Mode Instability Research Articles

Global dynamics and topology of two-phase mixing layer flow through simultaneous gas and liquid velocity measurements

This study reports the first time-resolved particle image velocimetry characterization of a planar two-phase mixing layer flow, whose velocity field is measured simultaneously in gas and liquid streams. Two parallel air and water flows meet downstream of a splitter plate, giving rise to an initially spanwise invariant configuration. The aim is to elucidate further the mechanisms leading to the flow breakup in gas-assisted atomization. The complete experimental characterization of the velocity field represents a database that could be used in data-driven reduced-order models to investigate the global behaviour of the flow system. After the analysis of a selected reference case, a parametric study of the flow behaviour is performed by varying the liquid ( $Re_l$ ) and gas ( $Re_g$ ) Reynolds numbers, and as a consequence also the gas-to-liquid dynamic pressure ratio ( $M$ ), shedding light on both time-averaged (mean) and unsteady velocity fields. In the reference case, it is shown that the mean flow exhibits a wake region just downstream of the splitter plate, followed by the development of a mixing layer. By increasing both $Re_l$ and $Re_g$ , the streamwise extent of the wake decreases and eventually vanishes, the flow resulting in a pure mixing layer regime. The spectral analysis of the normal-to-flow velocity fluctuations outlines different flow regimes by variation of the governing parameters, giving more insights into the global characteristics of the flow field. As a major result, it is found that at high $Re_g$ and $M$ values, the velocity fluctuations are characterized by low-frequency temporal oscillations synchronized in several locations within the flow field, which suggest the presence of a global mode of instability. The proper orthogonal decomposition of velocity fluctuations, performed in both gas and liquid phases, reveals finally that the synchronized oscillations are associated with a low-frequency dominant flapping mode of the gas–liquid interface. Higher-order modes correspond to interfacial wave structures travelling with the so-called Dimotakis velocity. For lower gas Reynolds numbers, the leading modes describe higher frequency fingers shedding at the interface.

Stability Analysis of a Rocky Slope with a Weak Interbedded Layer under Rainfall Infiltration Conditions

Landslides not only cause great economic and human life losses but also seriously affect the safe operation of infrastructure such as highways. Rainfall is an important condition for inducing landslides, especially when a fault and weak interlayer exist on the slope, which can easily transform into a landslide and cause instability under the action of rainfall. To explore the effects of a soft interlayer, a fault, and extreme rainfall on slope stability, this paper takes the landslide on the right side of the G104 Jinglan Line in Shengzhou City, Shaoxing City, Zhejiang Province, China, as an example. The cause, failure mechanism, and characteristics of the landslide are analyzed through field investigation and borehole exploration in the landslide area. The slope is simulated by numerical analysis, and the stability of the landslide under natural conditions and extreme rainstorm conditions is calculated using the strength reduction method. The stability of the slope before and after treatment is compared, and the effectiveness of the treatment measures is verified by combining the field monitoring data. At the same time, the complex geological structure and rainfall are considered to have been the main factors leading to the G104 landslide. Near the fault, the weak interlayer of the landslide was easily disturbed, the deformation trend of the deep displacement was consistent with rainfall, and the axial force of the anti-slide piles at the weak interlayer was correspondingly large. For a wedge rock slope, “excavation unloading” and “prestressed anchor + prestressed anchor cable + anti-slide pile” are effective treatments. This paper reveals the effects of a weak interlayer, a fault, and strong rainfall on a rocky high slope, providing predictions of instability modes and time evolution patterns for similar complex geological slopes under rainfall infiltration conditions and providing references for their treatment measures.

