The continued development of shallow continental shelf regions with offshore wind farm (OWF) structures raises the question of what potential hydrodynamic impacts may be expected. One such impact is a reduction in the ocean currents that results from the additional frictional drag from the turbine foundation structures. To understand this potential "blocking" effect, we construct a fluid mechanical model consisting of an idealized circular patch of OWF with increased friction. The idealized OWF is then subjected to a steady mean flow superimposed on much stronger elliptical tidal currents—a common scenario in shelf seas with OWF installations. Due to the quadratic dependence of friction on fluid velocity, the elliptical tidal currents result in a linearized friction acting on the mean flow that is no longer parallel to the mean flow. This "anisotropic" friction has the effect of deflecting, in addition to reducing, the mean flow in the region of the OWF. However, it is found that a good approximation to the reduction of flow caused by OWFs can be obtained by the simplest linear, isotropic representation of the friction, i.e., a linear drag law. The flow reduction within the OWFs is found to be primarily dependent on the ratio of the increase in drag coefficient inside the farm to that of the surroundings, with weaker dependencies on the parameters describing the tidal ellipse. The magnitudes of the flow reductions in the idealized model appear to be in approximate agreement with more realistic modeling results, and are expected to capture the basic balance of the mean flow in the blocking of ocean currents by many OWFs in the North Sea, especially with increasing size in future development scenarios.

We investigate the stability and accuracy of a machine-learning-based turbulence closure model. To this end, we construct a turbulence closure model for a shell model, which is a toy model of turbulence, based on the inference of sub-grid scale (SGS) variables using a recurrent neural network, and conduct an extensive parameter survey of the constructed model. The model stably and accurately reproduces the statistics of grid-scale variables when the cutoff wave number ${\kappa }_c$ is higher than $0.2{\eta }^{-1}$, where $\eta$ denotes the Kolmogorov length. This is because in this case, SGS variables are subordinate to grid-scale ones. On the other hand, when ${\kappa }_c$ is lower than $0.2{\eta }^{-1}$, the model becomes stochastically unstable. However, an appropriate regularization in the inference step of SGS variables realizes a sufficiently long lifetime of the model.

In fluid dynamics, a classic calculation pertaining to suspensions of uniform spheres predicted that the variance of the velocity should diverge with system size. Experiments, on the other hand, find that while the variance grows with system size in small systems, it asymptotes to a fixed value for sufficiently large systems. Here, I show that this discrepancy between theory and experiment is resolved by accounting for the inertia of the particles. Using the unsteady Stokes‘ Green’s functions, the leading order contribution to the variance is determined to be finite for systems of infinite extent.

Liquid sheets are omnipresent in nature and applications. The cross sections of liquid sheets are elongated two-dimensional (2D) drops the two ends of which contract towards each other because of surface tension $\left(\sigma \right)$. If sufficiently thin, sheets can rupture due to van der Waals forces. Burton and Taborek, however, have shown that regardless of sheet thickness $2{\tilde{h}}_0$, a contracting inviscid liquid sheet can break even in their absence. Here we use 2D simulations and theory to show that for small yet finite viscosity $\mu$, contracting liquid sheets will escape from pinch-off when van der Waals forces are absent due surprisingly to two distinct mechanisms that depend on Ohnseorge number $\mathrm{Oh}=\mu /\sqrt{\rho \sigma {\tilde{h}}_0}$ ($\rho$: density). For $\mathrm{Oh}\to 0$, escape is shown to be due to viscous resistance, while for larger but yet still small Oh, it can be attributed to vorticity generation at the free surface. The distinct mechanisms yield different scaling laws relating minimum sheet thickness when escape occurs to Oh.

Electrokinetic transport occurs at the two-liquid interfaces due to its inevitably spontaneous charging induced by imbalanced partition and/or specific adsorption. The diffuse feature of the liquid-liquid interface is essential in interpretation of its electrokinetic behavior and the interplay of the two charging mechanisms is strongly dependent on the interfacial physicochemical properties, which are often ignored in previous studies and may lead to the impractical electrokinetic predictions. We propose a diffuse interface framework which includes a modified Boltzmann formulation, to incorporate the solvent mixing effect and unify the description of both possible charging mechanisms. The permittivity- and viscosity-related solvent mixing effects are stressed when imbalanced ion partition dominates and the viscosity ratio is large. The effects of permittivity-dependent ion partition and organic impurity ions are exhaustively discussed for nonpolar and polar organic liquids. For polar organic liquid with moderate permittivity, the water velocity presents a nonmonotonic dependency on the impurity concentration under different pHs, resulting from the competitive effect of the two charging mechanisms. A semiempirical correction formula for the sharp interface model is proposed to eliminate the modeling deviations, while the viscosity interpolation model is demonstrated to have a great impact on the interpretation of the electroosmotic velocity profile. Our work sheds light on the further studies of the complex electrokinetic multiphase flows with complex geometry, large deformation, contact line dynamics, and weak nonequilibrium transport.

