The classical flame instability problem of a flickering diffusion flame is investigated experimentally, with an emphasis on the underlying vortex dynamics and flame pinch-off mechanism. To study the natural development of flame instability, an innovative particle seeding approach is adopted in the particle image velocimetry (PIV) measurement to minimize the perturbation of the seeding stream on the flame's outer shear layer. By taking advantage of the high-speed simultaneous measurement of PIV and flame chemiluminescence, we are able to obtain for the first time the time-resolved flame surface contour together with both its inner and outer flow fields for a jet diffusion flame in a near-quiescent environment. Based on analyzing the evolutions of the phase-averaged flow and flame structures, we find that the buoyancy-induced outer vortex ring (OVR) plays a pivotal role in flame flickering by inducing periodic curving, neck-in, and pinch-off of the flame surface for both buoyancy- and momentum-driven diffusion flames. Based on quantitatively tracking the vortex core's position and vorticity, the OVR dynamics can be divided into three stages, manifesting as a hydrodynamic instability developing along the outer shear layer. We further report the disappearance of flame pinch-off for certain momentum-driven flames with sufficiently high fuel flow rates. To understand this phenomenon, the flame pinch-off can be interpreted as a consequence of “physical extinction,” which occurs as the inward convection of bulk flow dominates over the outward fuel diffusion, thereby leading to an insufficient fuel supply to the flame surface. We show that this competing mechanism between diffusion and convection can be quantified by a characteristic Peclet number, which is validated based on our experimental results.

To achieve decarbonization targets, wind turbines are growing in hub height and rotor diameter, and they are being deployed in new locations with diverse atmospheric conditions not previously seen, such as offshore. Physics-based analytical wake models commonly used for design and control of wind farms simplify atmospheric boundary layer (ABL) and wake physics to achieve computational efficiency. This is accomplished primarily through a simplified model form that neglects certain flow processes, such as atmospheric stability, and through the parametrization of ABL and wake turbulence through a wake spreading rate. In this study, we systematically analyze the physical mechanisms that govern momentum and turbulence within a wind turbine wake in the stratified ABL. We use large-eddy simulation and analysis of the streamwise momentum deficit and wake-added turbulence kinetic energy (TKE) budgets to study wind turbine wakes under neutral and stable conditions. To parse the turbulence in the wake from the turbulent, incident ABL flow, we decompose the flow into the base ABL flow and the deficit flow produced by the presence of a turbine. We then analyze the decomposed flow field budgets to study the effects of changing stability on the streamwise momentum deficit and wake-added TKE. The results demonstrate that stability changes the relative balance of turbulence and advection for both the streamwise momentum deficit and wake-added TKE primarily through the nonlinear interactions of the base flow with the deficit flow. The stable cases are most affected by increased shear and veer in the base flow and the neutral case is most affected by the increased ambient turbulence intensity. These differences in the base flow that arise from stratification are relatively more important than the buoyancy forcing terms in the wake-added TKE budget. The wake-added TKE depends on the ABL stability. An existing wake-added TKE model that neglects the effects of ABL stability yields $15–25\%$ error compared to large-eddy simulation, with errors that are higher in stable conditions than neutral. These results motivate future research to develop fast-running models of wake-added TKE that account for stability effects.

Anomalous dissipation is a mechanism to dissipate kinetic energy which is established by a sufficiently spatially rough velocity field. It implies that the rescaled mean kinetic energy dissipation rate becomes constant with respect to Reynolds number $\mathrm{Re}$, the dimensionless parameter that characterizes the strength of turbulence, given that $\mathrm{Re}\gg 1$. The present study aims at bridging this statistical behavior of high-Reynolds-number turbulence to one specific structural building block of fluid turbulence—local vortex stretching configurations which take in the simplest case the form of Burgers's classical vortex stretching model from 1948. We discuss the anomalous dissipation in the framework of Duchon and Robert for this analytical solution of the Navier-Stokes equations, apply the same analysis subsequently to a generalized model of randomly oriented Burgers vortices by Kambe and Hatakeyama, and analyze finally direct numerical simulation data of three-dimensional homogeneous, isotropic box turbulence in this respect. We identify local high-vorticity events in fully developed Navier-Stokes turbulence that approximate the analytical models of strong vortex stretching well. They correspond to precursors of enhanced anomalous dissipation.