Vertical convection regimes in a two-dimensional rectangular cavity: Prandtl and aspect ratio dependence

Vertical convection is the fluid motion that is induced by the heating and cooling of two opposed vertical boundaries of a rectangular cavity (see e.g. Wang et al., J. Fluid Mech., vol. 917, 2021, A6). We consider the linear stability of the steady two-dimensional flow reached at Rayleigh numbers of O( $10^8$ ). As a function of the Prandtl number, $Pr$ , and the height-to-width aspect ratio of the domain, $A$ , the base flow of each case is computed numerically and linear simulations are used to obtain the properties of the leading linear instability mode. Flow regimes depend on the presence of a circulation in the entire cavity, detachment of the thermal layer from the boundary or the corner regions and on the oscillation frequency relative to the natural frequency of oscillation in the stably temperature-stratified interior, allowing for the presence of internal waves or not. Accordingly, the regime is called slow or fast, respectively. Either the global circulation or internal waves in the interior may couple the top and bottom buoyancy currents, while their absence implies asymmetry in their perturbation amplitude. Six flow regimes are found in the range of $0.1 \leq Pr \leq 4$ and $0.5 \leq A \leq 2$ . For $Pr \lessapprox 0.4$ and $A>1$ , the base flow is driven by a large circulation in the entire cavity. For $Pr \gtrapprox 0.7$ , the thermal boundary layers are thin and the instability is driven by the motion along the wall and the detached boundary layer. A transition between these regimes is marked by a dramatic change in oscillation frequency at $Pr = 0.55 \pm 0.15$ and $A <2$ .

Influence of parametric forcing on Marangoni instability

We study a thin, laterally confined heated liquid layer subjected to mechanical parametric forcing without gravity. In the absence of parametric forcing, the liquid layer exhibits the Marangoni instability, provided the temperature difference across the layer exceeds a threshold. This threshold varies with the perturbation wavenumber, according to a curve with two minima, which correspond to long- and short-wave instability modes. The most unstable mode depends on the lateral confinement of the liquid layer. In wide containers, the long-wave mode is typically observed, and this can lead to the formation of dry spots. We focus on this mode, as the short-wave mode is found to be unaffected by parametric forcing. We use linear stability analysis and nonlinear computations based on a reduced-order model to investigate how parametric forcing can prevent the formation of dry spots. At low forcing frequencies, the liquid film can be rendered linearly stable within a finite range of forcing amplitudes, which decreases with increasing frequency and ultimately disappears at a cutoff frequency. Outside this range, the flow becomes unstable to either the Marangoni instability (for small amplitudes) or the Faraday instability (for large amplitudes). At high frequencies, beyond the cutoff frequency, linear stabilization through parametric forcing is not possible. However, a nonlinear saturation mechanism, occurring at forcing amplitudes below the Faraday instability threshold, can greatly reduce the film surface deformation and therefore prevent dry spots. Although dry spots can also be avoided at larger forcing amplitudes, this comes at the expense of generating large-amplitude Faraday waves.

Nonlinear in-plane buckling of small-curved and large-curved FG porous microbeams via strain gradient-based isogeometric collocation formulations

In the current investigation, for the first time, the changes in the limit loads and equilibrium branches associated with the nonlinear in-plane stability characteristics of curved microbeams are explored in the presence of different microstructural gradient tensors. In this regard, multiple microsize-dependent equilibria are analyzed relevant to thermomechanical loaded small-curved, medium-curved, and large-curved microbeams made of functionally graded porous (FGP) metal reinforced with nanofillers possessing clamped end supports. To this purpose, based upon the strain gradient elasticity within the framework of the third-order shear flexible curved beam model, the isogeometric collocation formulations incorporating Greville abscissae are constructed resulting in higher-continuity characters as well as remarkable accuracy for higher-order approximations. It is deduced that for the small-curved FGP reinforced microbeam, no limit load can be found due to the absence of the buckling phenomenon, but after rising the temperature by an enough amount, the initial instability mode appears. However, for the medium-curved FGP reinforced microbeam, the limit instability mode of buckling occurs which results in the normalized upper limit load equal to 0.7161 based on the classical theory and 0.7606 based on the strain gradient elasticity (6.21% enhancement). Also, it results in the normalized lower limit load equal to 0.3060 based on the classical theory and 0.3521 based on the strain gradient elasticity (15.07% enhancement). On the other hand, for the large-curved FGP reinforced microbeam, the bifurcation mode of buckling occurs which results in the normalized upper limit load equal to 1.0494 based on the classical theory and 1.1358 based on the strain gradient elasticity (8.23% enhancement). Also, it results in the normalized lower limit load equal to 0.2225 based on the classical theory and 0.2513 based on the strain gradient elasticity (12.94% enhancement).

