Shear Flow Instability Research Articles

A study of ions' shear flow instabilities and parallel electron current in pure pair‐ion and pair‐ion‐electron plasmas

AbstractThe pair‐ion plasma has attained special attention due to equal masses and equal but opposite charges. The electrostatic fluctuations with sheared effect are investigated in ideal low‐density and low‐temperature pure pair‐ion (PI) and pair‐ion electron (PIE) plasmas in different cases. These instabilities are also studied with homogeneous and inhomogeneous density effects. The growing D'Angelo mode can become the electrostatic instability with shear flow in uniform PIE plasma. It is observed that the shear flow also gives rise to an electrostatic instability in temperature anisotropic pure pair‐ion plasma. It is also seen that in pair‐ion plasma, the presence of small concentration of electrons results in significant changings in real frequency and growth rate of ion acoustic waves (IAWs). The effect of current driven field aligned flow of electrons on IAWs is also discussed in this article. Kinetic and fluid models are used to study the growth rate of IAWs when both the ionic species have similar shear flow and when both the ionic species have different shear flow.

Effects of Crushing Characteristics on Rheological Characteristics of Particle Systems

A particle system’s large-deformation shear flow exhibits obvious random characteristics, making accurate modeling of the particle system difficult. Particle systems, which are frequently used in engineering, are prone to breakage, which introduces additional uncertainty into the system. The purpose of this study was to conduct ring-shear experiments on a variety of common engineering materials in order to quantify the effect of the dynamic crushing process of the particle system on the instability of shear flow. Different shear fracture characteristics may result in a change in the volume trend of the system, from dilatancy to shrinkage. While the mean value of the crushable system’s stress ratio does not increase with shear rate, the stress ratio’s fluctuation characteristic parameters are negatively correlated with shear rate. As particles become more easily sheared, the initial value of the stress ratio fluctuation increases. The effect of shear rate on the fluctuation in the system stress ratio is determined indirectly by the degree of system fragmentation. The study of the particle system’s fluctuation characteristics will aid in developing a stochastic dynamic model for the landslide system in the future, allowing for improved prediction and prevention of landslide disasters.

Vertical Shear Processes in River Plumes: Instabilities and Turbulent Mixing

In this paper, the problem of vertical shear flow instabilities at the base of a river plume and their consequences in terms of turbulent energy production and mixing is addressed. This study was carried out using 2D non-hydrostatic simulations and a linear stability analysis. The initial conditions used in these simulations were similar to those observed in river plumes near estuaries. Unstable stratified sheared flows follow three stages of evolution: (i) the generation of billows induced by vertical shear instabilities, (ii) intensification, and (iii) elongation. The elongation of the generated billows is related to the strain intensity, which depends on the physical setting involved (velocity shear, stratification thickness, and bottom slope). Two vertical shear instabilities were found in our study: the Holmboe and Kelvin–Helmholtz instabilities. The Kelvin–Helmholtz instability has a smaller growth time and longer wavelengths; the Holmboe instability is characterized by a longer growth time and shorter wavelengths. The Kelvin–Helmholtz instability is intensified when the bottom is sloped and for large shears. The Holmboe instability is stronger when the stratification thickness is reduced compared to the shear thickness and when the bottom is sloped. For mixing, the flow can be: (i) pre-turbulent, (ii) quasi-turbulent, or (iii) turbulent. The pre-turbulent flow corresponds to more mass mixing than momentum mixing and to more Eddy Kinetic Energy dissipation than Eddy Available Potential Energy dissipation. Such a flow is encountered over a flat bottom whatever the initial shear is. The quasi-turbulent and turbulent flows are reached when the bottom is sloped and when the stratification thickness is reduced. Using turbulent mixing statistics (mixing coefficients, mixing efficiency, Eddy Kinetic Energy, and Eddy Available Potential Energy dissipation rates), we showed that, despite their slow growth, Holmboe instabilities contribute more efficiently to turbulent mixing than Kelvin–Helmholtz instabilities. Holmboe instabilities are the only source of turbulent mixing when sharp density gradients are observed (small buoyancy thickness experiment). Our simulations highlight the contribution of the Holmboe instability to turbulent mixing.