This study introduces an approach, point-cloud aerodynamics transfer learning (PCDA-TL), to address the challenges faced by parameter-perspective surrogate models in shape-aerodynamics modeling. The traditional models struggle with diverse aircraft configurations, heterogeneous dimensions, and extreme high dimensionality. In contrast, the geometric-perspective PCDA-TL leverages complete aircraft surface data (point cloud) for inferring discrete aerodynamic characteristics, thereby unifying modalities across different configurations and parametric designs. This method, combined with transfer learning, enables the reuse of historical computational fluid dynamics (CFD) data in the unified point-cloud space, enriching the training dataset and reducing the need for new samples. Experimental results demonstrate that PCDA-TL exhibits exceptional accuracy and flexibility, outperforming traditional surrogate models in handling diverse aircraft configurations, heterogeneous dimensions, and extreme high dimensionality. Notably, the model achieves effective predictions with minimal samples and is capable of near-real-time prediction of aerodynamic characteristic distribution without the need for volume grids. This approach approximates the precision of expensive CFD simulations, thereby reducing labor requirements and facilitating the process of aerodynamic design.

In the present study, we conduct direct numerical simulations of two-way force-coupled particle-laden compressible turbulent boundary layers at the free-stream Mach number of 2.0 for the purpose of examining the effects of particles on the transport of momentum and kinetic energy. By analyzing turbulent databases with various particle Stokes numbers and mass loadings, we observe that the presence of particles suppresses turbulent fluctuations and can even laminarize flow under high-mass-loading conditions. This is reflected by the wider and more coherent near-wall velocity streaks, reduced Reynolds stresses, and diminished contributions to skin friction and turbulent kinetic energy production. Additionally, the particle feedback force becomes more dominant in turbulent production near the wall and at small scales as mass loadings increase, which is found to be caused by the residual velocity fluctuations from particles swept down from the outer region. Furthermore, we identify that particle dissipation, resulting from the relative velocity between the fluid and particles, accounts for less than 1% of mean kinetic energy viscous dissipation and less than 10% of turbulent kinetic energy dissipation in the case with the highest mass loading. This suggests a modest impact on the internal energy variation of the fluid if two-way heat coupling is introduced. The elevated mean temperature is found in the near-wall region and is ascribed to the influence of the particle feedback force and reduced turbulent diffusion in high-mass-loading cases.

This work studies the nonlinear formation and secondary instability of jet meanders due to baroclinic instability. The continuously stratified current-undercurrent system in the Western Pacific Ocean is extracted as an idealized model problem. Two-dimensional linear eigenmode analysis identifies surface (upper) and subsurface (lower) amplified baroclinic modes for the two currents, respectively. A weakly nonlinear instability framework is developed to resolve the temporal evolution of the most unstable eigenmode, its smaller-scale harmonics and the mean flow distortion under the quasigeostrophic scaling. After initial rapid amplification, these modes reach amplitude saturation and phase locking due to nonlinear interaction. The saturation of the upper mode results in upper-current meanders, whereas it can split the undercurrent into multiple cores. In comparison, the saturation of the lower mode leads to undercurrent meanders, which drive deeper waters to flow in the undercurrent direction but negligibly affect the upper layer. The two saturation states succumb to modest secondary instability, which is identified through a Floquet-based secondary instability analysis for a fully three-dimensional shape function. The fundamental resonance is found to dominate the upper-mode case, where the perturbation takes the form of mesoscale cyclones and anticyclones. Conversely, significant detuned resonance is identified for the lower-mode case, which quickly induces aperiodic motions in terms of the meanders. Implications for realistic oceanic flows are also discussed.