The wall heat flux (WHF) in the hypersonic boundary layer over the windward side of a lifting body, namely, the hypersonic transition research vehicle model, is comprehensively investigated by direct numerical simulations. The freestream over the model is at Mach 6 and the angle of attack $2^{\circ }$ results in strong three-dimensionality of the boundary layer affected by noncanonical effects, such as wall curvature and pressure gradient. The boundary layer thickness and friction Reynolds number are much larger in the central region than those in the side region. The turbulent statistics of WHF, such as heat-transfer coefficients, probability density functions, and frequency spectra, weakly depend on the streamwise location but strongly on the azimuthal location. The mean and fluctuation of WHF are stronger in the side region, which is of the thinner boundary layer thickness and stronger dilatation motions. The traveling-wave-like alternative positive and negative structures (APNSs) consisting of expansion and compression motions are shown to play a crucial role in the evolution of WHF, according to its space-time features. Moreover, APNSs in central and side regions are significantly different in scale and strength. For exploring the generation mechanism of extreme events of WHF fluctuation, the conditional analysis is performed to quantitatively identify the coherent structures and energy transfer mechanisms in extreme events. The results indicate that the velocity streaks and APNSs are the primary structures inducing extreme events by modifying viscous dissipation and pressure-dilatation work, respectively. Additionally, the most dominant energy transfer mechanisms of extreme positive events from central to side regions shift from pressure-dilatation work to viscous dissipation.

This study presents a model scale experimental investigation on multiscale characteristics of cavity dynamics and induced pressure pulses around a highly skewed propeller using synchronous measurement and digital holographic measurement technology. The experimental studies reveal three distinct cavitation patterns, namely, the tip vortex and sheet cavitation (TVSC), the vortex cavitation (VC), and no cavitation (NC) under different advance coefficients and cavitation numbers. Propeller cavitation has significant effects on induced pressure pulses. In the low-frequency range, a predominant frequency component of blade passing frequency (BPF) is observed at approximately 105 Hz caused by the rotational motion of the propeller for all kinds of flow patterns. In addition, when cavitation occurs, the amplitude of pressure pulses increases significantly across a broad frequency spectrum larger than 2 BPF. For cases at an advance coefficient less than 0.75, the cavitation pattern varies from NC to TVSC with decreasing cavitation number. A regular tip vortex cavity first appears and connects on the propeller blade tip, then the well-developed tip vortex grows continually and a large-.scale transparent sheet cavity attaches on the back surface. Finally, the tip vortex almost disappears with only small-scale cavities shed downstream at the trailing edge of the sheet cavity at low cavitation number. In contrast, for cases at an advance coefficient larger than 0.75, the cavitation pattern varies from NC to VC as the cavitation number decreases. Concurrently, under the influence of vortices, an indistinct foamy cavity forms across the entire leading edge of the propeller front surface, accompanied by the shedding of small-scale cavities at the blade tips. Meanwhile, the small-scale shedding cavities are primarily composed of microbubbles with radii predominantly less than 100 µm. Additionally, the statistical probability density functions of the bubble radii adhere to a gamma distribution. Moreover, the mechanism leading to the formation and evolution of induced pressure pulses is analyzed and quantitatively verified based on experimental results. As cavitation develops with the decrease of cavitation number, the amplitude increases in the mid-frequency band spanning from 2 to 13 BPF for all kinds of cavitation patterns. Meanwhile, a distinct dominant frequency is observed in the mid-frequency region, which is associated with the fragmentation and shedding of small-scale cavities. Finally, the mechanism causing the pressure pulses in the high-frequency band higher than 13 BPF is investigated. The high-frequency pressure pulses are relatively small and stable when there is no cavitation observation or a stable vortex tube appearance at the propeller blade tip. In contrast, the pressure pulses fluctuate at a decrease rate of 6 dB per octave, caused by the collapse of microbubbles in the high-frequency region.

