Absolute Instability Research Articles

Liquid plugs in narrow tubes: application to airway occlusion

We study liquid plugs in the pulmonary airways based on the two-phase axisymmetric weighted residual integral boundary-layer model of Dietze et al. (J. Fluid Mech., vol. 894, 2020, A17), which was originally developed to study liquid films coating the inner surface of a cylindrical tube in interaction with a core gas flow. The augmented form of this model, which was never applied beyond a proof of concept, allows for the representation of liquid pseudo-plugs. Here, we demonstrate its predictive power vs experiments and direct numerical simulations, in terms of the dynamics of plug formation and the characteristics of developed liquid plugs, such as their shape, flow field, speed and length, as well as the associated wall stresses and their spatial derivatives. In particular, we show that the augmented model allows us to establish a direct continuation path from travelling-wave solutions (TWS) to travelling-plug solutions (TPS). We then apply the model to predict mucus plugs in the conducting zone of the tracheobronchial tree, based on the lung architecture model of Weibel. We proceed by numerical continuation of travelling-state solutions in terms of the airway generation, whereby we impose the wavelength of the linearly most-amplified convective instability (CI) mode or that of the absolute instability (AI) mode. We identify the critical airway generation for liquid-plug formation (TWS/TPS transition), maximum potential for wall-stress-induced epithelial cell damage and CI/AI transition, and investigate how these phenomena are affected by the main control parameters, i.e. airway orientation vs gravity, air flow rate, mucus properties and airway size.

Absolute instability of power law liquid jets

Non-Newtonian fluid threads are common in many natural and synthetic processes. An appreciation of how such threads break into droplets has been a subject of study for a long time. In this paper, we investigate the absolute instability of a cylindrical thread, modeled as a power law fluid, falling under gravity surrounded by an inviscid medium. Particular attention is paid to investigating the effects of the gas-to-liquid density ratio and the Reynolds number as well as the influence of the flow index number on critical Weber numbers (which mark the transition between convective and absolute instability). Our results determine the convective to absolute instability boundary for a number of different parameter values.

Gravity-driven flow of liquid bridges between vertical fibres

Liquid bridges are formed when a flowing liquid interacts with multiple parallel fibres, as relevant to heat and mass transfer applications that utilize flow down fibre arrays. We perform a comprehensive experimental study of flowing liquid bridges between two vertical fibres whose spacing is controlled dynamically in our experimental apparatus. The bridge patterns exhibit a regular periodic spacing typical of absolute instability for low flow rates, but become spatially inhomogeneous above a critical flow rate where the base flow is convectively unstable. The shapes of individual bridges and their associated dynamics are measured, as they depend upon the liquid properties, and fibre geometry/spacing. The bridge length scales similarly to static bridges between parallel fibres. The bridge dynamics exhibits a dependence on viscosity and scale with the impedance. A simple energy balance is used to derive a scaling relationship for the bridge velocity that captures the general trend of our experimental data. Finally, we demonstrate that these scalings similarly apply when the fibres are dynamically separated or brought together.

Absolute and convective instabilities in a liquid film over a substrate moving against gravity

Absolute and convective instabilities in a liquid film over a substrate moving against gravity

The effect of asymmetry on the absolute instability of confined jets and wakes

The effect of asymmetry on the absolute instability of confined jets and wakes

Boundary layer stability on a rotating wind turbine blade section

Wall-resolved large eddy simulations of the flow on a rotating wind turbine blade section are conducted to study the rotation effects on laminar-turbulent transition on the suction surface. A chord Reynolds number of 1×105 and angles of attack (AoA) of 12.8°, 4.2°, and 1.2° are considered. Simulations with and without rotation are performed for each AoA. For AoA=12.8°, rotation increases the reverse flow from 7% of the free-stream velocity in the non-rotating case to 16% of it in the rotating case in the laminar separation bubble (LSB), triggering an oblique instability mechanism in the latter, leading to a faster breakdown to small-scale turbulence. However, rotation delays transition and reattachment in 3%–4% of the chord due to the acceleration of the boundary layer upstream of the LSB, which is subject to a strong adverse pressure gradient (APG), stabilizing Tollmien–Schlichting (TS) waves. Regarding AoA=4.2° and 1.2°, rotation slightly decelerates the attached boundary layer since the APG is very mild but accelerates the separated flow downstream, stabilizing Kelvin–Helmholtz (KH) modes. This mitigates the oblique instability mechanism and slows down the breakdown of KH vortices in the rotating case. In these cases, the transition location is little affected by rotation, possibly due to a rotation-independent absolute instability. Rotation also generates a spanwise tip-flow in the LSB for AoA=4.2° and 1.2°, which is highly unstable and triggers stationary and traveling crossflow modes. Nevertheless, the amplitudes of these modes remain too low to trigger transition.

