This paper is associated with a poster winner of a 2021 American Physical Society's Division of Fluid Dynamics (DFD) Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2021.GFM.P0041.

This paper is associated with a poster winner of a 2021 American Physical Society's Division of Fluid Dynamics (DFD) Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available online at the Gallery of Fluid Motion (https://doi.org/10.1103/APS.DFD.2021.GFM.P0037).

This paper is associated with a poster winner of a 2021 American Physical Society's Division of Fluid Dynamics (DFD) Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2021.GFM.P0005.

This paper is associated with a video winner of a 2021 American Physical Society's Division of Fluid Dynamics (DFD) Gallery of Fluid Motion Award for work presented at the DFD Gallery of Fluid Motion. The original video is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2021.GFM.V0013.

This paper is associated with a video winner of a 2021 American Physical Society's Division of Fluid Dynamics (DFD) Gallery of Fluid Motion Award for work presented at the DFD Gallery of Fluid Motion. The original video is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2021.GFM.V0060.

This paper is associated with a video winner of a 2021 American Physical Society's Division of Fluid Dynamics (DFD) Gallery of Fluid Motion Award for work presented at the DFD Gallery of Fluid Motion. The original video is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2021.GFM.V0073.

This paper is associated with a video winner of a 2021 American Physical Society's Division of Fluid Dynamics (DFD) Gallery of Fluid Motion Award for work presented at the DFD Gallery of Fluid Motion. The original video is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2021.GFM.V0053.

This paper is associated with a poster winner of a 2021 American Physical Society's Division of Fluid Dynamics (DFD) Gallery of Fluid Motion Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2021.GFM.P0036.

We derive the general dispersion relation for interfacial waves along a planar viscoelastic boundary that separates two viscoelastic bulk media, including the effect of gravity. Our unified theory contains Rayleigh waves, capillary-gravity-flexural waves, Lucassen waves, bending waves in elastic plates, and the standard dispersion-free sound waves, as limiting cases. To illustrate our results, we consider waves at a viscoelastic interface immersed in water and at an air-water interface. We furthermore investigate waves at a viscoelastic interface separating two identical viscoelastic bulk media, for which we consider both Kelvin-Voigt and Maxwell materials, as applicable to polymer gels and solutions. For all cases, we study how material properties determine the crossovers, scaling, and existence regimes of the various interfacial waves. Since we include viscoelastic effects for all media involved, our theory allows to model waveguiding phenomena in biology, such as pressure pulses in axon membranes, which are possibly relevant for acoustic nerve pulse propagation phenomena.

We experimentally evaluate the use of active wall-normal surface deformations as a method of actuation for the control of wall-bounded flows. Circular surface deformations are generated locally beneath a laminar boundary layer at a Reynolds number of ${\mathrm{Re}}_{{\delta }^{*}}=340$, where ${\delta }^{*}$ is the displacement thickness, and high-speed particle image velocimetry is used to investigate how the resulting motions vary as a function of the frequency and amplitude of actuation. We consider frequencies ranging from $\text{St}=0.1$ to 1.0 where St is the Strouhal number based on the actuator diameter and freestream velocity, and amplitudes ranging from 0.005 to 0.020 times the actuator diameter (0.12 to 0.49 times the local boundary-layer thickness). We find that the actuation strategy can effectively produce both high- and low-speed motions with similar magnitudes which reach up to roughly one-third of the freestream velocity in some cases. The frequency of actuation dictates the spatial structure of these motions, while the amplitude of actuation dictates their strength. The motions are found to vary considerably, with $\text{St}=0.1$, 0.2, 0.6, and 0.7 producing single flow structures concentrated along the centerline of the actuator (type-1 modes) while the remaining St produce structures with double extrema displaced in the spanwise directions (type-2 modes). Overall, the results indicate that surface deformations at the lowest frequencies ($\text{St}\le 0.2$) are the most promising for flow control because the resulting motions are stronger, more stable, and are concentrated along the centerline of the actuator. Finally, we show that a simple linear model adequately captures the input-output dynamics of the actuated flow—a promising result for future implementation in active control systems.