When several intruders move in a granular medium, coupling effects are observed, the motion of one intruder affecting that of others. In this paper, we investigate experimentally how the drag forces acting on a pair of spherical intruders moving amid grains at constant velocity vary with the transverse separation between them and their depth. When intruders are sufficiently far apart, they do not influence each other, and the average drag felt by each of them matches that of a single intruder. However, for small distances between intruders and at a given depth, the average drag per intruder decreases, highlighting a collaborative effect that facilitates motion. This collaboration effect is amplified when the depth of the intruders increases. We propose a model for the drag reduction of a pair of intruders based on the breakup of contact chains, caused by the perturbation generated by the neighbor intruder. Our findings provide new insights into the interaction effects on the motion of solids in sand, such as those observed in animal locomotion, root growth, and soil survey.

A method is proposed to identify the vortex boundary and center of rotation based on tubular surfaces of constant stagnation pressure and minimum of the stagnation pressure gradient. The method is derived from Crocco's theorem, which ensures that the gradient of stagnation pressure is orthogonal to both the velocity and vorticity vectors. The method is Galilean invariant, requires little processing, and is robust. It enables visualization of complex turbulent flows and provides a physically consistent definition of vortex boundaries for quantitative analyses. This vortex boundary is a material surface that is representative of the kinematics of the flow by construction, constitutes a vortex tube, ensures the conservation of circulation in the inviscid limit, and provides a unique relation to the conservation of momentum equations and vortex loads.

Direct numerical simulation of flame-wall interaction (FWI) for two flame configurations under different laminar burning velocity to nonreacting wall friction velocity ratio, $S_L/u_{{\tau }_{\mathrm{NR}}}$, have been performed. The first configuration considered is a V-flame in a turbulent channel flow with isothermal inert walls and represents oblique wall interaction. The second configuration is representative of head-on interaction (HOI) of a planar flame interacting with a wall in a fully developed turbulent boundary layer. In the case of the V-flame with $S_L/u_{{\tau }_{\mathrm{NR}}}=0.4,$ a smaller flame angle is obtained when compared with that of the V-flame with $S_L/u_{{\tau }_{\mathrm{NR}}}=0.7$. This is a consequence of the differences in the turbulent burning velocities between the two V-flame cases, where the case with $S_L/u_{{\tau }_{\mathrm{NR}}}=0.4$ has a lower turbulent burning velocity when compared with that of the case with $S_L/u_{{\tau }_{\mathrm{NR}}}=0.7$. By contrast, the ratio of turbulent to laminar burning velocity is higher for the $S_L/u_{{\tau }_{\mathrm{NR}}}=0.4$ HOI case when compared to the corresponding HOI case with $S_L/u_{{\tau }_{\mathrm{NR}}}=0.7$. The flame orientations with respect to the streamwise component of velocity and wall-normal direction in addition to the $S_L/u_{{\tau }_{\mathrm{NR}}}$ values have been found to have a significant impact on the variations of wall heat flux, wall shear stress, and wall friction velocity in premixed FWI within turbulent boundary layers. The behaviors of nondimensional streamwise velocity, $u^{+}$, and nondimensional temperature using wall units, $T^{+}$, have also been investigated for different $S_L/u_{{\tau }_{\mathrm{NR}}}$ ratios and it is found that the standard log-law profiles in the case of $u^{+}$ and $T^{+}$ are not valid for the two configurations and the two $S_L/u_{{\tau }_{\mathrm{NR}}}$ ratios considered.