Generation of Gravity-Capillary Wind Waves by Instability of a Coupled Shear-Flow

The theory of surface wave generation, in viscous flows, is modified by replacing the linear-logarithmic shear velocity profile, in the air, with a model which links smoothly the linear and logarithmic layers through the buffer layer. This profile includes the effects of air flow turbulence using a damped mixing-length model. In the water, an exponential shear velocity profile is used. It is shown that this modified and coupled shear-velocity profile gives a better agreement with experimental data than the coupled linear-logarithmic, non smooth profile, (in the air)–exponential profile (in the water), widely used in the literature. We also give new insights on retrograde modes that are Doppler shifted by the surface velocity at the air-sea interface, namely on the threshold value of the surface current for the occurrence of a second unstable mode.

Purely elastic linear instabilities in parallel shear flows with free-slip boundary conditions

We perform a linear stability analysis of viscoelastic plane Couette and plane Poiseuille flows with free-slip boundary conditions. The fluid is described by the Oldroyd-B constitutive model, and the flows are driven by a suitable body force. We find that both types of flow become linearly unstable, and we characterise the spatial structure of the unstable modes. By performing a boundary condition homotopy from the free-slip to no-slip boundaries, we demonstrate that the unstable modes are directly related to the least stable modes of the no-slip problem, destabilised under the free-slip situation. We discuss how our observations can be used to study recently discovered purely elastic turbulence in parallel shear flows.

Cold-Air Pool Processes in the Inn Valley During F\xf6hn: A Comparison of Four Cases During the PIANO Campaign

We present a comprehensive analysis of four south föhn events observed during the Penetration and Interruption of Alpine Foehn (PIANO) field campaign in the Inn Valley, Austria, in the vicinity of Innsbruck. The goal is to detect and quantify processes of cold-air pool (CAP) erosion by föhn as well as processes of föhn breakdown. Despite differences in föhn breakthrough and strength, the four cases exhibit similarities in CAP evolution: initially, the CAP experienced strongest warming in the centre of Innsbruck, where the föhn jet from the Wipp Valley interacted with the CAP in the Inn Valley. The resulting shear-flow instability at the föhn–CAP interface caused turbulent CAP erosion and, together with vertical warm-air advection, led to CAP depression over the city centre. This depression drove pre-föhn westerlies near the surface that caused cold-air advection inside the CAP west of the city centre and warm-air advection in the east. Ultimately, the latter contributed to stronger CAP erosion in the east than in the west. This stronger heating also explains the preferential initial föhn breakthrough at the valley floor east of Innsbruck. In two of the cases, subsequent westward propagation of the föhn–CAP boundary across the city accompanied by northerly (deflected) föhn winds led to a complete föhn breakthrough. Föhn breakdown occurred either by a backflow of the CAP remnant or by a cold-frontal passage. This study emphasizes the importance of both turbulence and advection in the CAP heat budget and reveal their large spatio–temporal variability.

Elastically driven Kelvin–Helmholtz-like instability in straight channel flow

Originally, Kelvin-Helmholtz instability (KHI) describes the growth of perturbations at the interface separating counterpropagating streams of Newtonian fluids of different densities with heavier fluid at the bottom. Generalized KHI is also used to describe instability of free shear layers with continuous variations of velocity and density. KHI is one of the most studied shear flow instabilities. It is widespread in nature in laminar as well as turbulent flows and acts on different spatial scales from galactic down to Saturn's bands, oceanographic and meteorological flows, and down to laboratory and industrial scales. Here, we report the observation of elastically driven KH-like instability in straight viscoelastic channel flow, observed in elastic turbulence (ET). The present findings contradict the established opinion that interface perturbations are stable at negligible inertia. The flow reveals weakly unstable coherent structures (CSs) of velocity fluctuations, namely, streaks self-organized into a self-sustained cycling process of CSs, which is synchronized by accompanied elastic waves. During each cycle in ET, counter propagating streaks are destroyed by the elastic KH-like instability. Its dynamics remarkably recall Newtonian KHI, but despite the similarity, the instability mechanism is distinctly different. Velocity difference across the perturbed streak interface destabilizes the flow, and curvature at interface perturbation generates stabilizing hoop stress. The latter is the main stabilizing factor overcoming the destabilization by velocity difference. The suggested destabilizing mechanism is the interaction of elastic waves with wall-normal vorticity leading to interface perturbation amplification. Elastic wave energy is drawn from the main flow and pumped into wall-normal vorticity growth, which destroys the streaks.

