Kelvin-Helmholtz Instability Research Articles

Capabilities and limitations of smoothed particle hydrodynamics for the simulation of two‐phase flow instabilities

AbstractSmoothed particle hydrodynamics (SPH) is a mesh‐free, Lagrangian particle‐based method that is able to simulate multiphase flows in an economical manner. However, its ability to capture the flow regimes and regime transitions in two phase (liquid‐gas) internal flows, such as pipe or channel flows is not yet generally established. To address this lack in understanding, we first examine a laminar rising bubble case in order to evaluate the fluid‐fluid interface representation and transient interface evolution by the solver. With a focus towards the transition mechanism from a stratified flow regime to a slug flow regime, we investigate the Kelvin–Helmholtz instability (KHI) both qualitatively and quantitatively, initially focusing on a low density ratio () and then extending it to a high density ratio (). For the low density ratio, we conduct an analysis of the temporal evolution and demonstrate that the SPH solver captures the initial exponential growth in qualitative agreement with inviscid linear stability theory (LST) and reference numerical data for shear‐dominated flow with Richardson number . By conducting eight additional simulations for various for the high density ratio, we demonstrate that the numerically obtained parameter value for instability is around , which is in reasonable agreement with the theoretically expected value of . Based on the SPH results obtained for the range , we suggest a simple parameterization of the reduction of the effective growth rate proportional to .

Features of propagation in the atmosphere of nonlinear acoustic disturbances from pulse sources

The features of the propagation of nonlinear pulsed acoustic disturbances in the atmosphere are considered. Data are presented on the experimental observation of the formation of a shock front and the transition of a shock wave into a low-intensity acoustic wave with transformation of the pulse shape and expansion of the front at distances of more than 1000 km under conditions of both spherical and cylindrical propagation. The influence of Kelvin-Helmholtz instability during rapid gas compression on the formation of the shock front structure is discussed. Under atmospheric conditions, such instability significantly affects dissipative processes in the air and forms the front of a nonlinear wave.

Linear and nonlinear dynamics of self-consistent collisionless tearing modes in toroidal gyrokinetic simulations

We investigate tearing modes (TM) driven by current density gradient in collisionless tokamak plasmas by using the electromagnetic gyrokinetic simulation code ORB5. We elucidate the TM width by simulations for flat profiles, as the absence of background diamagnetic flows implies a small rotation speed, while finite gradients are included to investigate the TM rotation. For flat profiles, the initial saturation width of nonlinearly driven magnetic islands is related to the TM linear growth rate; however, large islands in the initial saturation phase are prone to current density redistribution that reduces the island width in the following evolution. Island-induced E×B and diamagnetic sheared flows develop at the separatrix, able to destabilize the Kelvin–Helmholtz instability (KHI). The KHI turbulence enhances a strong quadrupole vortex flow that reinforces the island decay, resulting in a strong reduction of the island width in an eventual steady state. This process is enhanced by trapped electrons. For finite gradients profile, the TM usually rotates in the electron diamagnetic direction but can change direction when the ion temperature gradient dominates the other gradients. The reduced growth of the TM by diamagnetic effects results in a moderate island size, which remains almost unchanged after the initial saturation. At steady state, strong zonal flows are nonlinearly excited and dominate the island rotation, as expected from previous theoretical and numerical studies. When β is increased, the TM mode is suppressed and a mode with the same helicity but with twisting parity, coupled with the neighboring poloidal harmonics, is destabilized, similar to the kinetic ballooning mode.

Suppression of the Kelvin-Helmholtz instability by coating in the double-cone ignition scheme

Suppression of the Kelvin-Helmholtz instability by coating in the double-cone ignition scheme

On the robustness of high-order upwind summation-by-parts methods for nonlinear conservation laws

We use the framework of upwind summation-by-parts (SBP) operators developed by Mattsson (2017, doi:10.1016/j.jcp.2017.01.042) and study different flux vector splittings in this context. To do so, we introduce discontinuous-Galerkin-like interface terms for multi-block upwind SBP methods applied to nonlinear conservation laws. We investigate the behavior of the upwind SBP methods for flux vector splittings of varying complexity on Cartesian as well as unstructured curvilinear multi-block meshes. Moreover, we analyze the local linear/energy stability of these methods following Gassner, Svärd, and Hindenlang (2022, doi:10.1007/s10915-021-01720-8). Finally, we investigate the robustness of upwind SBP methods for challenging examples of shock-free flows of the compressible Euler equations such as a Kelvin-Helmholtz instability and the inviscid Taylor-Green vortex.