Thermocapillary convection is particularly effective for the control of thin liquid film topography or for the actuation of microparticles at the liquid-air interface. Experiments with water are challenging, however, as its interface is prone to contamination by surface-active impurities that profoundly alter its hydrodynamic response. Despite numerous reports highlighting the hindrance of thermocapillary flows, quantitative information on interface contamination is definitely lacking. We therefore introduce a general framework in order to account for the presence of a low concentration of insoluble surfactants at the water-air interface. Focusing on the low-compressibility limit, we identify the inverse Marangoni number as the appropriate small parameter in the modeling. The transport equations can then be linearized without any further assumption regarding the other dimensionless groups. It is shown in particular that the surfactant concentration adapts to the thermocapillary forcing in order to cancel the interfacial viscous stress. Several experimentally relevant situations are discussed with emphasis on physical observables. Besides the excellent agreement between theory and experiment, our predictions provide a quantitative assessment of the impurity concentration.

Understanding the effect of wind forcing on steep unidirectional waves is important for the study of wind-wave interaction. In this paper, unidirectional random wave experiments are carried out in a large-scale wave tank in which waves interacted with turbulent wind generated by wind fans. The properties and evolution of deep-water gravity waves subject to following wind forcing are investigated through parametric laboratory experiments. The effect of wind forcing on the significant wave height varies with the initial wave steepness. Wind forcing increases the growth of waves of small initial steepness but attenuates large, steep waves as a result of the vertical angle of the wind to the free surface in our experiments. The energy input by wind forcing increases the high-frequency tail of the wave spectra, and this effect increases with fetch. The mean frequency increases under wind forcing. The effect of wind forcing on the probability of extreme events is investigated. Wind forcing enhances wave steepness, resulting in a deviation of the exceedance probability from first-order and second-order theoretical distributions and an increased value of kurtosis but not skewness.

In this work, the effects of the particle volume fraction gradient on fluid-particle interactions are studied. The phase interaction force is decomposed into three terms. For the first term, namely the symmetrized force density, we present theoretical reasoning and numerical evidence to assume that it is independent of the particle volume fraction gradient. The second term is the particle volume fraction gradient times a newly introduced diffusion stress. The third term is the divergence of the particle-fluid-particle (PFP) stress. If this assumption of independence of the particle volume fraction gradient for the first term can be verified, to the first order of the ratio of the mean distance between particles to the macroscopic lengthscale, all three terms can be studied and modeled in flows with uniform particle distributions. Models thus obtained are applicable to statistically inhomogeneous flows, with the second and third terms accounting for statistical inhomogeneity. To verify this assumption, numerical simulations of flows passing fixed arrays of particles are performed. Both uniform and nonuniform particle volume fractions are studied and compared for disperse multiphase flows with the particle Reynolds numbers ranging from 1 to 100, and particle volume fraction ranging from 1% to 26% in statistically steady states. It is found that the symmetrized force (first) term can be well approximated by the drag force obtained from studies of uniform flows. The diffusion stress is positive along the flow direction and negative in the directions perpendicular to the flow. In the case of moving particles, this stress could potentially cause particle aggregation in the flow direction and dispersion in the directions perpendicular to the flow. The diffusion stress is only important when there is a volume fraction gradient, while the PFP stress can be important in inhomogeneous flows with either nonuniform particle concentrations or nonuniform average relative velocities between the phases.

Vertical size segregation in bedload transport impacts the sediment rate and the river bed morphology. To better account for this process in sediment transport models, it is essential to understand the mechanisms acting at the grain scale. This paper focuses on the behavior of a single large particle called the intruder, segregating upwards in a granular bed made of smaller mono-dispersed beads, during bedload transport. Experiments were carried out in a narrow flume, where the distance between the sidewalls was of the order of the intruder diameter. The latter was initially buried a few diameters below the bed surface. While supplying the flume with constant rates of small beads and water, we used a high-speed camera and image analysis techniques to monitor both the trajectory of the intruder and the velocity of the granular bed. We performed approximately 300 experiments with six size ratios (large to small) ranging from 1.25 to 3.0 to get statistically representative intruder trajectories. This extensive and unusual data set allows for a more thorough validation of the observations made in the work of Rousseau et al. [Phys. Rev. Fluids 7, 064305 (2022)]. Specifically, our results highlight the transition in the intruder behavior occurring around a size ratio of 2. Below this value, the intruder spatial trajectory exhibits a greater variability and gets steeper as the size ratio increases. Above the value of 2 and whatever the size ratio, the spatial trajectory is almost linear with a constant slope, and the time taken by the intruder to reach the bed surface increases with the size ratio. In addition, our extensive data set reveals insights into the intruder kinematics. Notably, we observed that the intruder undergoes a size-ratio-dependent streamwise velocity lag with respect to the bulk flow. Based on these observations, we propose a simple kinematic model which predicts the segregation duration of an intruder in bedload transport, incorporating a parameter representing the linear trajectory and a drift coefficient characterizing the streamwise velocity lag. Both parameters introduce a size ratio dependency based on our statistical analysis.

