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This study introduces a novel approach for numerically solving the 2D Helmholtz equation. This work begins with the establishment of a sixth-order difference scheme tailored to solve the 2D Helmholtz equation under the conditions of homogeneous Dirichlet boundary and periodic boundary. Subsequently, we solve the constructed scheme using the Fast Fourier algorithm, thereby enhancing computational efficiency. Finally, to validate the efficiency and accuracy of the presented difference scheme, a series of numerical experiments were conducted.

The Kelvin‐Helmholtz waves have been observed along the Earth's low‐latitude magnetopause and have been suggested to play a certain role in the entry of solar wind plasma into Earth's magnetosphere. In situ observations of the KH waves (KHW) and, in particular, a nonlinear stage of the KH instability, i.e., rolled‐up KH vortices (KHVs), have been reported to occur preferentially for northward interplanetary magnetic field (IMF). Using Cluster data, we present the first in situ observation of nonlinearly developed KHW during southward IMF. The analysis reveals that there is a mixture of less‐developed and more‐developed KHW that shows inconsistent variations in scale size and the magnetic perturbations in the context of the expected evolution of KH structures. A coherence analysis implies that the observed KHW under southward IMF appear to be irregular and intermittent. These irregular and turbulent characteristics are more noticeable than previously reported KHW events that have been detected preferentially during northward IMF. This suggests that under southward IMF KHVs become easily irregular and temporally intermittent, which might explain the preferential in situ detection of KHVs when the IMF is northward. MHD simulation of the present event shows that during southward IMF dynamically active subsolar environments can cause KHV that evolve with considerable intermittency. The MHD simulations appear to reproduce well the qualitative features of the Cluster observations. Key Points First in‐situ observations of well‐developed KHW under southward IMF Solar‐wind IMF effects on the development and evoluction of KHW Turbulent/irregular characteristics of southward‐IMF KHW explains rare detection

We use the Kelvin‐Helmholtz instability (KHI) condition with particle and magnetic field observations from Jovian Auroral Distributions Experiment and MAG on Juno along the dawn flank of Jupiter's magnetosphere. We identify the occurrence of magnetopause crossings that show evidence of being KH (Kelvin‐Helmholtz) unstable. When estimating the k vector to be parallel to the velocity shear, we find that 25 of 62 (40%) magnetopause crossings satisfy the KHI condition. When considering the k vector of the maximum growth rate through a solid angle approach, we find that 60 of 62 (97%) events are KH unstable. This study shows evidence of KH waves at Jupiter's dawn flank, including primary drivers such as high velocity shears and changes in plasma pressure. Signatures of magnetic reconnection were also observed in ∼25% of the KH unstable crossings. We discuss these results and their implication for the prevalence of KHI at Juno's dawn magnetopause as measured by Juno. Plain Language Summary The Kelvin‐Helmholtz instability occurs when a boundary separating two fluids of different densities is perturbed and these fluids are moving at different speeds, directions, or both. The difference in speeds across the perturbed boundary that separates the fluids creates wave structures as these fluids diffuse into each other. The Kelvin‐Helmholtz instability may be observed at the boundary that separates a planetary magnetic field (magnetosphere) from the stream of charged particles emitted by the Sun (solar wind); this boundary is known as the magnetopause. This instability is confirmed to occur at Earth and Saturn, but is not confirmed at Jupiter. This study analyzes the properties of the plasma and magnetic field in Jupiter's magnetosphere and the surrounding solar wind to identify signatures of the Kelvin‐Helmholtz instability. We find that out of 62 occurrences where the Juno spacecraft crosses the magnetopause, 25 events signify that the Kelvin‐Helmholtz instability is possible—primarily due to large differences in velocities—and 37 events do not. Key Points There is evidence of Kelvin‐Helmholtz instability (KHI)‐driven waves along Jupiter's dawn flank magnetopause during the Juno prime mission 24 (38.7%) crossings satisfied the KHI condition and 38 (61.3%) crossings did not satisfy the KHI condition Magnetopause crossings that satisfied the KHI condition had, in general, larger velocity shears than those that did not