On the Effect of Two-Dimensional Plasma Inhomogeneity in a Magnetic Island on the Parametric Excitation Threshold of Trapped Upper Hybrid Waves and the Level of Anomalous Absorption in ECRH Experiments

The effect of two-dimensional localization of an upper hybrid (UH) wave in a magnetic island is found. The influence of this effect on the threshold and saturation level of the absolute parametric decay instability of an extraordinary wave, which results in the excitation of two two-dimensional localized UH waves, is investigated.

Absolute and Global Instability of Plane Submerged Jets

Absolute and Global Instability of Plane Submerged Jets

Instability processes in short and long laminar separation bubbles

This work studies the link between the bursting process of a flat plate laminar separation bubble and the modification of the stability characteristics of the separated shear layer due to changes in the flow parameters. A vast population of short and long laminar separation bubbles was surveyed by means of Particle Image Velocimetry instrumentation for different values of the Reynolds number, the free-stream turbulence intensity and the streamwise pressure gradient. A fine-step variation of the free-stream velocity allowed us to determine the critical Reynolds number at which bursting occurs. Successively, the most amplified wavelength and frequency were computed for both the short and the long bubble regimes. Once scaled with the boundary layer displacement thickness at separation, the average wavenumber of the vortices shed by the bubble was found to be constant and equal to about 0.9 in the short regime, accordingly to previous studies. Differently, this quantity reduces to about 0.6 in the long bubble regime, and a marked change in the Strouhal number of vortex shedding occurs. Also, the temporal growth of spanwise vortices was seen to occur in the recirculation region of long type bubbles, being linked to an absolute instability of disturbances. The currently acquired data demonstrate the existing link between the bursting process of a laminar separation bubble and a marked change in the instability mechanisms driving the transition process of the boundary layer. A simplified correlation for the prediction of bursting is provided in this work as a function of the free-stream turbulence intensity and the streamwise pressure gradient.

Convective and absolute instabilities of double-diffusive convection with shear

In this study, we investigate the spatiotemporal instability of double-diffusive convection with and without a Couette flow, focusing mainly on the characters of transverse rolls. In the absence of shear, double-diffusive convection is always absolutely unstable even in the oscillatory instability regime, which is different from other flows that can also take the form of oscillatory convection. In the pure diffusive convection, before the transition from the oscillatory instability to steady instability, a saddle shift phenomenon is observed, which is related to the subcritical bifurcation of the steady branch. The presence of shear breaks the symmetry of oscillatory instability and along the neutral stability curve the spatiotemporal evolution of disturbance is determined by the competition between the shear intensity and the phase speed of oscillatory eigenmode traveling upstream. Therefore, as the shear intensity increases a transition from the absolute instability to the convective instability is expected, whereas as buoyancy strengthens the absolute instability eventually sets in again. On the other hand, the spatiotemporal instability of the sheared fingering convection is similar to the sheared Rayleigh–Bénard convection, in which the flow always undergoes a transition from the convective instability to absolute instability. In this case, increasing the Prandtl number or decreasing the diffusivity ratio between the two components, the region of convective instability expands due to the increasing viscous dissipation caused by the shear flow.

A zinc oxide resonant nano-accelerometer with ultra-high sensitivity

Nanoelectromechanical system accelerometers have the potential to be utilized in next-generation consumer electronics, inertial navigation, and seismology due to their low cost, small size, and low power consumption. There is an urgent need to develop resonant accelerometer with high sensitivity, precision and robustness. Here, a zinc oxide resonant nano-accelerometer with high sensitivity has been designed and prototyped using zinc oxide nanowires. Within a device two nanowires were symmetrically placed close to a notched flexure to evaluate acceleration based on differential resonant frequencies. Additionally, microleverages were integrated in the accelerometer to enhance its sensitivity by amplifying the inertial force. High performance of the accelerometer has been demonstrated by the measured absolute sensitivity (16.818 kHz/g), bias instability (13.13 μg at 1.2 s integration time) and bandwidth (from 4.78 to 29.64 kHz), respectively. These results suggest that zinc oxide nanowires could be a candidate to develop future nanoelectromechanical resonant accelerometer potentially used for inertial navigation, tilt measurement, and geophysical measurements.