We present an experimental study on the excitation of superharmonic internal wave by resonant interaction of internal wave modes in finite-depth nonuniform stratifications. In a nonuniform stratification, the primary wave field composed of a single horizontally propagating vertical mode or combination of two horizontally propagating vertical modes is forced from one end of the tank using the wave generator at a forcing frequency ${\omega }_0$. The spontaneous excitation of a superharmonic wave at frequency $2{\omega }_0$ by resonant interaction of the internal wave modes of the primary wave field forced at frequency ${\omega }_0$ is observed. We experimentally demonstrate that even an isolated single mode could resonantly interact with itself to excite a superharmonic wave at frequency $2{\omega }_0$ in a nonuniform stratification, which is inhibited in the case of a uniform stratification. The resonant peak frequencies at which the strength of superharmonic signal is maximum, and the corresponding vertical structure of the superharmonic internal wave mode, qualitatively agree well with the theoretical predictions obtained from the weakly nonlinear analysis. The paper concludes with a discussion on experiments performed to observe superharmonic triadic resonant interactions in an oceanlike nonuniform stratification profile, for which the excited superharmonic internal wave modes were found to be trapped within the pycnocline region.

When particles of a few tens of microns are spread on the surface of water, they aggregate under the action of capillary forces and form a thin floating membrane, a particle raft. In a tank with a raft made of graphite powder, we generate in the laboratory gravity surface waves, whose wavelength about 17 cm is very large compared to the thickness of the raft of order $10\mathrm{\mu }\mathrm{m}$. For a sufficiently strong wave amplitude, the raft breaks up progressively by developing cracks and producing fragments whose sizes decrease on a timescale long compared to the period of the wave. We characterize the breaking mechanisms. Then we investigate the area distribution of the fragments produced during the fragmentation process. The visual appearance of the fragments distributed in size and surrounded by open water bears a notable resemblance to the floes produced by the fracturing of sea ice by waves in the polar oceans. Fragmentation concepts and morphological tools built for sea ice floes can be applied to our macroscopic analog, on which the entire dynamic evolution is accessible. However, the mechanics of the two systems differ, as our particle raft breaks due to the viscous stresses, whereas the sea ice fractures due to its bending by the waves.

Wave interaction with a floating finite elastic plate is considered, based on the linearized velocity potential theory for fluid flow, and the thin elastic plate model for plate deflection. The shape of the plate can be arbitrary, and free edge conditions are imposed at its edge. The solution procedure is established by dividing the domain into two subdomains—one below free surface and the other below the plate. The velocity potential in each subdomain is expanded into a series of eigenfunctions in the vertical directions based on separation of variables. This avoids numerical difficulty in computation of the fifth derivatives in the plate covered subdomain. Then the three-dimensional problem is decomposed into an infinite number of coupled two-dimensional problems in the horizontal plane. Each two-dimensional problem is transformed into an integral equation along the plate edge. On the artificial vertical interface between two subdomains, an orthogonal inner product is introduced for the eigenfunctions, through which the edge conditions, together with continuous conditions of pressure and velocity, are satisfied. The boundary integral equations and the derivatives along the plate edge are solved numerically through the boundary element method and the finite difference scheme. Extensive results are provided and analyzed for plates with various thicknesses and shapes, including the plate displacement, average curvature, disturbed far-field amplitude, scattering cross section, and the wave exciting force.

This study explores the flow physics and mixing characteristics produced by the interaction of two transversally injected jets along the spanwise direction with a supersonic crossflow using experimental and numerical techniques. Results show that smaller interjet spacing reduces the crossflow entrainment from the top into the interjet region, while wider spacing facilitates greater entrainment. The investigation further reveals that the gap created by the two injected jets allows the crossflow to decelerate and then accelerate to a higher supersonic Mach number as it flows along the interjet region. Investigation of the shock structures revealed that in the case of smaller interjet spacing, the strong part of the two bow shocks created by the transverse jets interacts with each other, whereas with large interjet spacing, the weak part of the two bow shock waves interacts. This leads to a larger local pressure jump in the interjet spacing with a smaller injector gap than the larger one. Various streamwise vortices, such as horseshoe and counter-rotating vortex pairs (CVPs), are seen to form for spanwise tandem injection in crossflow. The interaction of such vortices is seen to be significant in the case with smaller injector spacing compared to the larger one. The oil flow visualization reveals the formation of a herringbone-shaped separation region in the wake of the jets, and the size of this separation zone diminishes with the reduction in injector spacing. The mixing characteristics investigated using Mie scattering and computations reveal that with an increase in injector spacing, the mixing efficiency increases.