Coupled Richtmyer–Meshkov and Kelvin–Helmholtz instability on a shock-accelerated inclined single-mode interface

The coupling of Richtmyer–Meshkov instability (RMI) and Kelvin–Helmholtz instability (KHI), referred to as RM-KHI, on a shock-accelerated inclined single-mode air–SF $_6$ interface is studied through shock-tube experiments, focusing on the evolution of the perturbation distributed along the inclined interface. To clearly capture the linear (overall linear to nonlinear) evolution of RM-KHI, a series of experiments with a weak (relatively strong) incident shock is conducted. For each series of experiments, various $\theta _{i}$ (angle between incident shock and equilibrium position of the initial interface) are considered. The nonlinear flow features manifest earlier and develop faster when $\theta _{i}$ is larger and/or shock is stronger. In addition, the interface with $\theta _{i}>0^{\circ }$ evolves obliquely along its equilibrium position under the effect of KHI. RMI dominates the early-time amplitude evolution regardless of $\theta _{i}$ and shock intensity, which arises from the discrepancy in the evolution laws between RMI and KHI. KHI promotes the post-early-stage amplitude growth and its contribution is related positively to $\theta _{i}$ . An evident exponential-like amplitude evolution behaviour emerges in RM-KHI with a relatively strong shock and large $\theta _{i}$ . The linear model proposed by Mikaelian (Phys. Fluids, vol. 6, 1994, pp. 1943–1945) is valid for RM-KHI within the linear period. In contrast, the adaptive vortex model (Sohn et al., Phys. Rev. E, vol. 82, 2010, p. 046711) can effectively predict both the interface morphology and overall amplitude evolutions from the linear to nonlinear regimes.

Hybrid-Vlasov Modelling of Ion Velocity Distribution Functions Associated with the Kelvin–Helmholtz Instability with a Density and Temperature Asymmetry

The Kelvin–Helmholtz instability (KHI), characterized by vortices forming at a perturbed velocity shear layer, is a prominent candidate mechanism for mass, momentum, and energy transport across boundaries with velocity shear in various space plasma environments. It is of particular interest at the flanks of Earth’s magnetopause, which separates the plasma of the magnetosphere from the adjacent shocked solar wind flow in the magnetosheath. In the present study, we use local hybrid-Vlasov simulations to investigate the ion velocity distribution functions (VDFs) associated with KHI in a magnetopause-like, transverse velocity shear layer setting (magnetic field perpendicular to the shear plane). We look for signatures of ion finite Larmor radius (FLR) effects, which could be utilized in spacecraft measurements to recognize when such effects are active, influencing KHI evolution and driving plasma mixing. We show that when a density/temperature asymmetry exists across the shear layer, FLR effects produce a heat flux along the vortex edges. With a magnitude (≳0.1 mW m−2) that is a significant fraction of the total magnetosheath energy flux, the heat flux provides a distinct signature that could be measured with a single spacecraft. During the late nonlinear stage of KHI, mixed non-Maxwellian ion VDFs are additionally found within the vortices. Our results are also valid in the presence of a small magnetic shear across the magnetopause.

Quantum analog to flapping of flags: interface instability for co-flow binary superfluids

We study the interface dynamics in immiscible binary superfluids using its holographic description, which naturally consists of an inviscid superfluid component and a viscous normal fluid component. We give the first theoretical realization of interface instability for two superfluid components moving with identical velocity, providing a quantum analog to the flapping of flags that is common in daily life. This behavior is in sharp contrast to the one from Gross-Pitaevskii equation for which no such co-flow instability develops in an isolated uniform system because of Galilean invariance. The real time evolution triggered by the dynamical instability exhibits intricate nonlinear patterns leading to quantum turbulence reminiscent of the quantum Kelvin-Helmholtz instability. Moreover, we show that such interface dynamics is essentially different from the Landau instability for which the frictionless flow becomes thermodynamically unstable above a critical superfluid velocity. Our study uncovers the rich interface dynamics of quantum fluids and the emergence of complex flow phenomena.