Onset of absolute instability on a pitching aerofoil

A global transient linear stability analysis of the three-dimensional time-dependent flow around an aerofoil undergoing small-amplitude pitching motion is performed using the optimally time-dependent (OTD) framework. The most salient linear instabilities associated with the instantaneous basic state are computed and tracked over time. The resulting OTD modes reflect the variations in the basic state and can be used as predictors of its spatial and temporal evolution, including the formation of a laminar separation bubble and its gradual spanwise modulation via primary global instability, leading to secondary instability and finally rapid breakdown to turbulence. The study confirms and expands upon earlier stability analyses of the same case based on the local properties of spanwise averaged velocity profiles in the bubble that predicted the onset of absolute instability soon followed by rapid breakdown of the separation bubble. The three-dimensional structure of the most unstable OTD mode is extracted, which compares well with both the locally absolutely unstable mode and the evolution of the basic state itself.

Role of spontaneous thermal emissions in inflationary laser Raman instability

The role of thermal fluctuations on the stimulated Raman backscattering instability is investigated by means of Vlasov and particle-in-cell (PIC) simulations in a regime of strong linear Landau damping of the Langmuir wave. The instability is initially convective and amplifies thermal noise, leading to a low-amplitude back-scattered laser sideband. Linear Landau damping of the Langmuir sideband modifies and flattens the electron velocity distribution function at the resonant velocity, leading to a gradual decrease in the Landau damping rate and an increase in the convective amplification. The Langmuir wave traps electrons resulting in a rapid nonlinear absolute instability and large amplitude flashes of backscattered light off large amplitude Langmuir waves with trapped electrons, leading to the production of hot electrons. Conditions for simulating realistic thermal noise with Vlasov and PIC simulations are discussed and defined.

Absolute instability of moisture‐coupled waves on the equatorial beta‐plane

AbstractThe instabilities produced by a linear model of the tropical atmosphere coupled to a prognostic equation for water vapour are investigated. The basic model with no meridional wind supports unstable eastward‐propagating waves. For parameter regimes relevant to the Indo‐Pacific warm pool, the long‐time asymptotic behaviour of the unstable waves is found to be absolutely unstable, so that the amplitude of disturbances will grow in time at every point in the domain. The absolute instability of the system is realized at planetary length‐scales and intraseasonal frequencies. Other parameter choices for the system do not produce this same behaviour at these length‐ and time‐scales. It is shown that the resultant long‐time behaviour of the instability is characterized by roughly equal roles for temperature and moisture fluctuations in setting the thermodynamic tendency of the waves. With the inclusion of momentum damping, the phase speed of the absolutely unstable solution is about 7 ms. Addition of a strong background meridional moisture gradient, as in recent studies on the Madden–Julian Oscillation (MJO), appears to remove the absolute instability from the system. In a background state that varies slowly in the zonal direction, it is shown analytically that localized regions of instability may be formed, again using parameter choices relevant to the warm pool. The dynamics and thermodynamics of these local instabilities show some correspondence with the observed development of the MJO as it propagates through the warm pool.

On the stability of a particular class of one-dimensional states of dynamic equilibrium of the Vlasov–Poisson electron gas

The one-dimensional problem of the linear stability of dynamic states of local thermodynamic equilibria with respect to small perturbations was studied for the case when the Vlasov–Poisson electron gas contains electrons with a stationary distribution function that is constant in physical space and variable in a continuum of velocities. The absolute instability of all considered one-dimensional dynamic states of any local thermodynamic equilibrium was proved using the direct Lyapunov method. The scope of applicability of the Newcomb–Gardner–Rosenbluth sufficient condition for linear stability was outlined. An a priori exponential estimation was obtained for the rise of small one-dimensional perturbations from below. Analytic counterexamples to the spectral Newсomb–Gardner theorem and the Penrose criterion were constructed. Earnshaw’s theorem was extended from classical mechanics tostatistical one.

On the low-frequency flapping motion in flow separation

Transitional separating flow induced by a rectangular plate subjected to uniform incoming flow at Reynolds number (based on the incoming velocity and half plate height) 2000 is investigated using direct numerical simulation. The objective is to unveil the long-lasting mystery of low-frequency flapping motion (FM) in flow separation. At a fixed streamwise-vertical plane or from the perspective of previous experimental studies using pointwise or planar measurements, FM manifests as a low-frequency periodic switching between low and high velocities covering the entire separation bubble. The results indicate that in three-dimensional space, FM reflects an intricate evolution of streamwise elongated streaky structures under the influence of separated shear layer and mean flow reversal. The FM is an absolute instability, and is initiated through a lift-up mechanism boosted by mean flow deceleration near the crest of the separating streamline. At this particular location, the shear bends the vortex filament abruptly, so that one end is vertically struck into the first half of the separation bubble, whereas the other end is extended in the streamwise direction in the second half of the separation bubble. These two ends of vortex filament are mutually sustained and also stretched by the vertical acceleration and streamwise acceleration in the first and second halves of the separation bubble, respectively. This process periodically switches the low-velocity (or high-velocity) streaky structure to a high-velocity (or low-velocity) streaky structure encompassing the entire separation bubble, and thus flaps the separated shear layer up and down in the vertical direction. A ‘large vortex’ shedding manifests when the streaky structure switches signs. This large vortex is fundamentally different from the spanwise vortex shedding residing in the shear layer originated from the Kelvin–Helmholtz instability and successive vortex amalgamation. It is also believed that the three-dimensional evolution of streaky structures in the form of FM is applicable for both geometry- and pressure-induced separating flows.

