Extreme waves have posed a significant threat to human safety and the integrity of marine structures at sea or near coastal regions. As a possible explanation for the formation of extreme waves, modulation instability has been studied extensively in recent years. Peregrine solutions of the nonlinear Schrödinger equation (NLSE) describe the nonlinear evolution of slowly varying wave envelopes. Limited studies have been found in the literature for Peregrine solutions at higher orders as mechanisms of the formation of large-amplitude waves. Additionally, the characteristics of higher harmonics generated during the evolution of Peregrine solutions remain unexplored. This study employs a high-precision numerical model based on a high-order spectral method to simulate the nonlinear evolution of the first-, the second-, and the third-order Peregrine solutions. Experiments were carried out in a wave flume to implement the high order solutions, which demonstrates the physical understanding of the solutions in the application in water waves and validates the model. A phase manipulation method is utilized to decompose the higher harmonics of the wave elevations. The results examine the evolution of wave profile, skewness, and kurtosis for the first three orders of Peregrine solutions. Higher harmonics of the wave elevations during modulation and demodulation are extracted and analyzed for the first time. The one-dimensional and two-dimensional Fourier transforms are used to analyze the amplitude spectrum and the joint wavenumber-frequency spectrum, respectively, during the evolution of the wave trains. Through spectral analysis, the nonlinear energy transfer characteristics of Peregrine solutions are identified.

Despite extensive studies on compressible turbulent channel flows (CTCFs) over the past few decades, two types of streamwise driving forces—the uniform body force and the density-weighted body force—have been inconsistently employed by different researchers. However, the impact of such discrepancy on numerical results remains poorly understood. In this paper, we conduct direct numerical simulations of CTCFs with symmetric isothermal cold walls and cases featuring one isothermal cold wall alongside one isothermal quasi-adiabatic wall, aiming to systematically and quantitatively compare the differences on turbulence statistics when applying these two types of driving forces. Our analysis focuses on mean momentum, energy, and vorticity transport, as well as ejection and sweeping events, to elucidate the observed variations. While the differences are minimal in symmetric channel flows, as noted by Huang et al. [J. Fluid Mech. 305, 185 (1995)], they become more significant and cannot be easily neglected when the flow exhibits strong compressibility or substantial wall temperature differences. These findings underscore the importance of carefully considering the choice of driving force in direct numerical simulations and analysis of thermodynamically asymmetric turbulent channel flows with sufficiently high Mach numbers or significant wall temperature differences.

Collective phenomena in fluid environments exhibit fascinating dynamics, observed in fish schools, bird flocks, and bacteria colonies. What are the benefits for individuals or groups in collective swimming? In this paper, we introduce inverse reinforcement learning (IRL) as a new approach to address this question. In IRL, rewards of individuals or a group are inferred through observations of their states and actions. This is in contrast with forward optimization or reinforcement learning approaches, where an objective is specified and states and actions are inferred. The algorithm is demonstrated for a group of four artificial swimmers in a two-dimensional viscous flow described by the Navier-Stokes equations. We examine the capabilities of IRL in the discovery of group and individual objectives in the collective behavior of the swimmers. We demonstrate the ability to distill a reward function from efficient swimming patterns. The reward functions are interpreted using sensitivity analysis and symbolic regression techniques. In this paper, we use synthetic data for observations and trajectories, generated by a policy that is learned first by performing forward reinforcement learning with the goal of maximizing swimming efficiency. The IRL methodologies are readily applicable to real-world and experimental data of natural swimmers. The study introduces a new direction for bioinspired fluid mechanics by, not a priori specification of objective functions, but discovering them from observations of natural and artificial swimmers.

