One mechanistic interpretation of baroclinic instability is that of mutual constructive interference of Rossby edge waves. The suppression of baroclinic instability over slopes has been widely established, where previous research argues that a sloping boundary modifies the properties of these Rossby edge waves, but does not provide a mechanistic explanation for the suppression that is valid over all parameter space. In the context of an Eady problem modified by the presence of a sloping boundary, we provide a mechanistic rationalization for baroclinic instability in the presence of slopes that is valid over all parameter space, via an equivalent formulation explicitly in terms of Rossby edge waves. We also highlight the differences between edge-wave phase shifts and normal-mode phase tilts, showing that the edge-wave phase shifts should be the ones that are mechanistically relevant, and normal-mode phase tilt is a potentially misleading quantity to use. Further, we present evidence that the edge-wave phase shifts but not normal-mode phase tilts are well correlated with geometric quantities diagnosed from an analysis framework based on eddy variance ellipses. The result is noteworthy in that the geometric framework makes no explicit reference to the edge-wave structures in its construction, and the correlation suggests the geometric framework can be used in problems where edge-wave structures are not so well defined or readily available. Some implications for parametrization of baroclinic instability and relevant eddy-mean feedbacks are discussed. For completeness, we also provide an explicit demonstration that the linear instability problem of the present modified Eady problem is parity-time symmetric, and speculate about some suggestive links between parity-time symmetry, shear instability, and the edge-wave interaction mechanism.

In this study, we introduce a comprehensive theoretical model for viscous liquid systems exhibiting Rayleigh-Plateau instability, accommodating cases both with and without a solid fiber. Employing the lubrication approach and implementing the hydrodynamic interaction at the solid-liquid interface, we formulate one-dimensional evolution equations for the breakup of viscous liquid threads and films on a fiber. Through several validations, we showed that our model exhibits a good agreement with experimental results in comparison to numerical simulations. Finally, our model, which incorporates the flow effect from the inner boundary condition by reconsidering the ansatz of a conventional long-wave approximation, provides a necessary condition for satellite droplet formation and determines the most unstable mode proportional to ${k^{*}}^2$, where $k^{*}$ is the most unstable wavenumber. In addition, we observed that the volume of the satellite droplets exponentially decays depending on the wavenumber. Moreover, our single model integrates the findings of Goren's liquid film on a fiber and Rayleigh's viscous liquid thread, demonstrating its versatility and relevance to a wide range of systems.

Heat transfer in wind turbulence over breaking waves is studied through direct numerical simulations. The air-water system is simulated on an Eulerian grid with the interface between the two phases captured by a coupled level set and volume-of-fluid method. To examine the effect of wave age, different cases representing slow, intermediate, and fast waves are considered for the scenario of air temperature being higher than the water temperature. The results show that the evolution of mean temperature profile responds nonmonotonically to the increasing wave age. At a small wave age, the mean temperature near the water surface increases after wave breaking. At intermediate and large wave ages, however, the temperature decreases after wave breaking, while the decrement magnitude is larger at the intermediate wave age. An investigation of the temperature fluctuation flux indicates that a combined effect of wave-coherent flux and turbulence-induced flux leads to a large magnitude of temperature decrement at the intermediate wave age. A further analysis of the production term in the transport equation of the turbulence-induced temperature flux elucidates the mechanism underlying the generation of the turbulence-induced flux at the intermediate wave age. The findings of the present study suggest that temperature responds in a more complex manner to wave age than velocity does and this phenomenon should be considered in models for air-sea interaction and weather forecasting.