Experimental investigation of hypersonic boundary layer instability with wavy wall located downstream of synchronization point

The wavy wall surface has been reported to be effective in suppressing the growth of second mode instability waves in hypersonic boundary layer, while the allocation of wavy wall relative to the synchronization point requires further study. Upon this work experimental investigation of hypersonic boundary layer instability with wavy wall located downstream of synchronization point based on 7° half-angle sharp cone at zero angle of attack was carried out in a hypersonic noisy wind tunnel. The evolution of instability waves with wavy wall surface is measured using both surface-mounted pressure fluctuation sensors and focused laser differential interferometer (FLDI). The results reveal that the growth of instability waves has been enhanced significantly when the wavy wall region is allocated downstream of the synchronization point when the wavy wall height is slightly smaller than the local boundary layer thickness. Additionally, second mode instability waves are observed at both crests and troughs within the wavy wall region based on the FLDI measurement and moreover, the high-frequency instability waves measured in the separation bubbles of troughs are speculated to be the transmission of second mode instability waves from the shear layer, rather than the local generation of second mode instability.

Computational multiphase micro‐periporomechanics for dynamic shear banding and fracturing of unsaturated porous media

AbstractDynamic shearing banding and fracturing in unsaturated porous media are significant problems in engineering and science. This article proposes a multiphase micro‐periporomechanics (PPM) paradigm for modeling dynamic shear banding and fracturing in unsaturated porous media. Periporomechanics (PPM) is a nonlocal reformulation of classical poromechanics to model continuous and discontinuous deformation/fracture and fluid flow in porous media through a single framework. In PPM, a multiphase porous material is postulated as a collection of a finite number of mixed material points. The length scale in PPM that dictates the nonlocal interaction between material points is a mathematical object that lacks a direct physical meaning. As a novelty, in the coupled PPM, a microstructure‐based material length scale is incorporated by considering micro‐rotations of the solid skeleton following the Cosserat continuum theory for solids. As a new contribution, we reformulate the second‐order work for detecting material instability and the energy‐based crack criterion and J‐integral for modeling fracturing in the PPM paradigm. The stabilized Cosserat PPM correspondence principle that mitigates the multiphase zero‐energy mode instability is augmented to include unsaturated fluid flow. We have numerically implemented the novel PPM paradigm through a dual‐way fractional‐step algorithm in time and a hybrid Lagrangian–Eulerian meshfree method in space. Numerical examples are presented to demonstrate the robustness and efficacy of the proposed PPM paradigm for modeling shear banding and fracturing in unsaturated porous media.

Simplified expression for transverse mode instability threshold in high power fiber lasers.

In this work, we propose an analytical expression for calculating the transverse mode instability (TMI) threshold power, which clearly shows the role of various fiber parameters and system parameters. The TMI threshold expression is obtained by solving the heat conduction equation and the nonlinear coupling equation using the fundamental mode fitted by Gaussian functions. The calculation results of the proposed TMI threshold expression are consistent with the experimental phenomena and simulation results from the well-recognized theoretical model. The influence of some special parameters on the TMI threshold and the power scaling is also investigated. This work will be helpful for fiber design and TMI mitigation of high-power fiber lasers.

Pattern selection mechanism from the equilibrium point and limit cycle.

The outbreak of infectious diseases often exhibits periodicity, and this periodic behavior can be mathematically represented as a limit cycle. However, the periodic behavior has rarely been considered in demonstrating the cluster phenomenon of infection induced by diffusion (the instability modes) in the SIR model. We investigate the emergence of Turing instability from a stable equilibrium and a limit cycle to illustrate the dynamical and biological mechanisms of pattern formation. We identify the Hopf bifurcation to demonstrate the existence of a stable limit cycle using First Lyapunov coefficient in our spatiotemporal diffusion-driven SIR model. The competition between different instability modes induces different types of patterns and eventually spot patterns emerge as stable patterns. We investigate the impact of susceptible, infected, and recovered individuals on the type of patterns. Interestingly, these instability modes play a vital role in selecting the pattern formations, which is directly related to the number of observed spot patterns. Subsequently, we explain the dynamical and biological mechanisms of spot patterns to develop an effective epidemic prevention strategy.