Below critical temperature, turbulence prevents the spontaneous phase separation of binary mixtures, resulting in a phase-arrested state of emulsion which is of significant interest for scientific and industrial applications. The current work is an extensive continuation of our initial theoretical investigation into the nature and universality of associated energy cascade [N. Pan and S. Banerjee, Phys. Rev. E 106, 025104 (2022)]. In addition to the previously derived divergence and correlator forms of the exact relations, a Banerjee-Galtier-type [S. Banerjee and S. Galtier, J. Phys. A: Math. Theor. 50, 015501 (2017)] divergence-free form of the exact relation is derived under the explicit assumption of homogeneity. By performing three-dimensional direct numerical simulations with up to ${1024}^3$ grid points, we show that the sum of the kinetic and active energy associates a Kolmogorov-like universal cascade with constant flux rate across inertial scales. Despite term-by-term deviations, the cascade rates computed from all three exact laws show excellent agreement, thereby confirming the equivalence of different exact relations and hence the feasibility of determining the net cascade rate from any of the three formulations. Notably, the two dominant flux rates of the divergence form are found to cross each other roughly at the domain size, which also serves as an infrared cutoff for the inverse cascade of the small-scale active energy. This behavior is phenomenologically justified based on the interplay between the flow and surface dynamics of a phase-arrested binary fluid. Finally, the cascade rate is also calculated from the scale-by-scale energy budget in Fourier space where the inertial range cascade rate becomes constant across scales and matches with that calculated from direct space variables.

In this study, we investigate the flow around a canonical blunt body, specifically a D-shaped body of width $D$, in a closed water channel. Our goal is to explore near-wake flow modifications when a series of rigid and flexible plates ($l=1.8D$) divided into filaments ($h=0.2D$) are added. We focus on assessing the interaction between the flexible filaments and the wake dynamics, with the aim of reducing the recirculation bubble and decreasing the velocity deficit in the wake. To achieve this, we conduct a comparative study varying the stiffness and position of the filaments at different flow velocities. The study combines Particle Image Velocimetry measurements in the wake behind the body with recordings of the deformation of the flexible filaments. Our observations show that the flexible filaments can passively reconfigure in a two-dimensional fashion, with a mean tip deflection angle that increases with the incoming flow velocity. Deflection angles up to approximately $\sim 9^{\circ }$ and vibration tip amplitude of around $\sim 4^{\circ }$ are achieved for flow velocities $U^{*}\simeq u_{\infty }/f_{n}D\ge 1.77$, where $f_n$ is the natural frequency of the flexible filaments. This reconfiguration results in a reduction of the recirculation bubble and a decrease in the velocity deficit in the wake and the estimated drag compared to the reference and rigid cases. In addition, curved filaments with a prescribed rigid deformation exhibit very similar behavior to that of flexible filaments, indicating that the vibration of flexible filaments does not significantly disturb the wake. The obtained results highlight the interest of testing flexible appendages in the wake of blunt bodies for designing effective flow control devices.

Motile microorganisms develop effective swimming gaits to adapt to complex biological environments. Translating this adaptability to smart microrobots presents significant challenges in motion planning and stroke design. In this work, we explore the use of reinforcement learning (RL) to develop stroke patterns for targeted navigation in a three-link swimmer model at low Reynolds numbers. Specifically, we design two RL-based strategies: one focusing on maximizing velocity (velocity-focused strategy) and another balancing velocity with energy consumption (energy-aware strategy). Our results demonstrate how the use of different reward functions influences the resulting stroke patterns developed via RL, which are compared with those obtained from traditional optimization methods. Furthermore, we showcase the capability of the RL-powered swimmer in adapting its stroke patterns to perform different navigation tasks, including tracing complex trajectories and pursuing moving targets. Taken together, this work highlights the potential of reinforcement learning as a versatile tool for designing efficient and adaptive microswimmers capable of sophisticated maneuvers in complex environments.

The problem of tracking the source of a passive scalar in a turbulent flow is relevant to flying insect behavior and several other applications. Extensive previous work has shown that certain Bayesian strategies, such as “infotaxis,” can be very effective for this difficult “olfactory search” problem. More recently, a quasioptimal Bayesian strategy was computed under the assumption that encounters with the scalar are independent. However, the Bayesian approach has not been adequately studied in realistic flows which exhibit spatiotemporal correlations. In this work, we perform direct numerical simulations (DNSs) of an incompressible flow at ${\mathrm{Re}}_{\lambda }\simeq 150,$ while tracking Lagrangian particles that are emitted by a point source and imposing a uniform mean flow with several magnitudes (including zero). We extract the spatially dependent statistics of encounters with the particles, which we use to build Bayesian policies, including generalized (“space-aware”) infotactic heuristics and quasioptimal policies. We then assess the relative performance of these policies when they are used to search using scalar cue data from the DNSs, and in particular we study how this performance depends on correlations between encounters. Among other results, we find that quasioptimal strategies continue to outperform heuristics in the presence of strong mean flow but fail to do so in the absence of a mean flow. We also explore how to choose optimal search parameters, including the frequency and threshold concentration of observation.