We illuminate effects of surface-charge convection intrinsic to leaky-dielectric electrohydrodynamics by analyzing the symmetric steady state of a circular drop in an external field at arbitrary electric Reynolds number ${\mathrm{Re}}_E$. In formulating the problem, we identify an exact factorization that reduces the number of dimensionless parameters from four—${\mathrm{Re}}_E$ and the conductivity, permittivity and viscosity ratios—to two: a modified electric Reynolds number $\widetilde{\mathrm{Re}}$ and a charging parameter $\varpi$. In the case $\varpi <0$, where charge relaxation in the drop phase is slower than in the suspending phase, and, as a consequence, the interface polarizes antiparallel to the external field, we find that above a critical $\widetilde{\mathrm{Re}}$ value the solution exhibits a blowup singularity such that the surface-charge density diverges antisymmetrically with the $-1/3$ power of distance from the equator. We use local analysis to uncover the structure of that blowup singularity, wherein surface charges are convected by a locally induced flow towards the equator where they annihilate. To study the blowup regime, we devise a numerical scheme encoding that local structure where the blowup prefactor is determined by a global charging-annihilation balance. We also employ asymptotic analysis to construct a universal problem governing the blowup solutions in the regime $\widetilde{\mathrm{Re}}\gg 1$, far beyond the blowup threshold. In the case $\varpi >0$, where charge relaxation is faster in the drop phase and the interface polarizes parallel to the external field, we numerically observe and asymptotically characterize the formation at large $\widetilde{\mathrm{Re}}$ of stagnant, perfectly conducting surface-charge caps about the drop poles. The cap size grows and the cap voltage decreases monotonically with increasing conductivity or decreasing permittivity of the drop phase relative to the suspending phase. The flow in this scenario is nonlinearly driven by electrical shear stresses at the complement of the caps. In both polarization scenarios, the flow at large $\widetilde{\mathrm{Re}}$ scales linearly with the magnitude of the external field, contrasting the familiar quadratic scaling under weak fields.

Surfactant-laden thin liquid films overlaid on solid substrates are encountered in a variety of industrial and biological settings. As these films reach submicron thickness, they tend to become unstable owing to the influence of long-range dispersion forces. In the current study, we investigate how gravitational drainage affects the stability attributes of such thin liquid films. Using scaling arguments, we demonstrate that gravity and dispersion forces can exert their influence simultaneously over a wide range of film thicknesses. In the lubrication limit, we carry out linear stability analysis and nonlinear simulations to understand the evolution of draining thin films. Linear stability indicates the existence of two unstable modes and two cutoff wave numbers, as opposed to a single unstable mode and a unique cutoff wave number observed in stationary films. It is also found that surfactant-laden flowing films are more stable than stationary films with surfactants as well as draining films with clean interfaces. The origin of stabilization is identified as the enhanced surfactant perturbations generated due to drainage. We demonstrate that films exhibiting intermediate levels of surfactant activity and significant drainage exhibit the lowest rates of disturbance growth, leading to extending the time of rupture.

Biofilament-motor protein complexes are ubiquitous in biology and drive the transport of cargo vital for many fundamental life processes at the cellular level. As they move, motor proteins exert compressive forces on the filaments to which they are attached. If the filament is clamped or tethered in some way, this force leads to buckling and a subsequent range of dynamics. The follower force model, in which a single compressive force is imposed at the filament tip, is a simple filament model that is becoming widely used to describe an elastic filament, such as a microtubule, compressed by a motor protein. Depending on the force value, one can observe different states including whirling, beating, and writhing, though the bifurcations giving rise to these states are not completely understood. In this paper, we utilize techniques from computational dynamical systems to determine and characterize these bifurcations. We track emerging time-periodic branches and identify quasiperiodic states. We investigate the effect of filament slenderness on the bifurcations and, in doing so, present a comprehensive overview of the dynamics which emerge in the follower force model.

The verification of whether small-scale turbulence is isotropic remains a grand challenge. The difficulty arises because the presence of small-scale anisotropy is tied to the dissipation tensor, whose components require the full three-dimensional information of the flow field in both high spatial and temporal resolution, a condition rarely satisfied in turbulence experiments, especially during field scale measurement of atmospheric turbulence. To circumvent this issue, an intermittency-anisotropy framework is proposed through which we successfully extract the features of small-scale anisotropy from single-point measurements of turbulent time series by exploiting the properties of small-scale intermittency. Specifically, this framework quantifies anisotropy by studying the contrasting effects of burstlike activities on the scalewise production of turbulence kinetic energy between the horizontal and vertical directions. The veracity of this approach is tested by applying it over a range of datasets covering an unprecedented range in the Reynolds numbers $(\mathrm{Re}\approx {10}^3–{10}^6)$, sampling frequencies (10 kHz to 10 Hz), surface conditions (aerodynamically smooth surfaces to typical grasslands to forest canopies), and flow types (channel flows, boundary-layer flows, atmospheric flows, and flows over forest canopies). For these diverse datasets, the findings indicate that the effects of small-scale anisotropy persists up to the integral scales of the streamwise velocity fluctuations and there exists a universal relationship to predict this anisotropy from the two-component state of the Reynolds stress tensor. This relationship is important towards the development of next-generation closure models of wall turbulence by incorporating the effects of anisotropy at smaller scales of the flow.