Effect of Insert Porosity on Combustion Instability in a Lean Premixed Combustor Analyzed by a Proper Orthogonal Decomposition-Based Phase Reconstruction Technique

Abstract Lean premixed (LPM) combustion is very effective at mitigating emissions but is vulnerable to strong thermoacoustic instabilities. A porous insert in the shape of an annular ring placed at the dump plane of the combustor has been proven to be an effective passive technique for mitigating these instabilities across a wide range of operating conditions. However, it is unclear if the change results from the insert geometry or porosity of the insert. In this study, swirl-stabilized LPM combustion is investigated for three configurations—without any insert, with a porous insert, and with a geometrically similar solid insert. Acoustics, flow, and heat release rate behavior of the three test geometries are investigated using diagnostics including dynamic pressure and acoustic probes, particle image velocimetry (PIV), and OH* chemiluminescence (OH*CL) imaging. Synchronized measurements at a fixed equivalence ratio were acquired at 40 kHz using sound probes and at 3.5 kHz using PIV and OH*CL. Results include time-series and spectral measurements of pressure, velocity, and OH*CL, and mode analysis by proper orthogonal decomposition (POD). In addition, the dynamics of the instability are investigated by high-resolution phase reconstructions of velocity and OH*CL data using a novel implementation of POD introduced in this work. Results show two different instability modes: a longitudinal instability for the solid insert case and a helical, precessing vortex driven instability for the no insert case. In both cases, the flow field and heat release rate oscillations are coupled to produce the instability. No such coupling or oscillations is observed for the porous insert case. These results ascertain the unique capabilities of the porous insert in protecting against instability from different, simultaneous driving mechanisms and demonstrate that the insert porosity and flow dynamics associated with it are the primary mitigating factors.

The effect of small perturbation on dynamics of absorptive LiBr–water solution

In a binary solution of lithium bromide–water, even a small disturbance in the initial homogeneous mass fraction at the absorbing interface has profound effects on the entire system dynamics. This perturbation of absorption disrupts the equilibrium, leading to the formation of surface tension gradients and subsequently, Marangoni flows. While these flows are relatively weak, they result in a non-uniform distribution of density within the bulk, initiating buoyant convection. We investigate complexities of the Marangoni, solutal, and buoyant convection caused by localized disruptions in uniform absorption, all in the absence of any surfactants. We have conducted numerical simulations to explore fluid dynamics and heat and mass transfer, revealing three different regimes. Initially, shortly after disturbance, variations in mass fraction and flow within the cell are primarily governed by the Marangoni force. After a finite period, the emergence of buoyant convection leads to the strong growth of velocity and significant changes in temperature and mass fraction. Finally, the destabilization of the boundary layer becomes so significant that the emission of plumes is observed. At later times, the parallel existence of two types of patterns takes on a spatially fixed form. The central part, occupied by bands (visible on space-time maps), exhibits minimal changes in time, while a periodic structure is established near the wall. This behavior can be characterized as a relaxation–oscillation mode of instability.

Coupled instability modes at a solvent/non-solvent interface to decorate cellulose acetate flowers

Dispensing a water drop on the thin film of a solution composed of cellulose acetate (CA) in dimethyl formamide (DMF) forms a thin and porous CA layer at the water–DMF interface. While a denser water drop on a rarer CA–DMF film manifests a Rayleigh–Taylor instability—RTI, the dynamically forming porous layer at the water–DMF interface triggers a Saffman–Taylor instability—STI. The combined effects of RTI and STI enable the formation, growth, coalescence, and branching of an array of periodic finger patterns to finally develop into a flower-like morphology. A general linear stability analysis (GLSA) of a thin bilayer composed of a Newtonian and incompressible water layer resting on a Darcy–Brinkman porous medium could predict the length and the time scales of such a finger formation phenomenon. The GLSA uncovers the crucial roles of pressure gradients originating from the gravitational effects, osmotic forces, the Marangoni effect, and capillary forces on the dynamics of the finger formation. While the density difference between water and CA–DMF layer plays a crucial role in deciding the initial finger spacing, the osmotic pressure dictates the formation, growth, branching, and coalescence of fingers. The length-FL and number-Navg of fingers are found to scale as FL∼We0.33Re−0.25 and Navg∼We0.33Re0.25. Further, an inverse relationship of the concentration of CA (C) with ∼We−0.3 and ∼Re−0.7 highlights its role in the formation and growth of fingers. The loading of CA in DMF, the viscosity and density of the CA–DMF film, and the curvature of the fingers are found to be other parameters that decide morphologies.

