Numerical modeling of Kelvin–Helmholtz instability by using potential equation

Kelvin–Helmholtz (KH) instability is simulated using dissipative particle dynamics (DPD) at the mesoscopic particle level. To model two-phase flow, the ‘color’ repulsion model is introduced to describe binary fluids according to the Rothman–Keller method. The simulated results are compared with similar experiment and simulation using other techniques, and the work concludes that DPD is a promising method for simulating these systems. Furthermore, through the model and numerical simulation, the effects of intermiscibility, temperature, magnitude of velocity difference, and density ratio on the KH instability are investigated, respectively. It is shown that the poor intermiscibility reduces the mixing of two fluids and weakens the eddy currents. It is also found that as the temperature increases, the turbulence feature, i.e. plume-like structures, is more obvious. It is also revealed that as the initial horizontal velocity difference increases, the interface rolls up faster and higher. And it is also observed that as the density ratio increases, the KH instability becomes more suppressed.

Recent advancement in numerical techniques for Vlasov simulations and their application to cross-scale coupling in the plasma universe are discussed. Magnetohydrodynamic (MHD) simulations are now widely used for numerical modeling of global and macroscopic phenomena. In the framework of the MHD approximation, however, diffusion coefficients such as resistivity and adiabatic index are given from empirical models. Thus there are recent attempts to understand first-principle kinetic processes in macroscopic phenomena, such as magnetic reconnection and the Kelvin–Helmholtz (KH) instability via full kinetic particle-in-cell and Vlasov codes. In the present study, a benchmark test for a new four-dimensional full electromagnetic Vlasov code is performed. First, the computational speed of the Vlasov code is measured and a linear performance scaling is obtained on a massively parallel supercomputer with more than 12 000 cores. Second, a first-principle Vlasov simulation of the KH instability is performed in order to evaluate current status of numerical techniques for Vlasov simulations. The KH instability is usually adopted as a benchmark test problem for guiding-center Vlasov codes, in which a cyclotron motion of charged particles is neglected. There is not any full electromagnetic Vlasov simulation of the KH instability; this is because it is difficult to follow E⃗×B⃗ drift motion accurately without approximations. The present first-principle Vlasov simulation has successfully represented the formation of KH vortices and its secondary instability. These results suggest that Vlasov code simulations would be a powerful approach for studies of cross-scale coupling on future Peta-scale supercomputers.

Thermal convective instability is investigated in a thermally stratified plasma in the presence of shear flow, which is known to give rise to the Kelvin–Helmholtz (KH) instability. We examine how the KH instability and magnetothermal instability (MTI) affect each other. Based on the sharp boundary model, the KH instability coupled with the MTI is studied. We present the growth rate and instability criteria. The shear flow is shown to significantly alter the critical condition for the occurrence of thermal convective instability.

The impact of external force on compressible Kelvin–Helmholtz (KH) instability, considering hydrodynamic and thermodynamic nonequilibrium (TNE) effects during its evolution, is analyzed using a two-component discrete Boltzmann method. The results show that stronger external forces lead to a more complex evolution of the KH instability, causing significant changes in physical gradients, material mixing, and TNE behaviors. Physically, a higher external force amplifies compressive and rarefactive effects and disturbance waves, which in turn makes the KH evolution more intricate. Additionally, when the direction of external force aligns with the one of the initial density gradient, the KH vortex is resisted; otherwise, the KH and Rayleigh–Taylor instabilities are promoted. These results enrich our understanding of the mixing behavior in the compressible KH instability under external forces and provide a new perspective for experimental research and macroscopic model improvement.

Kelvin–Helmholtz instability in a twisting solar polar coronal hole jet observed by SDO/AIA