Submarine melting at ice-ocean interfaces such as at tidewater glaciers and ice shelves is influenced by physical and chemical environmental factors including salinity, water temperature, stratification, subglacial hydrology, meltwater plumes, and oceanic currents. The effect of these individual components on ice loss can be difficult to capture in common ice-melting models. In particular, turbulence, which can develop as a result of ambient meltwater plumes and subglacial discharge along ice-water interfaces, for example, can increase mixing of relatively warm or high salinity ambient water with meltwater, thus enhancing melting. To isolate and understand the fundamental effects of turbulence on ice melting, we performed experiments of an ice sphere melting in homogeneous isotropic turbulence (HIT) with negligible mean flow. This setup permits us to study melting in turbulence absent additional fluid flows such as mean shear generated by boundary flows, or density stratification due to thermal or salinity gradients. To reduce the effects of complex ice morphology, we selected an ice sphere to achieve a symmetric melting surface. Ambient water temperature was varied from 2 to $10{}^{\circ }\mathrm{C}$. Experiments were performed with both quiescent and turbulent flow surrounding the ice. For the turbulent melting cases, the turbulent kinetic energy of the flow was varied from 9.6 to $28.6{\mathrm{cm}}^2{\mathrm{s}}^{-2}$. To link turbulence metrics and flow patterns to melting, we performed particle image velocimetry to obtain measurements of the two-dimensional velocity fields surrounding the sphere and to capture melting rates in experiments in a nonintrusive manner. Here, we explore the development of convective melt plumes and boundary layer flows that develop along the ice-water interface. We present melting data as a function of turbulence metrics and ambient water temperature. Through novel parametrization of our empirical results, our findings increase the understanding of the impact of turbulence on melting rates and aim to improve predictive numerical simulations of ice loss.

Two-dimensional (2D) turbulence features an inverse energy cascade that produces large-scale flow structures such as large-scale vortices (LSVs) and unidirectional jets. We investigate the dynamics of such large-scale structures using extensive direct numerical simulations (DNS) of stochastically forced, viscously damped 2D turbulence within a periodic rectangular (Cartesian) domain $[0,L_x]\times [0,L_y]$. LSVs form and dominate the system when the domain aspect ratio $\delta =L_x/L_y\approx 1$, while unidirectional jets predominate at $\delta \gtrsim 1.1$. At intermediate values of $\delta$, both structures are metastable, and fluctuation-induced transitions between LSVs and jets are observed. Based on large-scale energy balance in the condensate, we derive and verify predictions for the dependence of the total kinetic energy and the flow polarity on the nondimensional control parameters. We further collect detailed statistics on the lifetimes of LSVs and jets from DNS runs of up to $10738$ viscous diffusive time units in length. The distribution of the lifetimes is consistent with that of a memoryless Poisson process. The data are compatible with an exponential dependence of the mean lifetime on the aspect ratio $\delta$. In addition, the mean lifetimes depend sensitively on the Reynolds number $\mathrm{Re}$: As $\mathrm{Re}$ increases, the energy gap between LSV (lower energy) and jet states (higher energy) arising from anisotropic dissipation increases, leading to an increase in lifetimes that is approximately exponential in $\mathrm{Re}$ for both LSVs and jets. Similarly, as the ratio of the forcing scale to the domain size increases, the transition rates increase sharply, confirming earlier findings. We investigate the transition dynamics in terms of kinetic energy, flow polarity, modal amplitude, and 2D phase-space diagrams, revealing that the transitions occur in two stages: In the initial stage, an efficient redistribution of kinetic energy by nonlinear triadic interactions facilitates a rapid transition from LSVs to jets and vice versa. In the second stage, the kinetic energy of the newly formed structure slowly adjusts to its associated (higher or lower) equilibrium value on a longer, viscous timescale, leading to a time delay that results in hysteretic transition behavior. Fluctuation-induced transitions may also occur between different numbers of jets. Our findings shed new light on the dynamics of coherent large-scale structures in anisotropic turbulence.

Long, flexible fibers transported by a turbulent channel flow sample nonlinear variations of the fluid velocity along their length. As the fibers tumble and collide with the boundaries, they bounce off with an impulse that propels them toward the center of the flow, similar to pole vaulting. As a result, the fibers migrate away from the walls, leading to depleted regions near the boundaries and more concentrated regions in the bulk. These higher concentrations in the center of the channel result in a greater net flux of fibers than what was initially imposed by the fluid. This effect becomes more pronounced as fiber length increases, especially when it approaches the channel height.

