We perform three-dimensional direct numerical simulations of surface-driven convection near the temperature of maximum density ${\tilde{T}}_{md}$. A dynamic surface boundary condition couples heat flux through the surface to the induced convection, creating a dynamic equilibrium between the surface water temperature and the convection below. In this system with a quadratic equation of state, we identified three convective regimes: (i) free convection when the surface water temperature is above ${\tilde{T}}_{md}$, (ii) penetrative convection when the surface water temperature is below ${\tilde{T}}_{md}$ and the convection is actively mixing the fluid layer, and (iii) decaying convection when the convection weakens. We then predict the transitions between these regimes. Understanding these transitions is essential for the predicting timing of ice formation in lakes and other natural systems.

A previous study in stochastically forced 1D Burgers flows reveals a dynamical synchronization of Fourier triadic phases during burst events associated with intense forward energy fluxes (Murray and Bustamante, J. Fluid Mech. 850, 624 (2018). Conversely, it is yet to be determined whether the dynamical evolution of Fourier phases is necessary for forming forward energy cascades in more general flow systems, particularly in 3D turbulent flows. We propose a “frozen-phase” experiment in which only the Fourier amplitudes evolve temporally, with a fixed set of Fourier phases prescribed. The method employed to freeze the phases can be considered a designed forcing term in the spectral space that only acts on the evolution equation of Fourier phases. The results suggest the essential role of Fourier phase dynamics in the formation of a “standard” energy cascade in 3D turbulent flows. However, forming an “attenuated” energy cascade without any phase dynamics is still possible. These findings are supported by the values of longitudinal velocity gradient skewness and the Kolmogorov constants, which deviate from classical ones when the phases are frozen.

In this study, we experimentally demonstrate the possibility of negative refraction of water waves, using a locally resonant metamaterial. This metamaterial exhibits a dispersion that encompasses elliptical and hyperbolic regimes, characterized by theoretical analysis and supported by experimental validation. In the frequency range associated with hyperbolic dispersion, we confirm and characterize the appearance of negative refraction. Our experimental achievement provides convincing evidence of the potential of metamaterials for water wave control.

In this study, we conduct numerical investigations into the impact of droplet collisions on solid surfaces, with a specific focus on the influence of wettability and initial diameter. Previous studies have proposed two distinct scaling laws, namely $W{e}^{1/2}$ and $W{e}^{1/4}$, where $We$ denotes the Weber number, to describe the maximum spreading diameter ratio in the capillary regime. Our energy analysis reveals that only the $W{e}^{1/2}$ scaling accurately characterizes the capillary regime. Additionally, we elucidate that the observed data slope of $1/4$ arises from the $W{e}^{1/2}$ scaling while the initial diameter also plays a role within the low-$We$ range. To address this, we introduce a modified Weber number ($W{e}^{*}$), dependent on wettability, defined through energy conservation and accounting for the initial diameter $apriori$. Utilizing the $W{e}^{*}$, we establish a generalized scaling for the maximum spreading diameter ratio, enabling the consolidation of numerical and experimental findings onto a single curve, regardless of wettability. Furthermore, this scaling demonstrates excellent agreement with numerical results for both low and relatively high-$We$ regimes but without splashing.

Recently, we showed experimentally that finite-size perturbations cause a supercritical non-normal mode elastic instability in inertialess viscoelastic channel flow, despite its proven linear stability. The nonmodal nature of the instability is characterized by two key features: a direct transition from laminar to chaotic flow and a dependence of the instability onset $W{i}_c$ on the external perturbation strength. It is also found that chaotic flows at $Wi>W{i}_c$, where $Wi$ is the main control parameter, in the transition, elastic turbulence (ET) and drag reduction (DR) flow regimes exhibit similar scaling of flow properties independent of the strength and structure of the external perturbations. Here we present properties of polymer solution channel flow with a smoothed inlet, resulting in up to an order of magnitude lower perturbation amplitude than in previous experiments. Nevertheless, universal scaling exponents of power-law fits of the flow properties with $Wi-W{i}_c$ in the transition regime and similar behavior in ET and DR at higher $Wi$ are obtained. It is noteworthy that due to the low perturbation intensity, three flow regimes are detected only at the inlet, while further downstream only the transition flow regime is observed and the spanwise velocity spectrum remains flat at the highest recorded location in the channel. Finally, the scaling exponent $\beta =-0.55\pm 0.04$ of the $W{i}_c$ as a function of external perturbation strength is obtained.