Models for solving the Reynolds-averaged Navier-Stokes equations are popular tools for predicting complex turbulent flows due to their computational affordability and their ability to provide or estimate quantities of engineering interest. However, results depend on a proper treatment of unclosed terms, which require progress in the development and assessment of model forms. In this study, we consider the Reynolds stress transport equations as a framework for second-moment turbulence closure modeling. We specifically focus on the terms responsible for decay of the Reynolds stresses, which can be isolated and evaluated separately from other terms in a canonical setup of homogeneous turbulence. We show that by using anisotropic forcing of the momentum equation, we can access states of turbulence traditionally not probed in a triply periodic domain. The resulting data span a wide range of anisotropic turbulent behavior in a more comprehensive manner than extant literature. We then considered a variety of model forms for which these data allow us to perform a robust selection of model coefficients, and we selected an optimal model that extends to cubic terms when expressed in terms of the principal coordinate Reynolds stresses. Performance of the selected decay model is then examined relative to the simulation data and popular models from the literature, demonstrating the superior accuracy of the developed model and, in turn, the efficacy of this framework for model selection and tuning.

We conduct experimental investigations on vortex-induced forces of an oscillating bluff body across subcritical to critical Reynolds ($\mathrm{Re}$) number regimes, and reveal variations in different hydrodynamic components versus $\mathrm{Re}$, thereby addressing a gap in understanding at high $\mathrm{Re}$. Specifically, the drag crisis cannot be mitigated by vibration, the excitation force is sensitive to both $\mathrm{Re}$ and vibration parameters, and the sensitivity of added mass coefficient to vibration decreases at high $\mathrm{Re}$. We confirm that current prediction theory at lower $\mathrm{Re}$ are not applicable to the full-scale one, underscoring the necessity of $\mathrm{Re}$ effects on hydrodynamic inputs.

The propagation of polydisperse bubbles inside a rectangular Hele-Shaw channel by the constant volumetric flux flow of an ambient viscous liquid is generally unsteady; pairs of neighboring bubbles will either separate or coalesce because their propagation speeds increase monotonically with their sizes. Thus, any group of bubbles will eventually rearrange itself in order of decreasing size, individual bubbles will separate, and, crucially, there are no stable multiple-bubble states. Remarkably, the introduction of a small axially uniform elevation to the channel's lower boundary (on the order of a percent of the channel's depth) leads to the creation of stable multiple-bubble states and, thus, disrupts the usual reordering by bubble sizes. The constituent bubbles of such states lie in alternation on opposite sides of the elevation. The elevation provides a mechanism for the trailing bubbles to reduce their propagation speeds when approaching their preceding nearest neighbors. The stable multiple-bubble states are always led by the smallest bubble while the trailing bubbles can be arranged in any order and, thus, their number grows factorially as the number of bubbles increases.

This experimental study aims to compare the role of plume dynamics and canopy-induced instabilities on the transport of inertial particles, with application to firebrand transport in spotfire spread. In an idealized “wind-driven” model system, we consider the impact of plume buoyancy, plume momentum, and canopy turbulence on the downstream transport of particles in the wake of a canopy, and in particular the mean and standard deviation of the distribution of landing sites. Experiments were conducted in a recirculating flume with model vegetation, a heated plume/jet source, and three-dimensional printed spherical plastic particles. In a first set of experiments, particles were released with a fixed starting elevation above the plumes' upper boundaries, such that the particles were not lofted by the plume. In these cases, observations suggest that plumes have a role in extending particles' streamwise transport by delaying their downward transport. The plumes also have a strong role in increasing absolute dispersion of the particles, although less so when dispersion is normalized by distance traveled. While canopy turbulence alone significantly increases particle dispersion, in the presence of the plume its impact is more limited. Canopy turbulence was also found to cause shorter mean landing positions. In a second set of experiments, particles were released at the plume source/outlet such that their initial vertical momentum was provided by the plume's momentum and buoyancy. In these cases, the impact of canopy turbulence on particle transport is observed more distinctly. The canopy coherent structures introduce a mechanical instability to the plume, which manifests as vertical oscillatory motions that lead to variability in the particles' initial conditions and, therefore, trajectories. This leads to particles settling at both shorter and longer downstream distances.