We are carrying out the experimental study of the emptying of a hermetically sealed cylindrical tank in a rotating frame. We determine the optimal rotational velocity for the tank, which minimizes the emptying time. Moreover, there exists a critical rotation velocity at which the emptying time exceeds that of the nonrotating case, depending on the relative duration of each of the three emptying regimes identified in this flow, namely, (i) a bubble regime, (ii) a vortical air jet regime, and (iii) a bathtub vortex regime. The three regimes, easily distinguished by the shape of the air-water interface, have different draining velocities. The lifetime of each regime, as well as the transitions between them, depend on both the water level and the rotating velocity of the platform.

Bubbles have always captivated our curiosity with their aesthetics and complexities alike. While the act of blowing bubbles is familiar to everyone, the underlying physics of these fleeting spheres often eludes reasoning. In this Letter, we discuss the dynamics of inflating a soap bubble using controlled airflow through a film-coated nozzle. We assess and predict the rate of inflation by varying the source pressure. Visualizing the previously unexplored internal flow reveals that air enters the bubble as a round jet, emerging from the nozzle opening and impinges on the expanding concave bubble interface to form a toroidal vortex. Several scaling laws of the associated vortical flow spanning the entire bubble and the vortex core are reported. The observed dynamics of this bubble-confined vortex ring formation indicate universality in certain aspects when compared to the free laminar vortex rings.

In this paper, we investigate the exit dynamics of a sphere launched underneath a liquid bath surface at a prescribed impact velocity. Spheres with radii approximate or smaller than the capillary length are considered. Following our previous work of a ligament drawn of a liquid bath [J. Fluid Mech. 922, A14 (2021)], a two-dimensional model is applied to describe the liquid dynamics, and the whole exit dynamics up to the descent or the pinch-off moments is considered. The process can be sequenced into a partial exit stage that forms a coated layer and a full exit stage with an attached ligament. A bouncing-off regime, a lower pinch-off penetration regime, and an upper pinch-off penetration regime are identified, separating by a penetration Weber number and a switching Weber number. The phase diagram is revealed, where the two critical Weber numbers are functions of the Bond number. By considering the energy evolutions, we show that the impact energy is mainly converted into the surface energy and the gravitational potential energy for the low- and large-gravity cases, respectively. The coated layer is mainly formed in the partial exit stage, whose maximum volume increases with the impact velocity but decreases with gravity effect. Stretching motion is shown to have negligible influence on the local pinch-off behavior, while it determines the appearance and the location of pinch-off. Our results can help to understand the exit behaviors of aquatic animals, and the design of microamphibious aircraft or energy collection devices.

We present a numerical study of a thin elastic sheet with small extensibility freely sedimenting in a viscous fluid. Two scenarios are investigated: sedimentation in free space and near an infinite wall, where the wall may be vertical or tilted. Elastic sheets with a rest shape of a square are modeled with a finite-element-based continuum model that accounts for in-plane stretching and out-of-plane bending. The fluid motion is computed by the method of regularized Stokeslets in free space and regularized Blakelets near a wall. During sedimentation, the interplay between gravity and the elastic response of sheets gives rise to complex deformation and reorientation dynamics, measured by a dimensionless elastogravitational number $\left({\mathrm{E}}_{\mathrm{G}}\right)$. In free space, sheets attain a stable orientation by aligning perpendicular to gravity. Sheets with larger deformability adopt more compact conformations and experience smaller hydrodynamic drag, thereby sedimenting faster. A sheet with a random initial orientation reorients to align perpendicular to gravity, accompanied by lateral drift due to the symmetry-breaking in conformations. We identified two reorientation mechanisms depending on flexibility. When a sheet is placed near an infinite wall, sedimentation is hindered compared to that in free space due to wall-induced hydrodynamic drag. Near a vertical wall, sheets exhibit asymmetric conformations that cause the sheet to drift, with the drifting dynamics determined by ${\mathrm{E}}_{\mathrm{G}}$. The difference in flexibility leads to a nonmonotonic trend in the evolution of wall-normal distance. Near a tilted wall, sheets show qualitatively different dynamics when the wall angle is large: they either deposit on or slide along the wall with a fixed wall-normal distance.