Although it is commonly expected that a metal disk placed on the surface of water will sink, our investigation has revealed a surprising phenomenon: a vertical jet directed onto the disk from above can allow it to remain afloat. This result defies intuition, as one would assume that the force of the jet's impact would cause the disk to sink. We have discovered that this phenomenon occurs as a result of water displacement from the top of the disk caused by the impacting jet, operating through a mechanism similar to the hydraulic jump. This displacement increases the effective immersed volume, resulting in an increased buoyant force that balances gravity. In contrast to the classical case, here the jump radius is fixed by the geometric parameters of a disk, a phenomenon we refer to as the boundary jump. To further explore this effect, we have presented a theoretical model based on scaling laws, which provides the conditions required for the disk to float. The prefactor was determined through an independent experiment. Finally, we conducted experiments on the disk's floating and sinking, which showed a good match with the proposed theory.

Small-scale statistics of the passive scalar field convected by turbulent flow of an incompressible fluid under a uniform mean scalar gradient are studied theoretically and numerically. The flow is assumed to be statistically homogeneous and isotropic. Attention is given to the effects of the mean scalar gradient on the anisotropy of the statistics, in particular, the anisotropy of the second- and third-order mixed velocity-scalar structure functions, $\langle \delta u_j\delta \psi \rangle$ and $\langle \delta u_j{\left(\delta \psi \right)}^2\rangle$, where $u_j(\mathit{x},t)(j=1,2,3)$ is the $j\mathrm{th}$ component of the velocity field, $\psi (\mathit{x},t)$ is the fluctuating part of the scalar field, $\delta \xi =\xi (\mathit{x}+\mathit{r},t)-\xi (\mathit{x},t), \xi =\psi ,u_j, \langle ·\rangle$ is the ensemble average, $\mathit{x}$ is the position, and $t$ is time. A theory of the effects is proposed by extending the idea of the linear response theory of turbulence. Its predictions are examined by direct numerical simulation (DNS) in a periodic box. In the DNS, the Schmidt number is unity, and the Taylor microscale Reynolds number is about 260 at a fully developed state of the turbulent velocity field. It is found that the predictions of the anisotropy are generally consistent with the DNS results.

We develop a numerical scheme to compute the dynamic electrophoretic velocity of a uniformly charged, dielectric, spherical colloidal particle under an unsteady electric field, for, in principle, arbitrary imposed electric field strength, $\beta =a^{*}{e}^{*}{E}_{\infty }^{*}/\left(k_B^{*}{T}^{*}\right)$. Here, $a^{*}$ is the characteristic size of the particle, $E_{\infty }^{*}$ is the applied field strength, and the factor $k_B^{*}{T}^{*}/e^{*}$ corresponds to the thermal voltage. We focus our computations on Debye lengths comparable to the particle size; i.e., $1/\left({\kappa }^{*}{a}^{*}\right)=\mathcal{O}\left(1\right)$, where $1/{\kappa }^{*}$ is the Debye length, and moderately-charged particles, i.e., ${\sigma }^{*}=\mathcal{O}({\epsilon }^{*}{k}_B^{*}{T}^{*}/\left(e^{*}{a}^{*}\right))$, where ${\sigma }^{*}$ is the surface charge density on the colloid and ${\epsilon }^{*}$ is the permittivity of the medium. For a suddenly applied field, the initial growth of the electrophoretic mobility (i.e., ratio of particle speed to field strength) occurs on the momentum diffusion time and is independent of $\beta$ in the practically relevant case of large Schmidt number, $\mathrm{Sc}={\nu }^{*}/D^{*}\gg 1$, where ${\nu }^{*}$ is the kinematic viscosity and $D^{*}$ is the mean ion diffusion coefficient. Subsequently, the Debye cloud deforms on the ion diffusion timescale, leading to the mobility approaching its steady-state in a $\beta$-dependent manner. For the stopping problem, where the field is suddenly switched off, most of the change in the particle speed occurs on the momentum diffusion timescale, and the particle fully stops after the Debye cloud regains its equilibrium spherical shape. Under an oscillatory field, the field frequency has a large influence on both the amplitude and phase lag of the mobility, as it determines if the Debye cloud has sufficient time to deform within an oscillation cycle. The time-average flow about the particle resembles a stresslet.