Numerical Study of High-g Combustion Characteristics in a Channel with Backward-Facing Steps

High gravity (high-g) combustion can significantly increase flame propagation speed, thereby potentially shortening the axial length of aero-engines and increasing their thrust-to-weight ratio. In this study, we utilized the large eddy simulation model to investigate the combustion characteristics and flame morphology evolution of premixed propane–air flames in a channel with a backward-facing step. The study reveals that both the increase in centrifugal force and flow velocity can enhance pressure fluctuations during combustion and increase the turbulence intensity. The presence of centrifugal force promotes the occurrence of Rayleigh–Taylor instability (RTI) between hot and cold fluids. The combined effects of RTI and Kelvin–Helmholtz instability (KHI) enhance the disturbance between hot and cold fluids, shorten the fuel combustion time, and intensify the dissipation of large-scale vortices. The increase in fluid flow velocity can raise the flame front’s hydrodynamic stretch rate, thereby enhancing the turbulence level during combustion to a certain extent and increasing the fuel consumption rate. When a strong centrifugal force is applied, the global flame propagation speed can be more than doubled. Within a certain range, the increase in high-g field strength can enhance the intensity of RTI and accelerate the transition of RTI to the nonlinear stage.

Multi-scale processes of the Kelvin-Helmholtz instability at Earth’s magnetopause

The Kelvin-Helmholtz Instability (KHI) is a large scale convective instability which occurs anywhere the velocity shear between two fluids is large, such as Earth’s magnetopause where the fast flowing magnetosheath abuts the relatively stagnant outer magnetosphere. The KHI was initially believed to contribute only to energy and momentum transfer from the solar wind to the magnetosphere, but was eventually shown to support mass transport and plasma heating. Recent advancements in in-situ observational capabilities and high scale computer modeling have once again shifted our understanding of the KHI from a large scale process, to an active environment which connects the global and kinetic scales through a variety of multi-scale processes and phenomena. In this mini-review, we provide an update on the latest findings in Kelvin-Helmholtz (KH) related processes at kinetic scales and the effects of the global environment on KH development.

Suppression of the superfluid Kelvin-Helmholtz instability due to massive vortex cores, friction and confinement

We characterize the dynamical instability responsible for the breakdown of regular rows and necklaces of quantized vortices that appear at the interface between two superfluids in relative motion. Making use of a generalized point-vortex model, we identify several mechanisms leading to the suppression of this instability. They include a non-zero mass of the vortex cores, dissipative processes resulting from the interaction between the vortices and the excitations of the superfluid, and the proximity of the vortex array to the sample boundaries. We show that massive vortex cores not only have a mitigating effect on the dynamical instability, but also change the associated scaling law and affect the direction along which it develops. The predictions of our massive and dissipative point-vortex model are eventually compared against recent experimental measurements of the maximum instability growth rate relevant to vortex necklaces in a cold-atom platform.

Observations of avalanche–substrate interactions in the Iymek rock avalanche deposit: A possible causative mechanism

Ubiquitous and complex avalanche–substrate interactions during rock avalanche emplacement have attracted widespread attention in recent years and are regarded as vital processes influencing mobility and damage potential through rapid changes in avalanche mechanical properties. However, the fundamental interaction mechanisms of avalanche mass on substrate and the resultant effect on mobility have yet to be elucidated for natural events. To better understand the mechanics of avalanche–substrate interactions, we present a detailed study on the spectacular synsedimentary deformation structures at the bottom of the gigantic Iymek rock avalanche deposit, including undulose structures, flame structures, mixed textures, clastic dikes, and cracked gravels. The cracked gravels demonstrate that the overriding avalanche mass exited high-energy shearing on the avalanche–substrate interface, where the stress in substrate far exceeded the overburden from the avalanche mass during the avalanche–substrate interaction. Along with high-energy shearing, two different interaction modes with the change of substrate materials are identified, i.e., the Kelvin–Helmholtz instability (KHI) characterized by undulose-to-flame structure transitions, and the Raleigh–Taylor instability (RTI) characterized by the formation of clastic dikes. The KHI is interpreted as a result of the growth of shear instabilities induced by high-energy shearing along the avalanche–substrate interface. The RTI is associated with local liquefaction of the water-bearing sandy substrate and was mainly induced by the high-frequency ground vibrations generated by high-energy shearing. Therefore, we propose that the overriding avalanche mass exited high-energy shearing on the substrate during the avalanche–substrate interaction, which motivated two predominant physical processes of the KHI and RTI along the avalanche–substrate interface. The shear-induced KHI is a potential mechanism of erosion and entrainment in rock avalanches and is responsible for promoting the incorporation of substrate materials into moving avalanche mass. These results not only yield profound insights into the interaction behaviours between rock avalanches and substrates but also provide a fundamental geological prototype to motivate further modelling work to elucidate rock avalanche dynamics.