We experimentally reveal that a sub-millimetric liquid jet can impact a heated substrate without making any contact with the underlying solid. These Leidenfrost jets are surfing on their own vapor layer and are observed under certain conditions related to jet radius, fluid velocity, incident angle and substrate temperature. We focus on the thickness of the vapor layer and on its typical area over which the jet bounces on the substrate. The experimental results are found to be in good agreement with models. We also observe a directed percolationlike transition appearing when the jet enters in contact boiling with the heated substrate.

Interfacial fluid dynamics has a rich history of systematically exploring intricate flows studied for their technological and heuristic value. Surface tension typically forms exceptionally smooth shapes, yet the same cohesive forces can precipitate the rearrangement and breakup of liquids through a wealth of hydrodynamic instabilities. This article summarizes, albeit nonexhaustively, recent efforts to tame interfacial flows in solidifying polymer melts. The article tackles both these flows' stable and unstable limits and focuses on the fundamental challenges and opportunities of harnessing interfacial effects to shape soft materials.

Direct numerical simulations of turbulent pipe flow with transverse wall oscillation and with no transverse wall oscillation are carried out at friction Reynolds numbers ${\mathrm{Re}}_{\tau }=170$, 360, and 720. The period and amplitude of the oscillation are selected to achieve high drag reduction in this low Reynolds number range. The focus of the current study is to identify the location and scales of motion most affected by drag reduction and how they impact drag reduction effectiveness. To answer this question, the streamwise and azimuthal spectra of relevant statistical quantities are analyzed with and without transverse wall oscillation. The effect of wall oscillation is found to suppress the intermediate- and large-scale motions in the buffer layer of the flow, while large-scale motions in the outer layer are enhanced. Since higher Reynolds number flows support development of a growing range of large-scale structures (both in length and height), it is suggested that their prevalence in the energy spectra combined with their negative effect on drag reduction account for a reduced effectiveness of wall oscillation as a drag reduction mechanism with increasing Reynolds number in the actuation regime investigated.

Recent numerical studies have suggested the potential of substrates with streamwise-preferential permeability to reduce drag in turbulent boundary layers. Such a substrate is theorized to facilitate relaxation of the no-slip condition and thereby reduce the skin friction. So far, these beneficial effects have not been demonstrated experimentally yet and therefore the scope of this work is to present this concept in air flow where the substrate geometry satisfies the theoretical permeability requirements for an expected reduction in drag. For this, a three-dimensional-printed structure with anisotropic permeability (${\varphi }_{xz}=2.7, {\varphi }_{xy}=3.9$) and small pores ($s\approx 250\mu \mathrm{m}$), akin to an acoustic liner, was developed. The substrate was investigated using direct force measurements and 2D-2C PIV in the range of $U_{\infty }\approx 5$–35 ${\mathrm{ms}}^{-1}$, corresponding to frictional Reynolds numbers of ${\mathrm{Re}}_{\tau }\approx 430$–1960. Results show an increase in drag of $0\%<\mathrm{\Delta }{C}_D<8\%$ and, while contrasting the model predictions, this agrees with DNS data on structures with similar geometric properties when using the inverse wall-normal Forchheimer coefficient, or inertial permeability, as the equivalent roughness parameter. Hence the present results constitute the first experimental evidence that this is the governing property for the drag behavior of acoustic liners. The absence of the predicted beneficial flow modulation effects is attributed to the investigated substrate not strictly satisfying the theoretical framework assumptions on characteristic length scales. However, to expand beyond this structural limitation, we analytically derive that, for realistic, geometrically resolved cases, this length scale mismatch is unavoidable and thereby render it unfeasible to model the substrate as a continuum for the virtual-origin approach. We expect that translating the abstraction of substrates with streamwise-preferential permeability into physical realisations relevant for practical applications would result in structures very similar to riblets.

Metachronal swimming consists of the sequential stroking of multiple appendages or cilia, resulting in a wave of appendage motion traveling along the body. Further, metachronal swimming spans the viscous to inertial regimes as it is used across seven orders of magnitude of Reynolds numbers ${\mathrm{Re}}_b$, where ${\mathrm{Re}}_b=VL/\nu$, and $V, L$, and $\nu$ are the characteristic swimming speed, body length, and fluid kinematic viscosity, respectively. Through analysis of morphological and kinematics data collected from the literature on a wide variety of metachronally swimming organisms, we examine how these factors affect swimming performance across ${\mathrm{Re}}_b$. Further, we find a strong relationship among the kinematics parameters, swimming speed, and fluid viscosity. This power law relationship, ${\mathrm{Re}}_b\sim Sw$, where $Sw=\omega AL/\nu$ is the Swimming number ($\omega$: average angular appendage tip speed, $A$: appendage tip excursion), is maintained for all flow regimes, explains why metachronal swimming is a successful locomotion mode at low Reynolds numbers, and may prove useful in designing bio-inspired robots. We also find that the Strouhal number $St=fA/V$, where $f$ is beat frequency, is relatively constant across a wide range of ${\mathrm{Re}}_b$ but suggest that $Sw$ better describes the underlying hydrodynamics of metachronal swimming.