Numerical study of implosion instability mitigation in magnetically driven solid liner dynamic screw pinches

Magnetized liner inertial fusion experiments on the Z accelerator suffer from magneto-Rayleigh–Taylor instabilities (MRTI) that compromise integrity of the imploding cylindrical liner, limiting achievable fusion fuel conditions and ultimately reducing magneto-inertial fusion target performance. Dynamic screw pinches (DSP) provide a method to reduce MRTI in-flight via application of magnetic field line tension to the imploding liner outer surface. In contrast with z-pinches that drive implosions with an azimuthal magnetic field, dynamic screw pinches enforce an additional axial drive magnetic field component, making the overall drive magnetic field helical. As the liner implodes, cumulative MRTI development is reduced by dynamically shifting the orientation of the fastest growing instability modes. Three-dimensional magnetohydrodynamic simulations show that the DSP mechanism effectively stabilizes initially solid cylindrical liner implosions driven by Z-scale current pulses, indicating that MRTI mitigation increases with the ratio of axial to azimuthal drive magnetic field components (i.e., the drive field ratio). We also performed a spectral analysis of the simulated imploding density distributions, extracting wavelength and pitch angle of the simulated MRTI structures to study their dynamics during the implosion. Simulations of liners initially perturbed with drive-field-aligned sinusoidal structures indicate that MRTI mitigation in DSP implosions decreases with perturbation wavelength, once again suggestive of magnetic field line tension effects.

Investigation of thermomagnetic convective flow in vertical layers between water and kerosene based magnetic fluids

In this article, the convective flow in a vertical layer subjected to a consistent magnetic field with nonzero gravity condition is investigated. One side of the vertical walls is heated, while the opposite side is cooling. The magnetic field strength, field orientation angle, magnetization effect, and thermal deviation of vertical walls play important roles as controlling parameters on the flow stabilization. The goal of this investigation is to analyze the flow characteristics and find out the significant distinction between water and kerosene based magnetic fluids under the variation of thermal and magnetic effects. The numerical results are obtained by the pseudo-spectral Chebyshev expansion method. The properties of all instability modes caused by three major mechanisms, namely; thermomagnetic, thermogravitational and magneto-gravitational are analyzed. In the normal magnetic field, the wave speed responds faster, and it is recognized by a relatively small wave number in water based fluid than that in kerosene based fluid. In oblique magnetic field, the waves propagate faster in both kerosene and water based fluids with the field inclination angle increases, but they still propagate slower in kerosene based fluid comparatively in water based fluid. According to the linear or non-linear magnetization law, both upward and downward propagating waves in kerosene based fluid propagate slower, and they are recognized by greater wave numbers than that in water based fluid. It is found that the basic flow in water based fluid is much more stable than in kerosene based fluid.

Stability analysis and control countermeasures of surrounding rock of gob-side entry formed by roof-cutting in inclined coal seams

The stability of the surrounding rock in the inclined coal seam stope is crucial for the safety of the gob-side entry. In this article, we systematically analyze the surrounding rock stability of the gob-side entry formed by roof-cutting (GEFR) in an inclined coal seam. We identify three forms of roof structure evolution in the formation process of GEFR and analyze the two main modules affecting the deformation of the surrounding rock structure. We determine the critical elements of surrounding rock deformation in different stages of the GEFR retaining process. Further, we propose a classification of the deformation of the surrounding rock structure of GEFR into stress and structural types during stabilization. We analyze the length of the gangue side's bearing area and calculate the lateral gangue's impact energy. We establish three instability modes of the roof based on the fractured state of the roof structure of the GEFR and provide a mechanical criterion of instability. Finally, based on the results of our theoretical analysis, we propose a control principle for the surrounding rock deformation of GEFR and establish countermeasures for controlling the roof-cutting angle and an asymmetric coupling support system. A field case study was conducted under conditions involving an inclined thick coal seam to investigate the surrounding rock deformation and overburden stress evolution using field monitoring data. The field test results confirm that the control measures of the control roof-cutting angle and the asymmetric coupling support system positively impact the stability of the surrounding rock of the roof-cutting entry in an inclined coal seam.