Freshwater achieves its maximum density at a pressure-dependent temperature which is above the freezing point, close to 4 °C at ambient pressure for pure water. If the temperature of a freshwater column is below the temperature of maximum density, radiative heating at the surface can generate convection, as warmer water at the surface becomes denser and sinks. This particular example of radiatively driven convection (RDC) is prevalent during springtime in temperate lakes. Scales for the vertical velocity, temperature fluctuations, and horizontal extent of the convective cells are derived theoretically and validated with the help of large eddy simulations. The Coriolis effects in temperate lakes are not dominant. However, it is shown that rotation has the effect of limiting the horizontal scale of the convective cells unless the Rossby number is large, in which case the size of the cells is solely determined by the length of daytime.

Stabilization schemes in wall-bounded flows often invoke fluid transpiration through porous boundaries. While these have been extensively validated for external flows, their efficacy in channels, particularly from the standpoint of nonmodal perturbations, is yet to be demonstrated. Here, we show that crossflow strengths previously considered “ideal” for optimizing stability in channels in fact admit strong nonmodal energy amplification. We begin by supplementing existing modal calculations and then show via the resolvent that extremely strong and potentially unfeasible crossflows are required to suppress nonmodal growth in linearly stable regimes. Investigation of unforced algebraic growth paints a similar picture. Here, a componentwise budget analysis reveals that energy redistribution through pressure-velocity correlations plays an important role in driving energy growth/decay. The superposition of a moving wall is also considered, and it is shown that while energy amplification generally worsens, it can potentially be suppressed in certain regions of parameter space. However, these flows are marred by rapidly declining mass transport, rendering their ultimate utility questionable. Our results suggest that crossflow-based stabilization might not be useful in internal flows.

The Moody diagram, a plot of friction factor versus flow rate, is a well-known engineering tool for estimating head loss in pipe flows. It comprises well-defined relationships between friction factor and flow rate over the majority of parameter space, but there is a gap in the transitional regime between laminar and turbulent flows. It is often left hatched because in this parameter range the friction is deemed indefinite, which Moody remarked could at least partially be due to the different initial conditions used to establish the flow. Here we investigate this issue and seek a systematic dependence for friction in the transitional regime. The novel method we use is to approach the transitional regime from above by reducing the flow speed from a turbulent flow state. We find that in different pipe flow setups, both driven by gravity, a single curve corresponding to a maximum density of the transitional flow structures is found. We test the generality of this result using an alternative method to drive the flow through the pipe, using a mass displacement device. Our investigation of the flow driven by a syringe produces yet a different curve, indicating that the method of driving the flow has a significant impact on both the final states and the paths leading to them in the transitional regime.

Liquid jets subjected to interfacial shear effects are frequently encountered in scientific research and industrial applications. The presence of external shear can induce an axial elastic tension due to the velocity gradient across the jet cross section. This elastic tension significantly modifies the linear instability characteristics of viscoelastic jets. Notably, increasing fluid viscoelasticity up to a certain threshold can lead to substantial stabilization of the axisymmetric mode. This problem is investigated within the framework of slender-jet approximations in the present paper, demonstrating that the effects of elastic tension are not adequately captured by the standard leading-order models. To address this, a series of higher-order approximation models is presented. The parabolic model effectively accounts for the nonuniform radial profile of basic velocity and the resulting elastic tension effects. Additionally, the averaged-parabolic model and reduced-order averaged-parabolic model retain essential features while offering greater simplicity and computational efficiency. Linear stability analysis results validate the effectiveness of these models in the long-wave region through comparison with a two-dimensional axisymmetric model. Finally, the asymptotic behaviors of the most unstable disturbances are presented. Due to the ability to incorporate the local elastic tension effects of elastic jets, these models establish a mechanism for jet stabilization and offer potential insights for future research.