The effects of compressibility on the quiescent momentum core (QMC) and its thermal counterpart, the quiescent thermal core (QTC), are studied using direct numerical simulation datasets of compressible channel flows with the semilocal friction Reynolds number at the channel centerline ${\text{Re}}_{\tau c}^{*}\approx 340\text{–}1270$ and the bulk Mach number $M_b=1.5$ and 3.0. The applicability of the traditional criterion for identifying the QMC interface in incompressible flows (i.e., velocity contours of 95% of the mean channel centerline velocity, $0.95U_c$) is thoroughly examined, followed by a detailed analysis of the Reynolds and Mach number dependence of QMC characteristics. The results show that the QMC in compressible flows retains fundamental similarities to that in incompressible flows at comparable ${\text{Re}}_{\tau c}^{*}$, with low streamwise turbulence intensity and nearly constant mean flow properties within the core. However, the intermittency factor increases slightly at $M_b=3.0$, suggesting a reduced probability of the presence of QMC in the inner region of the channel at higher Mach numbers. Conditional averaging reveals a sharp change in streamwise velocity and a local maximum in spanwise vorticity at the QMC interface, with the prograde shear layer identified as the primary structure responsible for the vorticity concentration. Using the same methodology applied for the QMC, the threshold for identifying the QTC interface is determined as temperature contours of 99% of the mean channel centerline temperature ($0.99T_c$). The QTC is characterized by a thermal interfacial layer with a strong temperature gradient and a jump in temperature across its interface. Geometric analysis reveals that the QTC interface is located closer to the wall, resulting in a significant increase in its thickness compared to that of the QMC. Both the QMC and QTC interfaces exhibit fractal dimensions of $D\approx 1.3$, consistent with that of turbulent/nonturbulent interfaces. These findings highlight the structural similarities between the QMC and the QTC, providing insight into momentum and energy transport in compressible turbulent flows.

We present an experimental study of immiscible, two-phase fluid flow through a three-dimensional porous medium consisting of randomly packed, monodisperse glass spheres. Our experiments combine refractive-index matching and laser-induced fluorescence imaging to resolve the morphology and stability of the moving interface resulting from the injection of one fluid into another. The imposed injection rate sets a balance between gravitational and viscous forces, producing interface morphologies which range from unstable collections of tangled fingers at low rates to stable sheets at high rates. The image data are complemented by time-resolved pressure measurements. We develop a stability criterion for the fluid interface based on the analysis of the 3D images and the pressure data. This criterion involves the Darcy permeability in each of the two phases and the time derivative of the pressure drop across the medium. We observe that the relative permeability encountered by the invading fluid is modified by the imposed flow rate in our experiment, which impacts the two-phase flow dynamics. We show that, in addition to the balance between the relevant forces driving the dynamics, local regions of crystalline order in the beadpack (crystallites) affect the stability of the invading front. This work provides insights into how disorder on multiple length scales in porous media can interact with viscous, capillary, and gravitational forces to determine the stability and dynamics of immiscible fluid interfaces.