Pattern formation of quantum Kelvin-Helmholtz instability in binary superfluids

We study theoretically nonlinear dynamics induced by shear-flow instability in segregated two-component Bose-Einstein condensates in terms of the Weber number, defined by extending the past theory on the Kelvin-Helmholtz instability in classical fluids. Numerical simulations of the Gross-Pitaevskii equations demonstrate that dynamics of pattern formation is well characterized by the Weber number $We$, clarifying the microscopic aspects unique to the quantum fluid system. For $We \lesssim 1$, the Kelvin-Helmholtz instability induces flutter-finger patterns of the interface and quantized vortices are generated at the tip of the fingers. The associated nonlinear dynamics exhibits a universal behavior with respect to $We$. When $We \gtrsim 1$ in which the interface thickness is larger than the wavelength of the interface mode, the nonlinear dynamics is effectively initiated by the counter-superflow instability. In a strongly segregated regime and a large relative velocity, the instability causes transient zipper pattern formation instead of generating vortices due to the lack of enough circulation to form a quantized vortex per a finger. While, in a weakly segregating regime and a small relative velocity, the instability leads to sealskin pattern in the overlapping region, in which the frictional relaxation of the superflow cannot be explained only by the homogeneous counter-superflow instability. We discuss the details of the linear and nonlinear characteristics of this dynamical crossover from small to large Weber numbers, where microscopic properties of the interface become important for the large Weber number.

Solar wind interaction with dusty plasma produces electrostatic instabilities and solitons

It is shown that the solar wind interaction with dusty plasma in planetary magnetospheres gives rise to electrostatic instabilities and solitary structures. Non-Maxwellian electrons increase the growth rate of shear flow instability and reduce the amplitude of solitary pulses formed by the modified dust ion acoustic wave (mDIAW) in nonlinear regime. Dust number density plays the similar role. The kappa ( $\kappa $ ) and Cairns distribution functions are used to take into account the role of non-Maxwellian electrons in the presence of stationary dust and flowing ions along the external magnetic field with inhomogeneous velocity. This theoretical model is general and it can be applied to various dusty plasma environments such as interstellar medium, cometary tails and planetary magnetospheres. Here it has been applied to the Saturn’s $F$ -ring plasma.

The impact of magnetic fields on momentum transport and saturation of shear-flow instability by stable modes

The Kelvin–Helmholtz (KH) instability of a shear layer with an initially uniform magnetic field in the direction of flow is studied in the framework of 2D incompressible magnetohydrodynamics with finite resistivity and viscosity using direct numerical simulations. The shear layer evolves freely, with no external forcing, and thus broadens in time as turbulent stresses transport momentum across it. As with hydrodynamic KH, the instability here features a conjugate stable mode for every unstable mode in the absence of dissipation. Stable modes are shown to transport momentum up its gradient, shrinking the layer width whenever they exceed unstable modes in amplitude. In simulations with weak magnetic fields, the linear instability is minimally affected by the field, but enhanced small-scale fluctuations relative to the hydrodynamic case are observed. These enhanced fluctuations coincide with increased energy dissipation and faster layer broadening, with these features more pronounced in simulations with stronger fields. These trends result from the magnetic field reducing the effects of stable modes relative to the transfer of energy to small scales. As field strength increases, stable modes become less excited, thus transporting less momentum against its gradient. Furthermore, the energy that would otherwise transfer back to the driving shear because of the stable modes is instead allowed to cascade to small scales, where it is lost to dissipation. Approximations of the turbulent state in terms of a reduced set of modes are explored. While the Reynolds stress is well-described using just two modes per wavenumber at large scales, the Maxwell stress is not.

Large-eddy simulation of foehn-cold pool interactions in the InnValley during PIANO IOP 2.

Processes of cold‐air pool (CAP) erosion in an Alpine valley during south foehn are investigated based on a real‐case large‐eddy simulation (LES). The event occurred during the second Intensive Observation Period (IOP 2) of the PIANO field experiment in the Inn Valley, Austria, near the city of Innsbruck. The goal is to clarify the role of advective versus turbulent heating, the latter often being misrepresented in mesoscale models. It was found that the LES of the first day of IOP 2 outperforms a mesoscale simulation, is not yet perfect, but is able to reproduce the CAP evolution and structure observed on the second day of IOP 2. The CAP exhibits strong heterogeneity in the along‐valley direction. It is weaker in the east than in the west of the city with a local depression above the city. This heterogeneity results from different relative contributions and magnitudes of turbulent and advective heating/cooling, which mostly act against each other. Turbulent heating is important for faster CAP erosion in the east and advective cooling is important for CAP maintenance to the west of Innsbruck. The spatial heterogeneity in turbulent erosion is linked to splitting of the foehn into two branches at the mountain range north of the city, with a stronger eastward deflected branch. Intensification of the western branch at a later stage leads to complete CAP erosion also to the west of Innsbruck. Above the city centre, turbulent heating is strongest, and so is advective cooling by enhanced pre‐foehn westerlies. These local winds are the result of CAP heterogeneity and gravity‐wave asymmetry. This study emphasizes the importance of shear‐flow instability for CAP erosion. It also highlights the large magnitudes of advective and turbulent heating compared to their net effect, which is even more pronounced for individual spatial components.

