Hazem El-Rabii

We study the development of the Kelvin‐Helmholtz instability (KHI) along the dusk dayside Earth's magnetopause with and without the presence of enhanced plasma density at the shear interface. Using three‐dimensional MAGE global simulations, we establish general KHI growth rate diagrams, which depend sensitively on the transverse profiles of both flow velocity and density. We find multiple KHI onsets promoting various growths along the magnetopause. Their associated KH frequencies and growth rates are found to follow the flow structure and decrease downstream. The magnetopause displacement, caused here by an abrupt southward‐to‐northward IMF turning, shifts KH onsets upstream and promotes density leakage that seeds an additional mixing layer at the interface. The presence of enhanced density modifies KHI frequency response suppressing small‐scale KHI structures while amplifying larger‐scales, as a low‐pass filter. We complement the analysis with dedicated high‐resolution scaled 2‐D Cartesian simulations, Doppler‐corrected for comparison with the global 3‐D results, and find good agreement with the linear KH growth rates. We show that the flow evolution along the magnetopause lowers the KHI frequencies down to Pc5–Pc4 ranges. Density effects further reorganize the frequency range of the KH unstable modes inducing the amplification of Pc6 to low‐Pc5 frequencies, suggesting that KHI can amplify fast magnetosonic waves propagating along standing field lines. The high‐resolution 2‐D simulations suggest that, in the nonlinear stage, the presence of a density pocket can suppress secondary instabilities.

We study the Kelvin–Helmholtz instability (KHI) for the general case of a compressible, nonhomogeneous, magnetized plasma flow. The study is limited to a vortex sheet interface with an imposed parallel magnetic field. We introduce a new formalism based on a convective Mach number Mc, a convective Alfvénic Mach number MAc, and a total convective Mach number that combines the two. We derive an analytic expression of the KHI growth rate for a homogeneous flow (i.e., zero Atwood number, A=0) that converges toward both the expression for unmagnetized compressible flow and Chandrasekhar's expression for magnetized incompressible flow. Otherwise, the dispersion relation is solved numerically and allows deriving general stability diagrams of magnetized KHI for the triplet (A,Mc,β−plasma) parameters. We show these parameters uniquely define all configurations for a parallel magnetic field. We also construct diagrams with respect to the convective Alfvénic Mach number, the β− plasma parameter, or the magnetic field showing which magnetic field strength is required for stabilizing a given shear flow. The theoretical growth rates are compared with 18 simulations made with the GAMERA code, currently used for 3D magnetospheric simulations. Finally, we apply our results to the analysis of a past KHI experiment performed at the OMEGA laser facility, showing linear theory succeeds to provide accurate estimates of the growth rate at early times. We further discuss how our results can inform future experiments in the high-Mach magnetized regime at the National Ignition Facility. Possible limitations of the study due to resistive, mixing, or turbulence effects are discussed.

The objective of this study is to develop a basic understanding of the interaction of shock waves with density inhomogeneities. We consider the particular instance of a planar air shock impinging on a spherical water droplet and discuss to what extent this interaction can lead to the inception of cavitation inside the droplet. The effort centers on early phases of the interaction, which are analyzed using both ray theory and a hydrodynamic code. Within the context of ray theory, the occurrence of focusing is examined in detail, and parametric equations are derived for the transmitted wavefront and its multiple internal reflections. It is found that wave patterns predicted by ray calculations compare extremely well with the more accurate numerical solutions from simulations. In particular, it is shown that the internal wavefront assumes a complex time-dependent shape whose dominant feature is the existence of cusp singularities. These singular points are shown to trace out surfaces that are the caustics of the associated system of rays. From the singularities of the energy flux density of the refracted wave, the parametric equations of the caustic surface associated with the kth reflected wavefront are deduced. As a consequence of the focusing process, simulations show the formation of negative-pressure regions in the internal flow field. These low-pressure zones are identified as possible spots at which cavitation may occur, depending on the magnitude of pressure reached. Finally, numerical results provide quantitative information on the dependence of negative-pressure peaks upon incident-shock-wave strength.

Direct observation of the droplet breakup process in high-speed gas flows is a critical challenge that needs to be addressed to elucidate the physical mechanisms underlying the fragmentation phenomenon. Here, we present a high-magnification and high-speed shadowdograph technique that allows the visualization of this process over its whole evolution and resolves detailed features of the breakup zone. The developed experimental method uses a high-speed camera equipped with a long-distance microscope. The backlight illumination source is provided by the laser-induced fluorescence of a dye solution that delivers short pulses at a high-repetition rate. Artefacts resulting from the laser coherence are therefore reduced.

The breakup of water droplets when exposed to high-speed gas flows is investigated using both high-magnification shadowgraphy experiments as well as fully three-dimensional numerical simulations, which account for viscous as well as capillary effects. After thorough validation of the simulations with respect to the experiments, we elucidate the ligament formation process and the effect of surface tension. By Fourier decomposition of the flow field, we observe the development of specific azimuthal modes, which destabilize the liquid sheet surrounding the droplet. Eventually, the liquid sheet is ruptured, which leads to the formation of ligaments. We further observe the ligament formation and shedding to be a recurrent process. While the first ligament shedding weakly depends on the Weber number, subsequent shedding processes seem to be driven primarily by inertia and the vortex shedding in the wake of the deformed droplet.

Herein, planar laser-induced fluorescence (PLIF) is used in combination with shadowgraphy to study water-droplet aerobreakup. The acquired shadowgraph data are in agreement with previous visualization studies but differ from the PLIF results, yielding new insights into the fragmentation process. In particular, the PLIF data reveal changes in droplet topology during fragmentation that result from the entrapment or formation of gas cavities inside the liquid phase. In some instances, topological modification can be observed to arise from the presence of these cavities. In addition, the cavities may act as weak spots, facilitating droplet split-off.

The breakup of water droplets when exposed to high-speed gas flows is investigated using both high-magnification shadowgraphy experiments as well as fully three-dimensional numerical simulations, which account for viscous as well as capillary effects. After thorough validation of the simulations with respect to the experiments, we elucidate the ligament formation process and the effect of surface tension. By Fourier decomposition of the flow field, we observe the development of specific azimuthal modes, which destabilize the liquid sheet surrounding the droplet. Eventually, the liquid sheet is ruptured, which leads to the formation of ligaments. We further observe the ligament formation and shedding to be a recurrent process. While the first ligament shedding weakly depends on the Weber number, subsequent shedding processes seem to be driven primarily by inertia and the vortex shedding in the wake of the deformed droplet.