Refraction of Oblique Shock Wave on a Tangential Discontinuity

The refraction of an oblique shock wave on a tangential discontinuity dividing two gas flows with different properties is considered. It is shown that its partial reflection occurs with the exception of the geometrical diffraction of an oblique shock. Another oblique shock, expansion wave or weak discontinuity that coincides with the Mach line can act as a reflected disturbance. This study focuses on the relationships that define the type of reflected discontinuity and its parameters. The domains of shock wave configurations with various types of reflected discontinuities, including characteristic refraction and refraction patterns with a reflected shock and a reflected rarefaction wave, are analyzed. The domains of existence of various shock wave structures with two types of reflected disturbance, and the boundaries between them, are defined. The domains of parameters with one or two solutions exist for the characteristic refraction. Each domain is mapped by the type of refraction with regard to the Mach number, the ratio of the specific heat capacities of the two flows and the intensity of a refracted oblique shock wave. The conditions of the regular refraction and the Mach refraction are formulated, and the boundaries between the two refraction types are defined for various types of gases. Refraction phenomena in various engineering problems (hydrocarbon gaseous fuel and its combustion products, diatomic gas, fuel mixture of oxygen and hydrogen, etc.) are discussed. The result can be applied to the modeling of the shock wave processes that occur in supersonic intakes and in rotating and stationary detonation engines. The solutions derived can be used by other researchers to check the quality of numerical methods and the correctness of experimental results.

Refraction of Oblique Shock Wave on a Tangential Discontinuity

Refraction of an oblique shock wave on a tangential discontinuity dividing two gas flows with different properties is considered. It is shown that its partial reflection occurs excepting of geometrical diffraction of an oblique shock. Another oblique shock, expansion wave or weak discontinuity that coincides with Mach line, can act as a reflected disturbance. This study focuses on relationships which define the type of reflected discontinuity and its parameters. Domains of existence of various shock-wave structures with reflected disturbances of two types and boundaries between them are defined. The domains of parameters with one or two solutions exist for the characteristic refraction. Conditions of the regular refraction and the Mach refraction are formulated, and boundaries between those two refraction types are defined for various types of gases. Refraction phenomena in various engineering problems (hydrocarbon gaseous fuel and its combustion products, diatomic gas, fuel mixture of oxygen and hydrogen etc.) are discussed.

Modulation Instability of Surface Waves in the Model with the Uniform Wind Profile

The modulation instability of surface capillary-gravity water waves is analysed in a shear flow model with a tangential discontinuity of velocity. It is assumed that air blows along the surface of the water with a uniform profile in the vertical direction. Such a model, despite its simplicity, plays an important role in hydrodynamics as the reference model for investigating basic physical phenomena of wave–current interactions and acquiring insights into a series of complex phenomena. In certain cases where the wavelength of interfacial perturbations is much bigger than the width of the shear flow profile, the model with the tangential discontinuity in the velocity is adequate for describing physical phenomena at least within limited spatial and temporal frameworks. A detailed analysis of the air-flow conditions under which modulation instability sets in is presented. It is also shown that the interfacial waves are subject to dissipative or radiative instability when negative-energy waves appear at the interface.

Modulation Instability of Surface Waves in the Model with the Uniform Wind Profile

The modulation instability of surface capillary-gravity water waves is analysed in a shear flow model with a tangential discontinuity of velocity. It is assumed that air blows along the surface of the water with a uniform profile in the vertical direction. Such a model, despite its simplicity, plays an important role in hydrodynamics as the reference model for investigating basic physical phenomena of wave-current interactions and acquiring insights into a series of complex phenomena. In certain cases where the wavelength of interfacial perturbations is much bigger than the width of the shear fow profile, the model with the tangential discontinuity in the velocity is adequate for describing physical phenomena at least within limited spatial and temporal frameworks. A detailed analysis of the air-flow conditions under which modulation instability sets in is presented. It is also shown that the interfacial waves are subject to dissipative or radiative instability when negativeenergy waves appear at the interface.

Properties of the whistler precursor upstream of the foreshock bubble shock: MMS observations

<p>Foreshock bubbles (FBs) are kinetic phenomena that can form when a rotational discontinuity or a tangential discontinuity interacts with backstreaming ions in the Earth’s foreshock region. The scale of FBs can be up to 10 R<sub>E</sub> and the expansion speeds can be more than 100 km/s. The expansion of the hot ions contributes to the formation of a new shock on the trailing edge of an FB. Using MMS data, we analyze properties of the FB shock and the whistler precursor upstream of it. For the twelve FBs we analyzed, the FB shock normal has a strong X component in GSE coordinates and the quasi-parallel FB shocks are in favor of the generation of the whistler precursor. When the Mach number is larger than 3.5, the whistler precursor disappears. The wave forms are not phase standing since the angle of the wave vector and shock normal is larger than 9 degrees. They have frequencies near <em>f<sub>LH </sub></em>and right-hand polarization with respect to the ambient magnetic field (in the spacecraft frame). The properties of the whistler precursor upstream of the FB shock are similar to those at interplanetary shocks.</p>

Electron and ion velocity distribution functions across one-dimensional tangential discontinuities: particle-in-cell simulations

<div><span>Tangential discontinuities are finite-width current sheets separating two magnetized plasmas with different macroscopic properties. Such structures have been measured in-situ in the solar wind plasma by various space missions. Also, under certain conditions, the terrestrial magnetopause can be approximated with a tangential discontinuity. Studying the microstructure of tangential discontinuities is fundamentally important to understand the transfer of mass, momentum and energy in space plasmas. The propagation of solar wind discontinuities and their interaction with the terrestrial magnetosphere play a significant role for space weather science. In this paper we use 1d3v electromagnetic particle-in-cell simulations to study the kinetic structure and stability of one-dimensional tangential discontinuities. The simulation setup corresponds to a plasma slab configuration which allows the simultaneous investigation of two discontinuities at the interface between the slab population and the background plasma. The initial discontinuities are infinitesimal and evolve rapidly towards finite-width transition layers. We focus on tangential discontinuities with and without perpendicular velocity shear. Three-dimensional velocity distribution functions are computed in different locations across the discontinuities, at different time instances, for both electrons and ions. We emphasize the space and time evolution of the velocity distribution functions inside the transition layers and discuss their deviation from the initial Maxwellian distributions. The simulated distributions show similar features with the theoretical solutions provided by Vlasov equilibrium models. </span></div>