On Kelvin-Helmholtz instability of particulate two-fluid flow

On Kelvin-Helmholtz instability of particulate two-fluid flow

Identification of Kelvin-Helmholtz generated vortices in magnetised fluids

The Kelvin-Helmholtz Instability (KHI), arising from velocity shear across the magnetopause, plays a significant role in the viscous-like transfer of mass, momentum, and energy from the shocked solar wind into the magnetosphere. While the KHI leads to growth of surface waves and vortices, suitable detection methods for these applicable to magnetohydrodynamics (MHD) are currently lacking. A novel method is derived based on the well-established λ-family of hydrodynamic vortex identification techniques, which define a vortex as a local minimum in an adapted pressure field. The J×B Lorentz force is incorporated into this method by using an effective total pressure in MHD, including both magnetic pressure and a pressure-like part of the magnetic tension derived from a Helmholtz decomposition. The λMHD method is shown to comprise of four physical effects: vortical momentum, density gradients, fluid compressibility, and the rotational part of the magnetic tension. A local three-dimensional MHD simulation representative of near-flank magnetopause conditions (plasma β’s 0.5–5 and convective Mach numbers Mf∼0.4) under northward interplanetary magnetic field (IMF) is used to validate λMHD. Analysis shows it correlates well with hydrodynamic vortex definitions, though the level of correlation decreases with vortex evolution. Overall, vortical momentum dominates λMHD at all times. During the linear growth phase, density gradients act to oppose vortex formation. By the highly nonlinear stage, the formation of small-scale structures leads to a rising importance of the magnetic tension. Compressibility was found to be insignificant throughout. Finally, a demonstration of this method adapted to tetrahedral spacecraft observations is performed.

Occurrence of Kelvin–Helmholtz Instability at Lunar Distance Magnetopause: ARTEMIS Observation

Kelvin–Helmholtz waves can be observed frequently at the near-Earth magnetopause and play an important role in the transport of particles, momentum, and energy from the solar wind to the magnetosphere. This work analyzes the occurrence of Kelvin–Helmholtz instability (KHI) at lunar distance magnetopause, which has not been thoroughly studied currently based on Acceleration, Reconnection, Turbulence, and Electrodynamics of the Moon's Interaction with the Sun satellite observations, and it also investigates the effect of the upstream solar wind and interplanetary magnetic field (IMF). Statistical results show that (1) the occurrence rate is about 15% of the time at lunar distance, lower than at the flank magnetopause, and (2) the occurrence rate decreases with the magnetoacoustic Mach number, Alfvén Mach number, solar wind velocity, and dynamic pressure but only shows a slightly positive correlation with solar wind density. Unlike at the dayside magnetopause, the occurrence rate of KHI diminishes as the solar wind velocity increases at the lunar distance magnetopause, and (3) the occurrence rate decreases with IMF amplitude and is influenced by IMF orientation. As a function of the IMF clock angle, the occurrence rate reaches its maximum at ∼24% when the clock angle is zero. The statistical results are basically consistent with the currently accepted linear theory of KHI, except for a lower rate for higher-speed solar wind. This work contributes to understanding the excitation and evolution of KHI along the magnetopause and plasma transport process in the tail magnetopause.

Numerical simulation of the primary breakup of fuel jet with incoming positive velocity gradient

To study the breakup process of fuel jets in air crossflow with a positive velocity gradient, the Volume of Fluid (VOF) method and adaptive grid technology are combined to simulate the two-phase flow of gas and liquid. A comparative analysis is conducted on the breakup and corresponding flow characteristics of direct fuel jets under uniform and positive velocity gradient airflow. The simulation results demonstrate that the morphological changes of the fuel column are caused by factors such as gas-liquid shear and asymmetric airflow vortices. The fuel jet undergoes primary breakup, which mainly contains columnar and surface breakup. The columnar breakup is dominated by Rayleigh-Taylor (R-T) instability, while the surface breakup is dominated by Kelvin-Helmholtz (K-H) instability. Compared with uniform flow, the expansion angle in the positive velocity gradient incoming flow increases by an average of 9.2%, and the wavelength of the surface wave increases by an average of 34%.