Absolute instability of the boundary-layer flows due to rotating a spheroid

This paper explores local absolute instability in the boundary layer flow over two distinct families of rotating spheroids (prolate and oblate). While convective instability was established in earlier work by Samad and Garrett [1], this study delves into the potential occurrence of local absolute instability. Some results of local convective instability under the assumption of stationary vortices are reproduced for a more comprehensive investigation. The analysis considers viscous and streamline curvature effects, demonstrating that the localized mean flow within the boundary layer over either family of the rotating spheroid is absolutely unstable for each fixed value of the eccentricity parameter e∈[0,0.8]. For certain combinations of Reynolds number Re and azimuthal wave number β, a third branch (Branch 3) of the dispersion relation intersects Branch 1 at a pinch point, indicating absolute instability. Neutral curves depict regions that are absolutely unstable, while below critical Reynolds numbers, the region is either convectively unstable or stable. The paper also illustrates the effect of increasing eccentricity on spatial branches within both convectively and absolutely unstable regions. From lower to moderate latitudes, the stabilizing effect of e on the onset of absolute instability is robust for the prolate family and almost negligible for the oblate family. At high latitudes of the prolate spheroid, the stabilizing effect of e is fainter but persists until close to the equator. Conversely, at high latitudes of the oblate spheroid, the stabilizing effect of e is more pronounced. The paper discusses the implications of the parallel flow assumption employed in the analyses.

Reducing the Instability of an Optical Lattice Clock Using Multiple Atomic Ensembles

The stability of an optical atomic clock is a critical figure of merit for almost all clock applications. To this end, much optical atomic clock research has focused on reducing clock instability by increasing the atom number, lengthening the coherent interrogation times, and introducing entanglement to push beyond the standard quantum limit. In this work, we experimentally demonstrate an alternative approach to reducing clock instability using a phase estimation approach based on individually controlled atomic ensembles in a strontium (Sr) optical lattice clock. We first demonstrate joint Ramsey interrogation of two spatially resolved atom ensembles that are out of phase with respect to each other, which we call “quadrature Ramsey spectroscopy,” resulting in a factor of 1.36(5) reduction in absolute clock instability as measured with interleaved self-comparisons. We then leverage the rich hyperfine structure of Sr87 to realize independent coherent control over multiple ensembles with only global laser addressing. Finally, we utilize this independent control over four atom ensembles to implement a form of phase estimation, achieving a factor of greater than 3 enhancement in coherent interrogation time and a factor of 2.08(6) reduction in instability over an otherwise identical single-ensemble clock with the same local oscillator and the same number of atoms. We expect that multiensemble protocols similar to those demonstrated here will result in reduction in the instability of any optical lattice clock with an interrogation time limited by the local oscillator. Published by the American Physical Society 2024

Absolute and convective instability of a round jet emerging into an ambient medium of different viscosity

Absolute and convective instability of a round jet emerging into an ambient medium of different viscosity

An Experimental Database for the Analysis of Bursting of a Laminar Separation Bubble

The bursting phenomenon consists in the switch of a laminar separation bubble from a short to a long configuration. In the former case, reduced effects on profile pressure distribution are typically observed with respect to the attached condition. On the contrary, long bubbles provoke significant variations in the loading coefficient upstream of the separation position, with increased risk of stall of the lifting surfaces. The present work presents an experimental database describing separated boundary layers evolving under different Reynolds numbers, adverse pressure gradients and free-stream turbulence levels. Overall, more than 80 flow conditions were tested concerning short and long bubbles for the characterization of separated flows under turbine-like conditions. Measurements were performed on a flat plate geometry using a fast-response Particle Image Velocimetry (PIV) system. For each flow case, two sets of 6000 flow records were acquired with an acquisition frequency equal to 300 and 1000 Hz. Based on existing criteria for the identification of the bursting phenomenon, the flow cases were clustered in terms of short and long bubble states. Additionally, the kind of instability (i.e., convective or absolute) developing into the separated boundary layer was identified based on flow statistics. The present data captures the existing link between the bursting of a laminar separation bubble and the onset of the absolute instability of the separated shear layer, with stationary vortices forming in the dead air region.