In this experimental study on a methane-hydrogen fired laboratory-scale pressurized annular combustor, various steady and transient operating conditions were explored. Under steady operation, the thermoacoustic stability depended strongly on the equivalence ratio, but only weakly on the mass flow rate and hydrogen power fraction. During transient equivalence-ratio ramps, the predominant instability of the system switched between standing and spinning azimuthal modes. The ramping rate influenced the thermoacoustic amplitude during the switching, as well as the onset and decay of the different modes. The strong acoustic reflection at the choked outlet produced significant harmonic content during both steady and transient operation. Nonlinear time-series analysis and clustering algorithms showed that the Jensen-Shannon complexity and the permutation entropy could accurately classify the modal dynamics in an unsupervised manner. The classification revealed that standing azimuthal modes, with several preferred orientations, dominated under steady operation. The amplitude of the heat-release-rate (HRR) oscillations around the annulus depended on the mode orientation. The energy contribution from the harmonic components was isolated via bandpass filtering, revealing that the orientation of the first harmonic ($n=2)$ followed the fundamental mode, eliminating negligible HRR oscillation regions at the pressure node of the fundamental mode. By filtering out the higher-order harmonic content, intermittent switching between high-amplitude periodicity and low-amplitude chaos in the fundamental azimuthal mode was uncovered. Tools from dynamical systems theory confirmed the existence of chaos and demonstrated that the intermittency belongs to the type-II Pomeau-Manneville class. This study provides evidence of the type-II intermittency route to chaos in an annular combustor with longitudinal and azimuthal modes.

While predicting the flow behavior for a well-defined particulate microstructure is fairly tractable, systematic tailoring of the particle properties to yield desired flows remains illusive. For example, we still do not know how to precisely control rheological response by tuning particle types and properties or how to tailor porous media for filtration applications. Here we show that the recent advances in automatic differentiation provide a platform for methodologically addressing such questions. We optimize the packing of a polydisperse system of periodically arranged circular rods to maximize flow rate in the direction of applied pressure gradient. We show that the optimum topology of the structured porous medium depends on the solid volume fraction and approaches a staggered square with the particles' diameter ratio of $\sqrt{2}-1$ as the solid volume fraction reaches $\pi /4[1+{(\sqrt{2}-1)}^2]$. Regardless of the porous medium topology, the divergence exponent of the pressure gradient is universal and is equal to $5/2$, as one finds from lubrication theory for a simple square lattice. These results are independent of the flow's Reynolds number and can provide a foundation to study inverse problems for suspension systems.

Here we discuss how the use of textured liquid-infused solids can expedite the dynamics of spreading of viscous drops, when the subjacent oil layer is less viscous. We characterize the nature and amplitude of the effect, and the laws governing the spreading at short time. More generally, our findings affirm the universality of the early dynamics of viscous contact, found to hold for drops that coalesce, spread, or even, like here, slip on their substrate.

The exploration of a two-dimensional wind-driven ocean model with no-slip boundaries reveals the existence of a turbulent asymptotic regime where energy dissipation becomes independent of fluid viscosity. This asymptotic flow represents an out-of-equilibrium state, characterized by a vigorous two-dimensional vortex gas superimposed onto a western-intensified gyre. The properties of the vortex gas are elucidated through scaling analysis for detached Prandtl boundary layers, providing a rationalization for the observed anomalous dissipation. The asymptotic regime demonstrates that boundary instabilities alone can be strong enough to evacuate wind-injected energy from the large-scale oceanic circulation.

A self-aligning particle (SAP) attains a permanent orientation without application of external torques in a low Reynolds number simple shear flow in contrast with the continuous rotation exhibited by most rigid bodies including thin fibers and disks. SAPs align close to the fluid lamellae, and we characterize the robustness of this flow alignment to secondary disturbances such as perturbation to the shear flow, Brownian motion, interparticle interactions, or the presence of a wall using dynamic simulations of representative SAP geometries. The robustness of the flow alignment of SAPs at all concentrations generates highly aligned microstructures inaccessible to traditional particle suspensions.

The presence of a dispersed phase substantially modifies small-scale turbulence. However, there has not been a comprehensive mechanistically based understanding to predict turbulence modulation. Based on the energy flux balance, we propose a theoretical model to predict the turbulent kinetic energy modulation in isotropic turbulence due to the dispersed phase. The comparison between model predictions and results from prior particle-resolved simulations and existing high-fidelity experiments supports the performance of the model over a range of turbulence and particle parameters. The model is then used to explore turbulence modulation characteristics over a wider parameter space formed by five independent system-controlling parameters, showing rather complicated dependence on the particle size and particle-to-fluid density ratio.