We present Magnetospheric Multiscale observations of an electron‐scale reconnecting current sheet in the mixing region along the trailing edge of a Kelvin‐Helmholtz vortex during southward interplanetary magnetic field conditions. Within this region, we observe intense electrostatic wave activity, consistent with lower‐hybrid waves. These waves lead to the transport of high‐density magnetosheath plasma across the boundary layer into the magnetosphere and generate a mixing region with highly compressed magnetic field lines, leading to the formation of a thin current sheet associated with electron‐scale reconnection signatures. Consistencies between these reconnection signatures and a realistic, local, fully‐kinetic simulation modeling this current sheet indicate a temporal evolution of the observed electron‐scale reconnection current sheet. The multi‐scale and inter‐process character of this event can help us understand plasma mixing connected to the Kelvin‐Helmholtz instability and the temporal evolution of electron‐scale reconnection. Plain Language Summary Like wind blowing over water, the stream of ionized gas released from the Sun, called the solar wind, can lead to waves and rolled‐up vortex structures at the boundary of Earth's magnetosphere, called the magnetopause. These so‐called Kelvin‐Helmholtz waves have been shown to be connected to various different plasma processes on different scales. This multi‐scale and multi‐process character makes them an ideal candidate to study the relation between these processes from both spacecraft observations and simulations. By using spacecraft data from the Magnetospheric Multiscale mission, which was designed for the study of small‐scale plasma processes in Earth's magnetosphere, we show observations of electron‐scale magnetic reconnection, an explosive energy conversion process in plasmas, in a region along the trailing edge of these waves. These observations shed new light on the multi‐scale and multi‐process character of the Kelvin‐Helmholtz instability and the energy conversion processes along its boundary. Key Points A reconnecting electron‐scale current sheet is observed by Magnetospheric Multiscale (MMS) in mixing plasma along the trailing edge of a Kelvin‐Helmholtz vortex Realistic 2.5D fully‐kinetic simulation shows reasonable agreement with MMS data Consistencies between the simulation and MMS indicate a temporal evolution of the reconnecting current sheet

Various physical processes in association with magnetic reconnection occur over multiple scales from the microscopic to macroscopic scale lengths. This paper reviews multi-scale and cross-scale aspects of magnetic reconnection revealed in the near-Earth space beyond the general global-scale features and magnetospheric circulation organized by the Dungey Cycle. Significant and novel advancements recently reported, in particular, since the launch of the Magnetospheric Multi-scale mission (MMS), are highlighted being categorized into different locations with different magnetic topologies. These potentially paradigm-shifting findings include shock and foreshock transient driven reconnection, magnetosheath turbulent reconnection, flow shear driven reconnection, multiple X-line structures generated in the dayside/flankside/nightside magnetospheric current sheets, development and evolution of reconnection-driven structures such as flux transfer events, flux ropes, and dipolarization fronts, and their interactions with ambient plasmas. The paper emphasizes key aspects of kinetic processes leading to multi-scale structures and bringing large-scale impacts of magnetic reconnection as discovered in the geospace environment. These key features can be relevant and applicable to understanding other heliospheric and astrophysical systems.

Unlike classical multi-layered micro-perforated panels (MPPs), which rely on sub-millimeter orifices for sound dissipation, we propose a multi-layered porous Helmholtz resonators absorber. It consists of alternately layered perforated porous material panels and perforated rigid panels with millimeter- to centimeter-scale orifices, primarily relying on porous materials for sound energy dissipation. Theoretically, perforated porous material panels are modeled as homogeneous fluid layers using double porosity theory, and the total surface impedance is derived through bottom-to-top impedance translation. A double-layered prototype was tested to validate the theoretical and numerical models, achieving near-perfect absorption peaks at 262 Hz and 774 Hz, with a subwavelength total thickness of 11 cm and a broadband absorption above an absorption coefficient of 0.7 from 202 Hz to 1076 Hz. Simulations of sound pressure, particle velocity, power dissipation, and sound intensity flow confirm that Helmholtz resonances in each layer enhance sound entry into resistive porous materials, causing absorption peaks. Parameter studies show this absorber maintains high absorption peaks across wide ranges of orifice diameters and panel thicknesses. Finally, an optimized triple-layer porous Helmholtz resonators absorber achieves an ultra-broadband absorption above a coefficient of 0.95 from 280 Hz to 1349 Hz with only 16.5 mm thickness. Compared with conventional MPPs, this design features significantly larger orifices that are easier to fabricate and less susceptible to blockage in harsh environments, offering an alternative solution for low-frequency and broadband sound absorption.

The purpose of this paper is to characterize and model waves that are observed within the potential core of subsonic jets and relate them to previously observed tones in the near-nozzle region. The waves are detected in data from a large-eddy simulation of a Mach 0.9 isothermal jet and modelled using parallel and weakly non-parallel linear modal analysis of the Euler equations linearized about the turbulent mean flow, as well as simplified models based on a cylindrical vortex sheet and the acoustic modes of a cylindrical soft duct. In addition to the Kelvin–Helmholtz instability waves, three types of waves with negative phase velocities are identified in the potential core: upstream- and downstream-propagating duct-like acoustic modes that experience the shear layer as a pressure-release surface and are therefore radially confined to the potential core, and upstream-propagating acoustic modes that represent a weak coupling between the jet core and the free stream. The slow streamwise contraction of the potential core imposes a frequency-dependent end condition on the waves that is modelled as the turning points of a weakly non-parallel approximation of the waves. These turning points provide a mechanism by which the upstream- and downstream-travelling waves can interact and exchange energy through reflection and transmission processes. Paired with a second end condition provided by the nozzle, this leads to the possibility of resonance in limited frequency bands that are bound by two saddle points in the complex wavenumber plane. The predicted frequencies closely match the observed tones detected outside of the jet. The vortex-sheet model is then used to systematically explore the Mach number and temperature ratio dependence of the phenomenon. For isothermal jets, the model suggests that resonance is likely to occur in a narrow range of Mach number, $0.82

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