A nonlocal energy-informed neural network for peridynamic correspondence material models

This paper presents a nonlocal energy-informed neural network to address the inherent zero-energy mode instability in peridynamic correspondence material models. Starting from the principle of virtual work, the task of solving peridynamic equilibrium equation is reformulated as a variational minimum problem of total potential energy, serving as the natural loss function for neural network. By minimizing the potential energy of the peridynamic body, the proposed neural network effectively eliminates the zero-energy modes. Importantly, this approach preserves the original peridynamic formulation without introducing a supplementary force vector state or modifying the nonlocal deformation gradient tensor. Additionally, there is no need for an artificial damping coefficient in adaptive dynamic relaxation, and the high memory consumption in implicit schemes is avoided. To improve the prediction accuracy near boundaries and to impose boundary conditions consistently with the local continuum theory, variable horizon method is introduced. Comparative studies of the proposed neural network with analytical solutions, finite element analyses or other control methods are conducted to verify the feasibility and accuracy of the proposed neural network in suppressing zero-energy mode oscillations. Furthermore, the convergence of the proposed approach and the influence of different activation functions on the prediction accuracy and convergence rate are investigated.

On the stability of a pair of vortex rings

The growth of perturbations subject to the Crow instability along two vortex rings of equal and opposite circulation undergoing a head-on collision is examined. Unlike the planar case for semi-infinite line vortices, the zero-order geometry of the flow (i.e. the ring radius, core thickness and separation distance) and by extension the growth rates of perturbations vary in time. The governing equations are therefore temporally integrated to characterize the perturbation spectrum. The analysis, which considers the effects of ring curvature and the distribution of vorticity within the vortex cores, explains several key flow features observed in experiments. First, the zero-order motion of the rings is accurately reproduced. Next, the predicted emergent wavenumber, which sets the number of secondary vortex structures emerging after the cores come into contact, agrees with experiments, including the observed increase in the number of secondary structures with increasing Reynolds number. Finally, the analysis predicts an abrupt transition at a critical Reynolds number to a regime dominated by a higher-frequency, faster-growing instability mode that may be consistent with the experimentally observed rapid generation of a turbulent puff following the collision of rings at high Reynolds numbers.

Principle of fundamental resonance in hypersonic boundary layers: an asymptotic viewpoint

The fundamental resonance (FR) in the nonlinear phase of the boundary-layer transition to turbulence appears when a dominant planar instability mode reaches a finite amplitude and the low-amplitude oblique travelling modes with the same frequency as the dominant mode, together with the stationary streak modes, undergo the strongest amplification among all the Fourier components. This regime may be the most efficient means to trigger the natural transition in hypersonic boundary layers. In this paper, we aim to reveal the intrinsic mechanism of the FR in the weakly nonlinear framework based on the large-Reynolds-number asymptotic technique. It is found that the FR is, in principle, a triad resonance among a dominant planar fundamental mode, a streak mode and an oblique mode. In the major part of the boundary layer, the nonlinear interaction of the fundamental mode and the streak mode seeds the growth of the oblique mode, whereas the interaction of the oblique mode and the fundamental mode drives the roll components (transverse and lateral velocity) of the streak mode, which leads to a stronger amplification of the streamwise component of the streak mode due to the lift-up mechanism. This asymptotic analysis clearly shows that the dimensionless growth rates of the streak and oblique modes are the same order of magnitude as the dimensionless amplitude of the fundamental mode $(\bar {\epsilon }_{10})$ , and the amplitude of the streak mode is $O(\bar {\epsilon }_{10}^{-1})$ greater than that of the oblique mode. The main-layer solution of the streamwise velocity, spanwise velocity and temperature of both the streak and the oblique modes become singular as the wall is approached, and so a viscous wall layer appears underneath. The wall layer produces an outflux velocity to the main-layer solution, inclusion of which leads to an improved asymptotic theory whose accuracy is confirmed by comparing with the calculations of the nonlinear parabolised stability equations (NPSEs) at moderate Reynolds numbers and the secondary instability analysis (SIA) at sufficiently high Reynolds numbers.