Deposition and erosion processes have significant effects on the environment, industrial applications, and porous media. In this work we study the deposition and erosion of solid particles at the microscale level and their direct consequences on the internal structure of porous media with complex internal morphology. We formulate a mathematical model to investigate these phenomena in a porous medium with branching structure consisting of axisymmetric channels, undergoing a unidirectional flow. The flow and the transport of solid particles are modeled with the Hagen-Poiseuille law and advection-diffusion-reaction equations, respectively. As a consequence of deposition and erosion, those channels tend to shrink or expand, respectively, based on some key parameters which are discussed in this paper. This is modeled by threshold laws: the fluid-solid interface erosion and deposition occur when the total shear stress is, respectively, greater or lower than some specified critical values, depending on the solid material. Depending on the gradients of initial pore radii and layer thicknesses, substantial differences in the branching evolution under erosion and deposition are observed. Therefore, we characterize the evolution of the internal morphology of the porous medium using geometric parameters.

We conduct direct numerical simulations of turbulent plane Couette flow, the shear flow between two differentially moving plates, to analyze how the system responds to a modulation in the driving velocity of one of the plates. We fix the shear Reynolds number to $R{e}_s=3\times {10}^4$, and add a zero-mean modulation of fixed amplitude to the constant velocity of the bottom plate. The period is set close to the large-eddy time scale, while the amplitude and shape of the forcing is varied. We find that the propagation of the perturbation, i.e., both amplitude and phase, can be largely captured using models based on laminar flow, regardless of the waveform used to force the flow. Furthermore, we find that linear superposition can effectively describe the flow's response to arbitrary perturbations as long as the modulation is not larger than the forcing of the base flow.

We report the observation of two identical Leidenfrost droplets rebounding from each other after a head-on collision on a hot surface, resembling billiard ball collision. The observed phenomenon contradicts the established understanding that predicts the coalescence of two colliding Leidenfrost droplets. The collision dynamics of the Leidenfrost droplets is investigated using pressure and energy balance analysis at the macroscale, and a molecular interaction analysis at the nanoscale. The results suggest that droplet properties and the temperature of the hot surface determine the state of the gas film between the colliding droplets. Droplets with lower surface tension form thicker gas films, while lower surface temperatures mitigate the interaction of vapor molecules within the gas film, both facilitating droplet rebound after their collision. The discovered Leidenfrost droplet phenomenon is highly controllable, and has potential for a variety of applications, such as the selective chemical synthesis as explored in this work.

Slender-jet equations are a set of nonlinear evolution equations that arise in the analysis of pinch-off singularities and govern the shape of and the axial velocity at leading order within a thinning liquid thread. Moreover, because they are a set of relatively simple transient partial differential equations that depend only on one spatial variable, they are also widely employed in simulating dripping and jetting from nozzles, dynamics of liquid bridges, and contraction of liquid filaments as their use results in drastic reduction in computational effort compared to solving the full set of equations governing such free surface flows. Here, a physically based derivation of the slender-jet equations is presented for situations in which the jet's surface is covered with surfactant and surface rheological (viscous) effects are important and, moreover, both the bulk fluid and the interface can be non-Newtonian. It is worth noting that a derivation of the general slender-jet equations governing the dynamics of jets consisting of arbitrary bulk and surface phases has heretofore been lacking in the literature and this deficiency is hence remedied in this paper. These general equations are then reduced to ones governing the dynamics of what is referred to as a Newtonian jet, i.e., a jet where the bulk liquid is an incompressible Newtonian fluid and its interface is a two-dimensional Newtonian fluid whose rheology is described by the widely used Boussinesq-Scriven constitutive equation. The one-dimensional (1D) slender-jet equations have recently been used to analyze the stability and breakup of primarily Newtonian jets but also of jets of non-Newtonian fluids with a Newtonian surface phase. However, most of the aforementioned studies have been carried out without benchmarking the results obtained from solving the 1D slender-jet equations against full free surface flow simulations or experiments. Therefore, we also present here a comparison of theoretical predictions obtained from slender-jet theory with computational results obtained from the use of a fully three-dimensional, axisymmetric (3DA) algorithm for a breaking surfactant-covered Newtonian jet first when the jet is undergoing Stokes flow and then also when inertia cannot be neglected. For Newtonian jets, analytical results obtained from slender-jet theory are shown to be in excellent accord with predictions obtained from the 3DA simulations.