Context. Hard X-ray (HXR) sources are frequently observed near the top of solar flare loops, which are also bright in soft X-ray (SXR) and extreme ultraviolet (EUV) wavebands. We revisit a recent scenario proposed by Fang et al. (2016) to trigger loop-top turbulence in flaring loops, which can help explain variations seen in SXR and EUV brightenings and potentially impact and induce HXR emission. It is conjectured that evaporation flows from flare-impacted chromospheric footpoints interact with each other near the loop top and produce turbulence via the Kelvin–Helmholtz instability (KHI). Aims. By performing a rigorous parameter survey, in which we vary the duration, total amount, and asymmetry of the energy deposition at both footpoints, we assess the relevance of the KHI in triggering and sustaining loop-top turbulence. We synthesize SXR and EUV emission and discuss the possibility of HXR emission through bremsstrahlung or inverse Compton processes, which scatter SXR photons to HXR photons via the inverse Compton mechanism. Methods. We performed 2.5D numerical simulations in which the magnetohydrodynamic model incorporates a realistic photosphere to coronal stratification, parametrized heating, radiative losses, and field-aligned anisotropic thermal conduction. We focus on the trigger of the KHI and the resulting turbulence, as well as identify various oscillatory patterns that appear in the evolutions. Results. We find that a M2.2-class related amount of energy should be deposited in less than four minutes to trigger a KHI interaction. Slower deposition, or lesser energy (< 0.33 × 1029 ergs) rather leads to mere loop-top compression sites bounded by shocks, without KHI development. Asymmetry in the footpoint deposition determines whether the KHI turbulent zone gets produced away from the apex, and asymmetric cases can show a slow-mode mediated, periodic displacement of the turbulent zone. Our reference simulation further demonstrates a clear 25 s periodicity in the declining phase of the SXR light curve, wherein compressional effects dominate. Conclusions. When turbulence is produced in the loop apex, an index of −5/3 can be found in the spectra of velocity and magnetic field fluctuations. Typical values for M-class flares routinely show KHI development. The synthesized SXR light curve shows a clear periodic signal related to the sloshing motion of the vortex pattern created by the KHI.

The Kelvin–Helmholtz instability (KHI) is a ubiquitous physical process in ordinary fluids and plasmas, frequently observed also in space environments. In this paper, kinetic effects at proton scales in the nonlinear and turbulent stage of the KHI have been studied in magnetized collisionless plasmas by means of hybrid Vlasov–Maxwell simulations. The main goal of this work is to point out the back-reaction on particles triggered by the evolution of such instability, as energy reaches kinetic scales along the turbulent cascade. Interestingly, turbulence is inhibited when KHI develops over an initial state that is not an exact equilibrium state. On the other hand, when an initial equilibrium condition is considered, energy can be efficiently transferred toward short scales, reaches the typical proton wavelengths, and drives the dynamics of particles. As a consequence of the interaction of particles with the turbulent fluctuating fields, the proton velocity distribution deviates significantly from the local thermodynamic equilibrium, the degree of deviation increasing with the level of turbulence in the system and being located near regions of strong magnetic stresses. These numerical results support recent space observations from the Magnetospheric MultiScale mission of ion kinetic effects driven by the turbulent dynamics at Earth’s magnetosheath and by the KHI in Earth’s magnetosphere.

It is well established that the magnetically structured solar atmosphere supports the propagation of MHD waves along various kind of jets including also the solar wind. It is well-known as well that under some conditions, namely high enough jet speeds, the propagating MHD modes can become unstable against to the most common Kelvin--Helmholtz instability (KHI). In this article, we explore how the propagation and instability characteristics of running along a slow solar wind MHD modes are affected when they are investigated in the framework of the ideal Hall-magnetohydrodynamics. Hall-MHD is applicable if the jet width is shorter than or comparable to the so called Hall parameter $l_\mathrm{Hall} = c/\omega_\mathrm{pi}$ (where $c$ is the speed of light and $\omega_\mathrm{pi}$ is the ion plasma frequency). We model the solar wind as a moving with velocity $\vec{v}_0$ cylindrical flux tube of radius $a$, containing incompressible plasma with density $\rho_\mathrm{i}$ permeated by a constant magnetic field $\vec{B}_\mathrm{i}$. The surrounding plasma is characterized with its density $\rho_\mathrm{e}$ and magnetic field $\vec{B}_\mathrm{e}$. The dispersion relation of MHD waves is derived in the framework of both standard and Hall-MHD and is numerically solved with input parameters: the density contrast $\eta = \rho_\mathrm{e}/\rho_\mathrm{i}$, the magnetic fields ratio $b = {B}_\mathrm{e}/{B}_\mathrm{i}$, and the Hall scale parameter $l_\mathrm{Hall}/a$. It is found that the Hall current, at moderate values of $l_\mathrm{Hall}/a$, stimulates the emerging of KHI of the kink ($m = 1)$ and high-mode ($m \geqslant 2$) MHD waves, while for the sausage wave ($m = 0$) the trend is just the opposite---the KHI is suppressed.