We perform CFD simulations to study vortex-induced vibrations (VIV) of a cylinder in the inertial-elastic flow at a Reynolds number of $\text{Re}=100$ and for a range of Weissenberg numbers of $0<\text{Wi}<10$. In this range of Reynolds and Weissenberg numbers, both inertia and elasticity of the flow must be considered when it interacts with a flexibly mounted cylinder. We use the FENE-P model to describe the viscoelastic fluid and investigate the effects of the Weissenberg number and the maximum polymer extensibility on the response of a flexibly mounted cylinder with one or two degrees of freedom placed in flow. In addition to the primary vortices, we observe secondary vortices in the wake that are formed due to viscoelasticity in the flow. For increased elasticity in the fluid, we observe significant polymer deformation in the upstream stagnation region resulting in a region of large elastic stress that acts as a wall around the cylinder. As a result, the stagnation point moves upstream of the cylinder creating a finite gap between the shear layers and the cylinder surface. The region of flow separation is both widened and extended further downstream. With increased elasticity, VIV amplitude is decreased in both one- and two-degree-of-freedom cases. We show that higher harmonic forces that are typically observed for the two-degree-of-freedom VIV responses in a Newtonian flow and cause increased fatigue damage in the structure are suppressed by adding elasticity to the flow.

This article presents an experimental investigation into the interaction of a freely evolving turbulent structure with a steadily forced, finite-width internal gravity wave beam. Specifically, a vortex ring is used as the simplified prototype for a propagating turbulent structure and we present an exploration into how it's passage affects the linear stability of the imposed (or forced) wave field. We use the term "vortex ring" to describe an initially axisymmetric, toroidal fluid structure with azimuthal vorticity. We first examine both the vortex ring and the imposed internal gravity wave beam separately and present how they develop in a quiescent, stratified environment. In the absence of any vortex ring, we find—in agreement with many previous studies—there is an amplitude threshold that the wave beam must surpass before it becomes linearly unstable by a process known as triadic resonance instability (TRI). In the absence of an imposed wave field, we present the propagation and collapse of a coherent vortex ring into a turbulent patch, and measure the transient spectrum of internal waves produced. We then combine these two phenomena and investigate how each impacts the other. While we find that the preexisting internal wave beam has no significant influence on the evolution of the incident vortex ring, we do find that the propagation and subsequent collapse of the ring provokes a response from the internal wave beam. This response allows us to demonstrate two key findings relating to the internal wave beams pathway to triadic resonance. First, the passage of a vortex ring propagating through a forced wave field can provide a nonlinear trigger for the transition to a triadic state when the amplitude of the imposed wave field is itself too small for the spontaneous growth of such a triadic state through TRI. Second, we find that in some cases the triadic states induced by this interaction are not self-sustaining and eventually decay, prompting the terminology "transient triads." These surprising findings are further confirmed by the unintentional release of trapped air arising from under our "magic carpet" wavemaker. These air bubbles turbulently propagate vertically through the imposed beam and, in some cases, induce similar triadic state transitions to those of the vortex ring. Our analysis leads to a discussion on the beam's pathway to instability and to question the structure of the underlying dynamical system arising from the distribution of spectral power in a finite-width beam.

The steady-state behavior of a single drop under shear flow has been extensively investigated in the limit of small deformation and negligible inertia effects. In this work, we combine the calculations proposed by Flumerfelt [R. W. Flumerfelt, J. Colloid Interface Sci. 76, 330 (1980)] for unconfined drops with interface viscosity, with those by Shapira and Haber [M. Shapira and S. Haber, Int. J. Multiphase Flow 16, 305 (1990)] for confined drops without interface viscosity. By merging these two approaches, we provide comprehensive analytical predictions for steady-state drop deformation and inclination angle across a wide range of physical conditions, from confined to unconfined droplets, including or excluding the effect of interface viscosity. The proposed analytical predictions are also robust concerning variations in the viscosity ratio, making our model general enough to include any of the above conditions.

