\mathrm{Ra}}^{*}=\mathrm{Ra}·\mathrm{Da})$ range ${10}^5<{\mathrm{Ra}}^{*}<{10}^7$. Our results indicate that the plume dynamics in porous RB convection are less coherent when the solid porous matrix is impermeable to heat flux, as compared to the case where it is permeable. The averaged vertical temperature profiles remain almost a constant value in the bulk, while the mean-square fluctuations of temperature increases with decreasing porosity. Furthermore, the absolute values of skewness and flatness of the temperature are much smaller in the porous RB cell than in the canonical RB cell. We found that intense thermal energy dissipation occurs near the top and bottom walls, as well as in the bulk region of the porous RB cell. In comparison with the canonical RB cell, the small-scale thermal energy dissipation field is more intermittent in the porous cell, although both cells exhibit a non-log-normal distribution of thermal energy dissipation rate. This work highlights the impact of impermeable solid porous matrices on the statistical properties of temperature and thermal energy dissipation rate, and the findings may have practical applications in geophysics, energy and environmental engineering, as well as other fields that involve the transport of heat through porous media.