The oscillatory flows present in an inkjet printhead can lead to strong deformations of the air-liquid interface at the nozzle exit. Such deformations may lead to an inward directed air jet with bubble pinch-off and the subsequent entrainment of an air bubble, which is highly detrimental to the stability of inkjet printing. Understanding the mechanisms of bubble entrainment is therefore crucial to improving print stability. In the present work, we use ultrafast x-ray phase-contrast imaging and direct numerical simulations based on the volume-of-fluid method to study the mechanisms underlying the bubble entrainment in a piezoacoustic printhead. We first demonstrate good agreement between experiments and numerics. We then show the different classes of bubble pinch-off obtained in experiments, and that those were also captured numerically. The numerical results are then used to show that the baroclinic torque, which is generated at the gas-liquid interface due to the misalignment of density and pressure gradients, results in a flow-focusing effect that drives the formation of the air jet from which a bubble can pinch off.

An extreme event is a sudden and violent change in the state of a nonlinear system. In fluid dynamics, extreme events can have adverse effects on the system's optimal design and operability, which calls for accurate methods for their prediction and control. In this paper, we propose a data-driven methodology for the prediction and control of extreme events in a chaotic shear flow. The approach is based on echo state networks, which are a type of reservoir computing that learn temporal correlations within a time-dependent data set. The objective is fivefold. First, we exploit ad hoc metrics from binary classification to analyze (1) how many of the extreme events predicted by the network actually occur in the test set (precision) and (2) how many extreme events are missed by the network (recall). We apply a principled strategy for optimal hyperparameter selection, which is key to the networks' performance. Second, we focus on the time-accurate prediction of extreme events. We show that echo state networks are able to predict extreme events well beyond the predictability time, i.e., up to more than five Lyapunov times. Third, we focus on the long-term prediction of extreme events from a statistical point of view. By training the networks with data sets that contain nonconverged statistics, we show that the networks are able to learn and extrapolate the flow's long-term statistics. In other words, the networks are able to extrapolate in time from relatively short time series. Fourth, we design a simple and effective control strategy to prevent extreme events from occurring. The control strategy decreases the occurrence of extreme events up to one order of magnitude with respect to the uncontrolled system. Finally, we analyze the robustness of the results for a range of Reynolds numbers. We show that the networks perform well across a wide range of regimes. This work opens up new possibilities for the data-driven prediction and control of extreme events in chaotic systems.

The statistics of clustered and free long-lived vortices in the inverse energy cascade of forced-dissipative two-dimensional turbulence are studied. Like-sign vortices are defined as clustered if they are found in a contiguous region bounded by a level set of the stream function. If this region in addition contains no vortices of the opposite sign, then the cluster is perfectly polarized. Vortices outside these regions are free. The vortices found in perfectly polarized clusters exhibit a scale-invariant distribution of areas, with number density $n\left(A\right)\sim A^{-1}$, while the free number density scales as $n\left(A\right)\sim A^{-3}$. Allowing clusters to contain vortices of the opposite sign results in a progressive loss of the $A^{-1}$ scaling as the polarization threshold is relaxed. The number of vortices in perfect clusters decreases in time via merger, while the number of free vortices increases as smaller vortices are ejected from clusters into the surrounding flow. Large clusters containing many vortices are preferentially disassembled by the vortex motions, their number decreases more quickly, and they exhibit different scaling laws than smaller clusters, which contain fewer and stronger vortices. A semiempirical mean-field theory is developed for the vortices in perfectly polarized clusters and is consistent with their observed statistics as long as small and large clusters are considered separately. As with the vortices, the cluster properties vary with scale, and this variation must be accounted for when developing a theory. The evolution of the vortex population in the forced-dissipative inverse energy cascade is found to involve two processes: the concentration of a constant amount of coherent enstrophy into a smaller and smaller fraction of the domain, and the simultaneous randomization of the surrounding flow as evidenced by decreasing polarization.