Kelvin–Helmholtz instability (KHI), driven by the velocity inhomogeneity at Earth's magnetopause, has been shown to play a major role in mixing the magnetospheric and the solar wind plasma during northward periods. In fact, when the magnetospheric and interplanetary magnetic fields are mostly perpendicular to the equatorial plane, KHI can develop at a low latitude without being significantly inhibited by the magnetic tension. In contrast, at a high latitude, the more complex magnetic configuration is believed to totally stabilize the instability. This intrinsic 3D dynamics is investigated in a simplified geometry showing that KHI is able to kink the magnetic field lines at a mid-latitude and to create current layers where magnetic reconnection spontaneously develops. It is shown that a mid-latitude reconnection is able to change the global topology of the magnetic field and to connect interplanetary field lines to the Earth's cups, allowing the solar wind to directly enter the magnetosphere.

The Kelvin–Helmholtz instability (KHI) has been considered important in the energy transfer and momentum coupling between the solar wind and planetary magnetospheres. To explore this issue, we employ a two-dimensional magnetohydrodynamic simulation to study the nonlinear evolution of the KHI at Mercury’s magnetopause using the parameters derived from a global hybrid simulation of MESSENGER’s first flyby of Mercury. Due to the absence of comprehensive plasma observations of Mercury’s magnetosphere, two scenarios are considered: one with a heavily loaded magnetosphere and the other with a weakly loaded magnetosphere, to demonstrate the development of the KHI under distinct levels of magnetospheric plasma density. Our results indicate that the KHI with a heavily loaded magnetosphere leads to a significantly more turbulent magnetopause and grows into the nonlinear fast-mode plane waves expanding away from the magnetopause. The momentum and energy flux quantified from our simulations reveal that the KHI with a heavily loaded magnetosphere can efficiently transport momentum and energy away from the magnetopause in the presence of the fast-mode plane waves. In the cases with a heavily loaded magnetosphere, observed in the inner magnetosphere, the momentum flux can reach 10−3 nPa, i.e., about 0.5% of the initial solar-wind dynamic pressure; the energy flux can be 10-2ergcm-2s-1, and the energy density is about 1.5%–3.0% of the initial solar-wind energy. In the cases with a very thin magnetosphere, observed away from the magnetopause, the momentum flux is negligible and the energy flux is smaller without the presence of the fast-mode plane waves in the magnetosphere.

<strong class="journal-contentHeaderColor">Abstract.</strong> Kelvin Helmholtz instability (KHI) is most likely to be the primary source for clear-air turbulence that is of importance in pollution transfer and diffusion and aircraft safety. It is exemplarily indicated by the critical value of Richardson (<em>Ri</em>) number, which is typically taken as 1/4. However, <em>Ri</em> is fairly sensitive to the vertical resolution of the dataset: a higher resolution systematically leads to a finer structure. The study aims to evaluate the performance of ERA5 reanalysis (137 model levels) in determining KHI spatial-temporal variabilities, by comparing it against a near-global high-resolution (10-m) radiosonde dataset during years 2017 to 2022, and to further highlight the global climatology and dynamical environment of KHIs. Overall, the occurrence frequency of <em>Ri </em>&lt; 1/4 in the free atmosphere is inevitably underestimated by the ERA5 reanalysis over all climate zones, compared to radiosonde, due largely to the severe underestimation in wind shears. Otherwise, the occurrence frequency of KHI indicated by <em>Ri </em>&lt; 1 in ERA5 is climatologically consistent with that from radiosondes in the free troposphere, especially over the midlatitude and subtropics in the Northern/Southern Hemisphere. Therefore, we infer that the threshold value of <em>Ri</em> should be approximated as 1, rather than 1/4, when using ERA5 for the KHI estimation. KHI occurrence frequencies revealed by both datasets exhibit significant seasonal cycles over polar, midlatitude, and subtropics regions, and they are consistently strong at heights of 10&ndash;15 km in the tropic region. In addition, the frequency at low-levels is positively correlated with the standard derivation of orography, and it is exceptionally strong over the Ni&ntilde;o 3 region at heights of 6&ndash;13 km. Furthermore, the dynamical environment of KHI favors strong wind shears probably induced by the mean flows and the propagation of orographic or non-orographic gravity waves.