Weakly nonlinear stability analysis of non-isothermal parallel flow in a vertical porous annulus

The study examines the stability of parallel airflow within a tall vertical coaxial circular annulus filled with a highly permeable porous medium under stable stratification. The linear stability theory predicts that the least unstable mode can be either axisymmetric or non-axisymmetric, depending on the values of the governing parameters. The curvature parameter, defined as the gap between coaxial circular cylinders, contributes to the stabilization of the flow. Depending on various controlling parameter values, the stably stratified non-isothermal annular parallel flow (SNAPF) can manifest three instability modes: thermal-shear, thermal-buoyant, and mixed or interactive. The instability type can change abruptly with Reynolds number, curvature parameter, and media permeability. A finite-amplitude instability analysis is examined using weakly nonlinear stability theory. The analysis demonstrates both subcritical and supercritical bifurcations near the instability boundary. The range of Reynolds numbers for subcritical bifurcation expands when switching from axisymmetric to non-axisymmetric disturbance. Bifurcation transitions between supercritical and subcritical occur due to changes in the least stable azimuthal mode. The study also investigates the equilibrium/threshold amplitude within the supercritical/subcritical instability regime, and it verifies the existence of subcritical/supercritical bifurcation through nonlinear kinetic energy balance. Furthermore, the finite-amplitude analysis anticipates that the lower critical Rayleigh number increases as the Reynolds number, curvature parameter, or media permeability decreases. An increase in the Reynolds number shifts the point of inflection in the velocity profile toward the inner cylinder, which subsequently leads to a reduction in the size of the core vortex region. In the subcritical instability regime, the radius of the primary vortex cell decreased significantly as the Rayleigh number increased. When the curvature is altered, a structural transition occurs in the isotherms from multicellular to unicellular.

Dynamics of acoustically-induced droplet instability

The advancement of the theory of droplet stability in the acoustic field is of significant value in improving ultrasonic atomization and ultrasonic levitation technology. In this work, in order to reveal the detailed mechanism of acoustic droplet instability and give the instability criterion for easy application, the dynamics of droplet instability in standing wave acoustic field (19.8 kHz) is studied by combining practical experiment, theoretical derivation and numerical calculation. The acoustic instability of the droplet occurring near the wave nodes is mainly manifested in two typical modes: disk instability and edge-sharpening instability. The appearance of these two instability modes depends on the relative magnitude of the standing wave field strength. Specifically, with the gradual enhancement of the intensity of the standing wave field, the instability mode of the droplet will gradually change from disc instability to edge-sharpened instability.The droplets show obvious self-accelerating expansion in the equatorial plane in the instability process. The positive feedback between the droplet aspect ratio and the negative pressure of acoustic radiation at the equator of the droplet is the reason for the above self-accelerating behavior. The theoretical results obtained through deduction indicate that the amplitude of the negative acoustic radiation pressure at the droplet equator is proportional to the square of the droplet aspect ratio. The surface tension of the droplet is the main factor hindering its deformation, while the acoustic radiation suction at the equator is the main factor driving the deformation of the droplet. Based on this, the force equilibrium equation of the droplet interface is established, and the dimensionless criterion of acoustic droplet instability, i.e. the acoustic Weber number <i>We</i><sub>a</sub>, is derived. When <i>We</i><sub>a</sub>≤1, the droplet interface stays in equilibrium, and when <i>We</i><sub>a</sub> >1, the equatorial acoustic suction is larger than the surface tension, and the droplet instability occurs, and the average error between the experimental results and the theoretical results is only 9%.