The effects of entropic instabilities on the laminar-turbulent transition dynamics of a blunted flat plate at Mach 4 are numerically investigated through linear and nonlinear approaches. Linear wave-packet analysis reveals amplifying oblique first modes as well as planar and oblique entropy-layer disturbances. The receptivity of entropic instabilities is found to be largest for actuation seeded in the entropy layer; the corresponding linear evolution is characterized by an intensification in the wall-normal plane, coupled with streamwise tilting. The transition process that arises from entropy-layer wave interactions via the oblique breakdown mechanism is examined in detail. Oblique entropy-layer disturbances interact nonlinearly with each other and induce streamwise streaks in the boundary layer. These undergo further destabilization downstream, through a combination of lift-up and Orr-like mechanisms, leading to turbulence onset. Sinuous subharmonic oscillations induced by the entropic disturbances are the dominant streak instabilities. Slanted hook-shaped structures are observed in the temperature perturbations, and are attributed to an Orr-like mechanism in the entropy layer. Further, temperature perturbations amplify on the crests of the low-speed streaks in the entropy layer and generate disturbances through triadic interactions. These disturbances aid in the transfer of perturbation energy into the boundary layer, eventually leading to spanwise homogenization and near-wall streak generation. Toward the end of the breakdown region, spectral broadening accompanied by the appearance of an inertial subrange in the boundary layer indicates the approach of the flow toward turbulence. The prominence of entropy-layer disturbances in streak generation and destabilization suggests oblique breakdown as a potentially important transition mechanism in high-speed blunt-nosed configurations.

The problem of thermal instability in rapidly rotating, self-gravitating fluid bodies has been widely modeled in spheres or spherical shells, which implicitly neglects the flattening effect due to the centrifugal force. In our previous paper [Kong, Phys. Rev. Fluids 7, 074803 (2022)], by self-consistently taking into account the centrifugal force, rapidly rotating stably stratified Boussinesq fluid was modeled in oblate spheroidal cavities whose geometric shapes are determined by the theory of figure. A closed-form solution was obtained for gravity and temperature. The stable stratification was demonstrated to be motionless in the corotating frame of reference. Based on this nonspherical model of the conduction state in a rapidly rotating spheroidal cavity, the problem of thermal instability is formulated and discussed by this paper in the regime of inertial convection, which is marked by asymptotically small Ekman number and sufficiently small Prandtl number. The critical properties of inertial modes are explicitly derived. The dependence of the onset of thermal inertial convection on the oblateness of spheroid is systematically explored.

We study a differentially heated square cavity with inlet and outlet ports at the top of the side walls, quantifying how the effective thermal conductivity changes with the temperature difference across the system. The side walls are insulating, the top surface is kept at a fixed high temperature, and the bottom surface at a fixed low temperature, leading to buoyancy-stabilized flow. We visualize the flow pattern for Reynolds number, $\mathrm{Re}=1$, and Prandtl number, $\mathrm{Pr}=50$, and characterize the heat transfer at the bottom surface using the Nusselt number, Nu, for $\mathrm{Re}=0.1,1,10$ and $\mathrm{Pr}=1,50$. As the Richardson number, $\mathrm{Ri}$, is increased, we observe the formation of a series of system-spanning vortices through the merging of Moffatt eddies growing from the bottom corners of the cavity. We find that the convection, which enhances the transport of heat, is strongly suppressed by increasing the temperature drop. As a result Nu drops by a factor 1–3 depending on the Reynolds number.