Wake meandering, the large-scale periodic oscillating motion of the far wake of a wind turbine, affects wake recovery, turbulence intensity, and the overall variability in power production. Two distinct mechanisms have hypothesized its formation. The first is that the wake is convected by large, upwind scales much greater than the wake width. The other is that the turbine rotor induces a motion similar to a bluff body that scales with the rotor diameter. In this work, we focus on elucidating and separating the effects of upwind scales, their interaction with the turbine, and turbine-related scales that impact wake meandering. Precursor simulations are developed to systematically vary only the upper bound of the length scale distribution. We carry out a series of large-eddy simulations under a range of inflow scenarios to investigate influences on wake meandering dynamics. Turbulence wake statistics reveal that the location of peak turbulence kinetic energy in the far wake and the onset of wake meandering moves downwind with lower upwind turbulence levels and short distribution of length scales; however, turbine-added kinetic energy scales well with the thrust velocity across all cases. Spectral analysis indicates that upwind length scales influence the broadening of low-frequency energy modes relevant to wake meandering in the far wake. Profiles tracking the wake center are constructed, and their distribution is shown to scale by the amplitude of the profile, collapsing all cases into a near normal distribution in far-wake locations. Using the wake center profiles, wake meandering is decomposed by a low-pass filter, which indicates two separate scales of wake meandering with different wake center distributions: (1) turbine-influenced scale with regular Strouhal number, $\text{St}\approx 0.3$, and corresponding harmonics, with the same scale wake center distribution across all upwind conditions and (2) upwind-produced scale if low upwind scale are present, $\text{St}<0.1$, with irregular wake center distributions. Spectral proper orthogonal decomposition confirms the relationship with separate dominant coherent structure modes at corresponding frequencies dependent on upwind conditions.

As a fluid object breaks, it often leaves behind satellite fragments. Here we show that satellite formation can follow universal dynamics, leading to robust satellite sizes. Specifically, we consider the breakup of a slowly stretched fluid bridge, which we realize experimentally using a soap-film bubble suspended between two plates. Combining experiments and one-dimensional simulations, we show that a main satellite bubble always forms as the bridge breaks. We discover that the size of the bubble is highly reproducible and can be dramatically increased by stretching the bridge faster or increasing its volume. The satellite size is a simple function of two nondimensional parameters: the normalized volume of the bridge and the Weber number, measuring inertia due to stretching as compared to surface tension. These observations can be explained by tracing the bridge evolution over a series of dynamical stages in which the bridge (i) closely follows a sequence of equilibrium bridge configurations, (ii) stretches as it begins to breakup after reaching an unstable equilibrium, and (iii) follows a universal breakup solution. The universal breakup solution is valid over a finite region near the center of the bridge, whose length is determined by the stretching during stage (ii). This length scale controls the satellite size, and the universality of the dynamics makes the system highly reproducible.

Thermoelectricity in electrolyte-filled slit channels is studied using analytical methods for solving the combined Stokes, Nernst-Planck, Poisson, and heat transport equations. Next to a temperature gradient, the scenario considered accounts for a pressure gradient and an electric field applied along the channel. Closed-form analytical expressions are derived for the thermoelectric current and the thermovoltage expressed by the Seebeck coefficient, which are compared to numerical results obtained using the finite-element method. A special focus is put on convective charge transport resulting from thermoosmotic flow, which is massively augmented when considering nanochannels with a Navier-slip condition at the channel walls. The corresponding convective transport has a negligible effect on thermoelectricity in the regime of strong electric double layer overlap. By contrast, when the Debye length is much smaller than the channel width, convection can yield a massive increase of the thermoelectric current and power. This occurs in the case of a nonvanishing slip length, where thermoelectricity in the absence of convection is taken as a reference. Generally, it can be concluded that boundaries with a nonvanishing slip length can induce a significant thermoelectric response via convective transport even in cases where the Debye length is much smaller than any length scale of the compartments or channels in which the liquid is contained.

The development of turbulent mixing layers can be altered by the application of anisotropic strain rates, potentially arising from radial motion in convergent geometry or movement through nonuniform geometry. Previous closure models and calibrations of compressible turbulence models tend to focus on incompressible flows or isotropic strain cases, which is in contrast to many real flow conditions. The treatment of bulk compression under anisotropic strain is investigated using the K-L turbulence model, a two-equation Reynolds-averaged Navier-Stokes (RANS) model that is commonly used for simulating interfacial instabilities. One-dimensional simulations of shock-induced turbulent mixing layers under applied axial or transverse strain rates are performed using three different closures for the bulk compression of the turbulent length scale. The default closure method using the mean isotropic strain rate is able to reasonably predict the integral width and turbulent kinetic energy of the mixing layer under the applied strain rates. However, the K-L model's performance is improved with the transverse strain closure, while the axial strain closure worsens the model. The effects of this new closure are investigated for the buoyancy-drag model, showing that a three-equation model which evolves the integral width and turbulent length scale separately is most effective for modeling anisotropic strain.