The evolution of the Kelvin–Helmholtz instability (KHI) and magnetohydrodynamic (MHD) wave emission is investigated at shear-flow boundaries of magnetized plasmas. While MHD wave emission has been suggested to be only possible during the nonlinear stages, we find that there is also significant wave emission during the KHI’s linear stages. These emitted MHD waves may have stronger impacts than KHI surface waves since they can act to transport energy away from the local region of the shear flow. The removal of energy from the shear-flow region, instead of just the local redistribution considered in previous studies, and its propagation away from the interface could have major implications for the evolution of astrophysical objects characterized by fast plasma flow shears.

Prediction of Kelvin–Helmholtz instability (KHI) is crucial across various fields, requiring extensive high-fidelity data. However, experimental data are often sparse and noisy, while simulated data may lack credibility due to discrepancies with real-world configurations and parameters. This underscores the need for field reconstruction and parameter inference from sparse, noisy data, which constitutes inverse problems. Based on the physics-informed neural networks (PINNs), the KH-PINN framework is established in this work to solve the inverse problems of KHI flows. By incorporating the governing physical equations, KH-PINN reconstructs continuous flow fields and infer unknown transport parameters from sparse, noisy observed data. The two-dimensional unsteady incompressible flows with both constant and variable densities are studied. To our knowledge, this is one of the first few applications of PINNs to unsteady incompressible flows with variable densities. To address the spatiotemporal multiscale issue and enhance the reconstruction accuracy of small-scale structures, the multiscale embedding (ME) strategy is adopted. To address the magnitude multiscale issue and enhance the reconstruction accuracy of small-magnitude velocities, which are critical for KHI problems, the small-velocity amplification (SVA) strategy is proposed. The results demonstrate that KH-PINN can accurately reconstruct the fields with complex, evolving vortices and infer unknown parameters across a broad range of Reynolds numbers. Additionally, the energy-decaying and entropy-increasing curves are accurately obtained. The effectiveness of ME and SVA is validated through comparative studies, and the anti-noise and few-shot learning capabilities of KH-PINN are also validated. The code for this work is available at https://github.com/CAME-THU/KH-PINN.

Kelvin–Helmholtz instability (KHI) is investigated in the context of a non-Maxwellian dusty plasma comprising of electrons, ions and dust particles. The generalized dispersion relation is derived, which is of a complex nature due to some of the source terms like density inhomogeneity and sheared flow A that are responsible for instability in the system. To discuss the instability, the dispersion relation is solved numerically to discuss the growth rates. The primary goal is to understand the dynamics of KH modes in non-Maxwellian plasmas defined by the Kappa and Cairns distribution parameters influence the creation and features of KHI. We have found that the development rates and threshold conditions for these instabilities are significantly altered in the presence of non-Maxwellian distributions, influencing the overall dynamics of space plasma environment. The results demonstrate that superthermal particles in the Cairns distribution speed up the KHI's development rate, but the Kappa parameter has a more stable influence in comparison with Cairns. The effects of different parameters are investigated like sheared velocity, magnetic field, and dust mass. Dust particles present there strongly influence the system dynamics by increasing the chances of growing modes. Increasing dust mass can produce more obvious instabilities in celestial environments such as comet tails and planetary rings, aiding our understanding of their production and evolution.

The drift kinetic approximation (DKA) is developed by combining the macro- and microdynamics of guiding center plasmas. It is shown that the DKA provides a better description for collisionless processes in plasmas than the Chew–Goldberger–Low approximation. A new theory of the Kelvin–Helmholtz instability (KHI) in collisionless space plasmas is established. Calculations show that the general pattern of the growth rate of the KHI versus flow velocity in the DKA is similar to that in compressional magnetohydrodynamics. However, the critical velocity decreases if pressure is anisotropic, and the growth rate and energy flux are reduced in the presence of wave–particle interactions.