We chart a singular landscape in the temporal domain of the inviscid Burgers equation in one space dimension for sine-wave initial conditions. These so far undetected complex singularities are arranged in an eye shape centered around the origin in time. Interestingly, since the eye is squashed along the imaginary-time axis, complex-time singularities can become physically relevant at times well before the first real singularity—the preshock. Indeed, employing a time-Taylor representation for the velocity around $t=0$, loss of convergence occurs roughly at 2/3 of the preshock time for the considered single- and multimode models. Furthermore, the loss of convergence is accompanied by the appearance of initially localized resonant behavior which, as we claim, is a temporal manifestation of the so-called tyger phenomenon, reported in Galerkin-truncated implementations of inviscid fluids [S. S. Ray et al., Phys. Rev. E 84, 016301 (2011)]. We support our findings of early-time tygers with two complementary and independent means, namely, by an asymptotic analysis of the time-Taylor series for the velocity, as well as by a singularity theory that employs Lagrangian coordinates. Finally, we apply two methods that reduce the amplitude of early-time tygers. One is tyger purging which removes large Fourier modes from the velocity, and is a variant of a procedure known in the literature. The other method realizes an iterative UV completion, which, most interestingly, iteratively restores the conservation of energy once the Taylor series for the velocity diverges. Our techniques are straightforwardly adapted to higher dimensions and/or applied to other equations of hydrodynamics.

Resolvent analysis has found applications in several areas of fluid mechanics, providing physical insight into both laminar and turbulent flows. In spite of such fact, the global (3D) resolvent is computationally expensive, which limits the size of the domain and the Reynolds number of the flows which can be considered. In this work, we derive a parabolic resolvent approach, which enables a significant increase in the computational efficiency of the calculation, for streaky structures in boundary layer flows. The computational speedup depends on the size of the problem and could be of more than one order of magnitude for the same accuracy as the global calculation. The method is derived based on an optimization method via the Lagrange multipliers over the linearized boundary layer equations and it is coupled to a Krylov-Arnoldi decomposition to the computation of suboptimals. The application of the method is exemplified for two problems: a Falkner-Skan boundary layer, where we obtain trends for both the optimals and suboptimals, and a turbulent boundary layer, where characteristics such as the double peak in the spectrum and the characteristic inner and outer length scales can be recovered when a variable eddy viscosity is considered. In both cases, a scaling is found for the dominant gain, given in terms of the fourth power of the Reynolds number, defined in terms of the relevant scale for the problem, the displacement thickness, and the modified Rotta-Clauser parameter for the laminar and turbulent boundary layers, respectively. For the laminar case, we further demonstrate that a forcing limited to the free-stream region is capable of generating streaky structures inside the boundary layer, a relevant feature for free-stream turbulence-induced transition.

The effect of precession in a rotating sphere filled with fluid was studied with direct numerical simulations, in both incompressible hydrodynamics (HD) and magnetohydrodynamics (MHD) scenarios. In both cases the asymptotic state and its dependence with both rotating and precession frequency was analyzed. For the MHD case no self-sustaining dynamos were found for the prograde precession case, whereas on the other hand a critical retrograde precession frequency was found above which dynamo action is self-sustained. It was also found that these correspond to small-scale dynamos with a developed turbulent regime. Furthermore, the presence of reversals of the magnetic dipole moment is observed, with greater waiting times between reversals for smaller precession frequencies.

We develop theory and perform laboratory experiments on reversing buoyancy particle-bearing wall jets in a uniform ambient fluid, examining the lofting characteristics of the jet and particle sedimentation. Theoretical considerations involving several parameters predict the lofting location and the deposition pattern. The suction forces present at the bottom wall dominantly influence the lofting location of the jet. The sediment dynamics are influenced by drag at the bottom wall, entrainment of ambient fluid into the jet, and several scale factors involving the settling of the particles. Our theory shows that the ratio of deposit width to length depends on the jet's drag coefficient and entrainment dynamics. Experimentally, we find that this ratio is higher when the particle concentration is large, suggesting that sedimenting particles exert a nonnegligible additional drag on the jet. The results clearly show changes in the jet dynamics brought about by the presence of particles in reversing buoyancy jets.