A sensor-based blended wall-modeling approach is proposed and applied to investigate the flow over a Gaussian-shaped bump geometry at three different Reynolds numbers ${\text{Re}}_L={10}^6, 2\times {10}^6,$ and $4\times {10}^6$, based on the freestream velocity and the bump length, and a freestream Mach number $M=0.2$. The flow exhibits favorable and adverse pressure gradients driven by the bump curvature, leading to a region of relaminarization around the apex for ${\text{Re}}_L={10}^6$, and flow separation downstream of the bump apex for all Reynolds numbers. This flow configuration serves as a challenging test case for wall-modeling approaches that typically assume the boundary layer to be fully turbulent, thus overestimating the friction and momentum losses in quasilaminar regions. To address this limitation, we propose two sensors capable of identifying relaminarization and retransition processes, taking into account a hysteresis timescale, and a blending strategy that combines, based on the local sensor value, an equilibrium wall model with either a no-slip or a laminar wall-model boundary condition. To evaluate the performance of the proposed wall-modeling approach, we compare spanwise periodic wall-modeled large-eddy simulation results with earlier experimental data, as well as earlier direct numerical simulation results. Previously developed laminar-to-turbulent transition sensors are also assessed. The predictive capabilities and robustness of our proposed approach are evaluated for all three Reynolds numbers. A posteriori analyses suggest that the sensors correctly identify the (pressure-gradient-driven) relaminarization present in the ${\text{Re}}_L={10}^6$ case, with the blended wall model improving flow predictions, while still being applicable without any change in the model parameters to the higher Reynolds number flows, which do not exhibit relaminarization.

We investigate the dynamics of pendulum chains immersed in turbulent boundary layers. We combine qualitative video analysis of the artist Ned Kahn's kinetic façades of buildings, and laboratory experiments on a unidimensional weakly coupled chain of pendulums. We performed analysis of both the façades and the laboratory scale model. We show that pendulum waves traveled in the direction of the wind. These waves originate from the excitation by the spatiotemporal pressure fluctuations. We identified two dispersion relation branches. The first branch corresponds to a resonant response of each pendulum at its natural frequency of oscillations. The second branch corresponds to an excitation by the advected pressure fluctuations along the chain. Using local pressure sensors, we show a quantitative agreement between the convection velocity of the pendulum chain waves and the pressure fluctuations. Eventually, we propose a model in Fourier space to describe the magnitude of each branch. We show that at a small wind speed, the pendulum response is dominated by the resonance at their natural frequency. At larger wind speed, the response becomes dominated by the advected pressure fluctuations.

In our previous papers [W. Li et al., Phys. Rev. Fluids 7, 103502 (2022); W. Li et al., Phys. Rev. Fluids 8, L011501 (2023)], the onset of single-inertial-mode convection in rapidly rotating, self-gravitating oblate spheroidal fluid was studied under the conditions of asymptotically small Ekman number and sufficiently small Prandtl number, leaving the general case of finite Prandtl number to be explored. This paper investigates the problem of thermal instabilities in rapidly rotating, self-gravitating, internally heated, oblate spheroidal fluid using a multimodal global asymptotic method valid for any moderate to large Prandtl number that reflects a typical parameter space in planetary liquid interiors. An analytical criterion for the onset of thermal convection in the multimodal form is derived. The dependence of the critical properties on the oblateness of spheroids is explored. More importantly, the theory discussed in this paper establishes a necessary foundation for studies of turbulent convection and dynamo actions in rapidly rotating oblate spheroidal planets, which will be the themes of the ensuing papers of this series.