It is generally believed that the thermodynamic and velocity fields are highly coupled in compressible wall-bounded turbulence. In the present study, we employ the second-order spectral stochastic estimation (SSSE) to investigate the scaling behaviors of the couplings between these fields, which include the velocity-temperature ($u\text{−}T$) and velocity-pressure ($u\text{−}p$) couplings. Particular attention is paid to the differences between the SSSE and the first-order spectral stochastic estimation (FSSE). Spectral analyses of the couplings in the logarithmic region suggest that the linear part of the $u\text{−}T$ coupling is strong at the scales corresponding to the energy-containing motions populating the same locus, whereas the quadratic term is centered at the scales corresponding to the very large-scale motions. In contrast, the linear component of the $u\text{−}p$ coupling shows a stronger isotropic behavior, whereas the quadratic component is located at the large spanwise scales. Several metrics are proposed to compare the accuracy of the FSSE and the SSSE in estimating the thermodynamic fields with the velocity input in the logarithmic region. The SSSE has an advantage over the FSSE in estimating the strong events and the variation tendencies of thermodynamic fields. As a result, the distributions of the estimated fields by the SSSE are closer to those of the raw fields. However, the abilities of the FSSE and the SSSE in capturing the transient characteristics of the near-wall thermodynamic fields are limited and of little difference, with the velocity field in the logarithmic region as input. Only the low-pass filtered signals can be recovered. The present work uncovers details about the multiphysics couplings in compressible wall turbulence.

We present an analytical solution of flow through disordered porous media with inertia effects at a finite Reynolds number ($\mathrm{Re}$), and consequently a truncated quadratic formula for easy use without any fitting parameters. The derivation is based on an effective capillary model in which the effective radius of capillaries varies with $\mathrm{Re}$. Inspired by the asymptotic solution of flow in curved capillaries [S. Murata, Y. Miyake, and T. Inaba, J. Fluid Mech. 73, 735 (1976)], the Oseen-form equation is derived to capture the flow behavior in each capillary. The analytical formula has been validated by comparisons with numerous available experimental data.

Within biological fluid dynamics, it is conventional to distinguish between “puller” and “pusher” microswimmers on the basis of the forward or aft location of the flagella relative to the cell body: typically, bacteria are pushers and algae are pullers. Here we note that since many pullers have “outboard” cilia or flagella displaced laterally from the cell centerline on both sides of the organism, there are two important subclasses whose far-field is that of a stresslet, but whose nearfield is qualitatively more complex. The ciliary beat creates not only a propulsive force but also swirling flows that can be represented by paired rotlets with two possible senses of rotation, either “feeders” that sweep fluid toward the cell apex, or “expellers” that push fluid away. Experimental studies of the rotifer Brachionus plicatilis in combination with earlier work on the green algae Chlamydomonas reinhardtii show that the two classes have markedly different interactions with surfaces. When swimming near a surface, expellers such as C. reinhardtii scatter from the wall, whereas a feeder like B. plicatilis stably attaches. This results in a stochastic “run-and-stick” locomotion, with periods of ballistic motion parallel to the surface interrupted by trapping at the surface.

Adjoint methods have been the pillar of gradient-based optimization for decades. They enable the accurate computation of a gradient (sensitivity) of a quantity of interest with respect to all system parameters in one calculation. When the gradient is embedded in an optimization routine, the quantity of interest can be optimized for the system to have the desired behavior. Adjoint methods, however, require the system's governing equations and their Jacobian. In this paper, we propose a computational strategy to infer the adjoint sensitivities from data when the governing equations might be unknown (or partly unknown), and noise might be present. The key component of this strategy is an echo state network, which learns the dynamics of nonlinear regimes with varying parameters, and it evolves dynamically via a hidden state. Although the framework does not make assumptions on the dynamical system, we focus on thermoacoustics, which are governed by nonlinear and time-delayed systems. First, we show that a parameter-aware echo state network (ESN) infers the parametrized dynamics. Second, we derive the adjoint of the ESN to compute two types of sensitivity: (i) parameter sensitivity, which is the gradient of a time-averaged cost functional with respect to physical or design parameters of the system, and (ii) initial condition sensitivity, which is the gradient of a cost functional of the final state with respect to the initial condition. Third, we propose the thermoacoustic echo state network (T-ESN), which embeds the physical knowledge in the network architecture for improved generalization. Fourth, we apply the framework to a variety of nonlinear thermoacoustic regimes of a prototypical system. We show that the T-ESN accurately infers the correct adjoint sensitivities of the acoustic energy with respect to the flame parameters and initial conditions. The results are robust to noisy data, from periodic, through quasiperiodic, to chaotic regimes. The inferred adjoint sensitivities are employed to suppress an instability via steepest descent. We show that a single network predicts the nonlinear bifurcations on unseen scenarios, which allows it to converge to the minimum of the acoustic energy. This work opens new possibilities for gradient-based data-driven design optimization.