Singular or weak solutions of the incompressible Euler equations have been hypothesized to acccount for anomalous dissipation at very high Reynolds numbers and, in particular, to explain the d'Alembert paradox of nonvanishing drag. A possible objection to this explanation is the mathematical property called “weak-strong uniqueness,” which requires that any admissable weak solution of the Euler equations must coincide with the smooth Euler solution for the same initial data. As an application of the Josephson-Anderson relation, we sketch a proof of conditional weak-strong uniqueness for the potential Euler solution of d'Alembert within the class of strong inviscid limits. We suggest that the mild conditions required for weak-strong uniqueness are, in fact, physically violated by violent eruption of very thin boundary layers. We discuss observational signatures of these extreme events and explain how the small length scales involved could threaten the validity of a hydrodynamic description.

This study investigates the coalescence of polymer solution drops on the solid substrates. When two drops meet at their contact line on a substrate, the liquid bridge connecting the two drops increases in size with time. The height and radius of the liquid bridge have a power-law dependence on time. In the early stage of drop coalescence, the exponents $\alpha$ and $\beta$ of the power law are influenced by the properties of the polymer solution. We argue that the balance between capillarity and viscoelasticity controls the process, where viscoelasticity must be considered in its full time and shear-rate dependency. As a simple proxy for the processes involved, the ratio of the polymer relaxation time to the viscous time of the drop, the elastocapillary ($\text{Ec}$), is instructive. In the vicinity of $\text{Ec}=1$ the exponents showed a minimum and increased to lower and higher values of $\text{Ec}$. A similar dependency is observed for the damping timescales of the capillary waves. For high elastocapillary numbers, i.e., high polymer relaxation time, drop coalescence on short timescales behaved as in the low-viscosity case. In addition, the bridge profile is influenced by a combination of factors including surface tension, viscosity, and polymer stress. In summary, we show that drop coalescence is strongly influenced by the viscoelasticity of the drops.

For a modulated wave train, the modulational instability disappears when $k_{1}h<1.363$ ($k_1$ is the wave number of the carrier wave and $h$ is the water depth) for collinear sidebands but still exists for oblique sidebands. With the prediction directly from the framework based on the Zakharov equation (ZE) rather than the nonlinear Schrödinger equation (NLSE), instability regions were obtained in different water depths. In this study, extensive numerical simulations were performed using a high-order spectral (HOS) method to investigate the modulational instability of a wave train with oblique sidebands in finite water depths. Considering the effects of multiple factors including water depth, wave steepness, and bandwidth, the results of growth rates were first investigated directly by HOS compared with ZE and NLSE. The results by HOS are in good agreement with those by ZE. Numerical simulations confirm that sidebands grow exponentially, suggesting that there is obvious modulational instability in shallow water at $k_{1}h=0.8$. The results also suggest that HOS and ZE have better applicability in large sidebands and shallow water. In addition, the results of the crest enhancement over time during the wave evolution were also investigated. The normalized maximum crest height can reach around 4 in deep water with a pair of collinear sidebands and exceed 2 in shallow water with oblique sidebands. The evident amplification also reveals the presence of modulational instability in shallow water. It is also found that spectral broadening and phase convergence are both important for crest enhancement. Each of the factors progressively becomes stronger during the modulation, causing the modulation peak to occur between their respective maximum. Moreover, the results of the phase changes were examined in detail. A phase-locking phenomenon for the carrier wave and two sidebands is also observed in finite water depths.

We solve the Stokes equations for the flow around two parallel translating and rotating cylinders using tools from complex analysis and conformal mapping. By considering cylinders of arbitrary size and separation, we generalize the solutions known for cylinders of equal size, and a cylinder near a plane wall. We then examine the limit when the cylinders are brought into contact, finding that it affects the separation points in the flow. Namely, they move to and are hidden in the point of contact between the cylinders.