Transverse Oscillations and Kelvin–Helmholtz Instability in Curved Arcade Loops with Siphon Flows

The effect of plasma flow in curved arcade loops on transverse waves and oscillations is examined analytically. The model under study is a semicircular magnetic slab with finite transverse extensions and a mass flow inside, in the zero-β plasma approximation. It is found that in the quasi-perpendicular propagation limit, the model supports two fast surface modes: one with higher (FSW+) and another with lower (FSW−) frequency. For a weak flow, the frequency of the FSW+ (FSW−) increases (decreases) as the flow speed grows in both propagating and quasi-standing wave regimes. We show that the FSW+ and FSW− are subjected to the Kelvin–Helmholtz (KH) instability, and the threshold flow is greater (less than) the internal Alfvén speed for the FSW+ (FSW−). The presence of plasma flow results in modifying the period ratio P 1/2P 2 of the fundamental harmonic to the first overtone with P 1/2P 2 less (more) than 1 for the FSW+ (FSW−), and this effect degenerates in the straight waveguide limit. The sub-Alfvénic flow can prohibit resonant absorption of kink modes when the frequencies of the FSW+ and FSW− become out of the Alfvén continuum. It is also shown that in the static case and for a weak flow case, the FSW+ (FSW−) is interpreted as a vertically (horizontally) polarized kink mode, while for moderate flow, both modes have oblique polarization. We apply the developed theory to interpret the observational cases of kink oscillations in coronal loops with signatures of a siphon flow and the onset of KH instability induced by the blowout jet along a loop-shaped magnetic structure.

Nonlinear, single-mode, two-dimensional Rayleigh-Taylor instability in ideal media.

A model for the single mode, two-dimensional Rayleigh-Taylor instability in ideal, incompressible, immiscible, and inviscid fluids is developed as an extension of a previous linear model based on the Newton's second law [A. R. Piriz et al., Am. J. Phys. 74, 1095 (2006)0002-950510.1119/1.2358158]. It describes the transition from linear to nonlinear regimes and takes into account the mass of fluids participating in the motion during the instability evolution, including the laterally displaced mass. This latter feature naturally leads to the bubble and spike velocity saturation without requiring the usual drag term necessary in the well-known buoyancy-drag model (BDM). In addition, it also provides an explanation to the latter phase of bubble reacceleration without appealing to the vorticity generation due to the Kelvin-Helmholtz instability. The model is in perfect agreement with the BDM buoyancy-drag model, but, apart from extending its range of application, it solves many of its issues of concern and provides a more consistent physical picture.

A comprehensive investigation on flame flickering characteristics of premixed conical flame at different inclination angles

To thoroughly investigate how the inclination angle affects the flickering of premixed conical flames, a series of experiments and simulations were carried out. Propane-air conical flames were established on a Bunsen burner, and various inclination angles were tested, resulting in a wide range of flame flickering frequency data. The findings revealed that the further the inclination angle deviates from 0°, the lower the flickering frequency. Consequently, an empirical correlation that factors in the inclination angle was developed. To gain a more comprehensive understanding of the flame flickering behavior under different gas inclination angles, researchers utilized Particle Image Velocimetry (PIV) and numerical simulation to visualize the velocity fields of a typical flame. The results demonstrated that deviated inclination angles not only alter the shear strength between the burnt gas and surrounding gas but also significantly change the flame flickering mode. These factors lead to various Kelvin-Helmholtz instability patterns and vortex shedding modes, ultimately impacting flickering frequency.

Kelvin-Helmholtz instability and heating in oscillating loops perturbed by power-law transverse wave drivers

Context. Instabilities in oscillating loops are believed to be essential for dissipating the wave energy and heating the solar coronal plasma. Aims. Our aim is to study the development of the Kelvin-Helmholtz (KH) instability in an oscillating loop that is driven by random footpoint motions. Methods. Using the PLUTO code, we performed 3D simulations of a straight gravitationally stratified flux tube. The loop footpoints are embedded in chromospheric plasma, in the presence of thermal conduction and an artificially broadened transition region. Using drivers with a power-law spectrum, one with a red noise spectrum and one with the low-frequency part subtracted, we excited standing oscillations and the KH instability in our loops, after one-and-a-half periods of the oscillation. Results. We see that our broadband drivers lead to fully deformed, turbulent loop cross-sections over the entire coronal part of the loop due to the spatially extended KH instability. The low RMS velocity of our driver without the low-frequency components supports the working hypothesis that the KH instability can easily manifest in oscillating coronal loops. We report for the first time in driven transverse oscillations of loops the apparent propagation of density perturbations due to the onset of the KH instability, from the apex towards the footpoints. Both drivers input sufficient energy to drive enthalpy and mass flux fluctuations along the loop, while also causing heating near the driven footpoint of the oscillating loop, which becomes more prominent when a low-frequency component is included in the velocity driver. Finally, our power-law driver with the low-frequency component provides a RMS input Poynting flux of the same order as the radiative losses of the quiet-Sun corona, giving us promising prospects for the contribution of decayless oscillations in coronal heating.