If carbon dioxide dissolves into a body of water, a ${\mathrm{CO}}_2$-rich boundary layer forms at the interface, which is denser in comparison to pure water. Continued dissolution of ${\mathrm{CO}}_2$ into the water barrier results in the layer becoming gravitationally unstable, leading to the onset of buoyancy-driven convection and, consequently, the shedding of a buoyant plume. In this work, we look at the influence of confinement on this process in two ways: In the first part we focus on expanding our understanding of the short-time, transient diffusion of ${\mathrm{CO}}_2$ into a vertical water barrier confined to a narrow cylindrical cell by varying the cylinder diameter and ${\mathrm{CO}}_2$ pressure. By adding sodium fluorescein, a pH-sensitive fluorophore, we directly visualize the dissolution and propagation of the ${\mathrm{CO}}_2$ across the liquid barrier. Combined with particle-tracking experiments we quantify the effects of the cylinder width and ${\mathrm{CO}}_2$ pressure on the initial diffusive behavior, the onset of convection, and the enhancement of the buoyancy driven convection of the subsequent transport. In the second part, we investigate the long-time, steady mass transfer dynamics in the liquid barrier by trapping a slug bubble underneath the liquid barrier and varying the barrier height and partial ${\mathrm{CO}}_2$ pressure. We find that initially the Sherwood number scales as Sh $\propto {\mathrm{Ra}}^{1/4}$ with the Rayleigh number Ra, but for a sufficiently large barrier the Sherwood number reaches a constant value. Building on the ideas of Ahlers et al. [Phys. Rev. Lett. 128, 084501 (2022)], rescaling the Rayleigh number with an aspect-ratio-dependent relevant length scale results in a universal Sh vs Ra dependence.

Turbulent flows at the surface of the ocean deviate from geostrophic equilibrium on scales smaller than about 10 km. These scales are associated with important vertical transport of active and passive tracers, and should play a prominent role in the heat transport at climate scales and for plankton dynamics. Measuring velocity fields on such small scales is notoriously difficult but new, high-resolution satellite altimetry is starting to reveal them. However, the satellite-derived velocities essentially represent the geostrophic flow component, and the impact of unresolved ageostrophic motions on particle dispersion needs to be understood to properly characterize transport properties. Here, we investigate ocean fine-scale turbulence using a model that represents some of the processes due to ageostrophic dynamics. We take a Lagrangian approach and focus on the predictability of the particle dynamics, comparing trajectories advected by either the full flow or by its geostrophic component only. Our results indicate that, over long times, relative dispersion is marginally affected after filtering out the ageostrophic component. Nevertheless, advection by the geostrophic-only flow leads to an overestimation of the typical pair-separation rate, and to a bias on trajectories (in terms of displacement from the actual ones), whose importance grows with the Rossby number. We further explore the intensity of the transient particle clustering induced by ageostrophic motions and find that it can be significant, even for small flow compressibility. Indeed, we show that clustering is here due to the interplay between compressibility and persistent flow structures that trap particles, enhancing their aggregation.

The storage of ${\text{CO}}_2$ in underground aquifers and its long-term feasibility during carbon sequestration depend on the mixing of ${\text{CO}}_2$ with brine. The mixing, in turn, greatly depends on the convective motions developed in aquifers due to the concentration difference between the two fluids and temperature gradient that might arise due to geothermal heating. In the current study, we examine the stability of thermosolutal convection subjected to vertical temperature and concentration gradients, considering depth-dependent permeability and thermal diffusivity in an anisotropic porous medium. We consider that the solute concentration declines through a first-order chemical reaction. Using the energy method and linear theory, we obtain the critical Rayleigh number required for system's instability. We investigate the effects of various dimensionless parameters, including solute Rayleigh number, Damköhler number, Lewis number, permeability parameter, and thermal diffusivity anisotropic parameter, on the dynamics of mixing. Our results show that the subcritical instability region is insignificant, as the stability limits obtained using the energy method and linear theory coincide. This result highlights the system's unique instability characteristic and its importance for analyzing and enhancing mixing processes in underground aquifers. We also present the applicability of the results to an aquifer for ${\mathrm{CO}}_2$ sequestration.