A simple demonstration of shear-flow instability

We describe a simple classroom demonstration of a fluid-dynamic instability. The demonstration requires only a bucket of water, a piece of string, and some used tealeaves or coffee grounds. We argue that the mechanism for the instability, at least in its later stages, is two-dimensional barotropic (shear-flow) instability and we present evidence in support of this. We show results of an equivalent basic two-dimensional numerical non-linear model, which simulates behavior comparable to that observed in the bucket demonstration. Modified simulations show that the instability does not depend on the curvature of the domain, but rather on the velocity profile.

Kinetic study of transverse electron-scale interface instability in relativistic shear flows

Interfacial magnetic field structures induced by transverse electron-scale shear instability (mushroom instability) are found to be strongly associated with electron and ion dynamics, which in turn will influence the development of the instability itself. We find that high-frequency electron oscillations are excited normal to the shear interface. Also, on a larger time scale, the bulk of the ions are gradually separated under the influence of local magnetic fields, eventually reaching an equilibrium related to the initial shear conditions. We present a theoretical model of this behavior. Such separation on the scale of the electron skin depth will prevent different ions from mixing and will thereafter restrain the growth of higher-order instabilities. We also analyze the role of electron thermal motion in the generation of the magnetic field, and we find an increase in the instability growth rate with increasing plasma temperature. These results have potential for providing a more realistic description of relativistic plasma flows.

Indentation cracking in silicate glasses is directed by shear flow, not by densification

Over the past decades, constitutive relations have been developed to compute the mechanical response of silicate glasses at the continuum length scale. They are now reliable enough that we can calculate indentation induced stress and strain fields and examine the impact of material parameters on indentation response, and especially hardness, pile-up and stress fields. In contrast to a presently widespread assumption in the literature, we show that (shear) flow stress is the primary determinant of these properties, and that densification plays a secondary role in the indentation response of all the silicate glasses. This result applies even for large values of the densification at saturation because of the high ratio between effective volumetric yield stress (i.e. yield pressure) and flow stress. It is well-known that, depending upon composition, silicate glasses exhibit very different sensitivities to indentation cracking, although all other standard mechanical properties remain quite similar. We point out that material damage incurred through plastic shear flow, and especially shear flow instability and localization may well control crack initiation, which would resolve the paradox. Shear flow instability and damage has not been quantitatively investigated in detail in silicate glasses as yet, neither experimentally nor theoretically. However, we believe it is key to an in depth understanding of cracking resistance in silicate glasses.

Dipolar and Kelvin-Stuart’s cat’s eyes vortices in magnetoplasmas with non-Maxwellian electron distribution

Linear and nonlinear propagation characteristics of drift ion acoustic waves are analyzed in an inhomogeneous plasma comprising of warm ions having shear flow parallel to the magnetic field and electrons that are followed by a distribution which is dictated by spectral indices, $r$ and $q$ in low and high phase density regions. In the linear regime, the dispersion relation of the drift-ion acoustic wave is derived and the condition for the onset of shear flow instability is presented. It is found that condition for the emergence of shear flow instability gets modified by generalized $(r,q)$ distribution and ion to electron temperature ratio. In the nonlinear regime, vortex formation with non-Maxwellian electron distribution is investigated and the effects of low and high energy electrons in this context are explored in detail. Interestingly, it is found that unlike the dipolar vortices, the electrons in the high phase space density regions do not significantly affect the Kelvin-Stuart’s cat’s eyes structures, however, the converse is true for the electrons belonging to the regions of low phase space density. Estimates of the size of these vortex structures in space plasmas are also given where the distribution function presented here is frequently encountered.

Barotropic instability of shear flows

AbstractWe consider barotropic instability of shear flows for incompressible fluids with Coriolis effects. For a class of shear flows, we develop a new method to find the sharp stability conditions. We study the flow with Sinus profile in details and obtain the sharp stability boundary in the whole parameter space, which corrects previous results in the fluid literature. Our new results are confirmed by more accurate numerical computation. The addition of the Coriolis force is found to bring fundamental changes to the stability of shear flows. Moreover, we study dynamical behaviors near the shear flows, including the bifurcation of nontrivial traveling wave solutions and the linear inviscid damping. The first ingredient of our proof is a careful classification of the neutral modes. The second one is to write the linearized fluid equation in a Hamiltonian form and then use an instability index theory for general Hamiltonian partial differential equations. The last one is to study the singular and nonresonant neutral modes using Sturm‐Liouville theory and hypergeometric functions.

Air-Pocket Entrapment Caused by Shear Flow Instabilities in Rapid-Filling Pipes

AbstractUnderstanding air-pocket formation in closed conduits is important in urban water systems subject to rapid-filling conditions, such as in the case of stormwater sewers and tunnels during in...

Foehn-cold pool interactions in the Inn Valley during PIANO IOP2.

A case‐study is presented of a south foehn emanating from the Wipp Valley, Austria, which encountered a cold‐air pool (CAP) in the Inn Valley near the city of Innsbruck. The analysis is based on data collected during the second Intensive Observation Period of the Penetration and Interruption of Alpine Foehn (PIANO) field experiment. Foehn was initiated on 3 November 2017 by an eastward moving trough and terminated in the afternoon of 5 November 2017 by a cold front passage. On two occasions, reversed foehn flow deflected at the mountain ridge north of Innsbruck penetrated to the bottom of the Inn Valley. The first breakthrough occurred in the afternoon of 4 November 2017. It was transient and locally limited to the northwest of the city. The second (final) breakthrough occurred in the morning of 5 November 2017 and was recorded by all surface stations in the vicinity of Innsbruck. It started with a foehn air intrusion to the northeast of Innsbruck and continued with the westward propagation of the foehn–CAP boundary along the valley. Subsequently observed northerly winds above the city were caused by an atmospheric rotor. A few hours later and prior to the cold front passage, the CAP pushed back and lifted the foehn air from the ground. During both nights, shear flow instabilities formed at the foehn–CAP interface, which resulted in turbulent heating of the CAP and cooling of the foehn. However, this turbulent heating/cooling was partly compensated by other mechanisms. Especially in the presence of strong spatial CAP heterogeneity during the second night, heating in the CAP was most likely overcompensated by negative horizontal temperature advection.

David J. Benney: Nonlinear Wave and Instability Processes in Fluid Flows

David J. Benney (1930–2015) was an applied mathematician and fluid dynamicist whose highly original work has shaped our understanding of nonlinear wave and instability processes in fluid flows. This article discusses the new paradigm he pioneered in the study of nonlinear phenomena, which transcends fluid mechanics, and it highlights the common threads of his research contributions, namely, resonant nonlinear wave interactions; the derivation of nonlinear evolution equations, including the celebrated nonlinear Schrödinger equation for modulated wave trains; and the significance of three-dimensional disturbances in shear flow instability and transition.

On the spectral instability and bifurcation of the 2D-quasi-geostrophic potential vorticity equation with a generalized Kolmogorov forcing

In this article, the spectral instability and the associated bifurcations of the shear flows of the 2D quasi-geostrophic equation with a generalized Kolmogorov forcing are investigated. To determine the linear instability of the basic shear flow, we write the corresponding eigenvalue problem as a system of finite difference equations whose nontrivial solutions are expressed in the form of continued fractions. By a rigorous analysis of these continued fractions, we prove the existence of a number Rc such that if the control parameter R, which is proportional to the Reynolds number and the intensity of the curl of forcing, is over Rc, then the basic shear flow loses its stability. To shed light on the bifurcation involved in the loss of stability of the basic shear flow, a natural method is used to reduce the quasi-geostrophic equation to a system of ordinary differential equations. Based on numerical experiments on the coefficients of this reduced system, we show that both supercritical and subcritical Hopf bifurcations occur depending on the frequency of the generalized Kolmogorov forcing. Moreover, we investigate the double Hopf bifurcations which occur at critical aspect ratios. Our results show that in the double Hopf bifurcation case, two periodic solutions, one stable and the other unstable, bifurcate on R>Rc.