Oblique shock

About: Oblique shock is a research topic. Over the lifetime, 6551 publications have been published within this topic receiving 119823 citations.

Upstream waves, shocklets, short large‐amplitude magnetic structures and the cyclic behavior of oblique quasi‐parallel collisionless shocks

Abstract: The re-formation process of more oblique quasi-parallel shocks is investigated using one-dimensional hybrid simulations. Several types of simulations have been performed. The simulation of a shock with a magnetic field-shock normal angle of 30° shows that a more oblique quasi-parallel shock exhibits reformation cycles with a larger length scale, that is of about 20 ion inertial lengths. This is considerably larger than the distance specularly reflected ions are able to propagate upstream before they are deflected so that their velocity in the shock normal direction is close to zero. These cycles are due to steepening and growth of upstream waves into pulsationlike structures when they are convected into the region of strongly increasing diffuse ion density immediately upstream of the shock. When the steepening wave packet crashes into the shock, the shock ramp dispersively radiates whistler waves into the region between the shock ramp and the approaching wave, while the steepening of the pulsation leads to phase standing whistler waves on the upstream side. Entropy production occurs either at the shock ramp or at the upstream edge of the pulsation when the steepening process has produced a large kink in the magnetic field and is due to nonadiabatic motion of the incident solar wind ions. In order to analyze the wave steepening, upstream waves have been isolated, and their subsequent interaction with a hot, tenuous ion beam representing the diffuse backstreaming ions has been studied. When an upstream wave is convected into or a region with increasing hot beam density, the wave steepens and becomes a pulsationlike wave packet. In order for the wave to grow to a pulsationlike structure the characteristic scale length of the density increase has to be of the same order as the wavelength of the original magnetosonic wave. Similar results are obtained when counterstreaming beam of hot ions is injected into a solar wind which does not initially contain a wave field. In this case the polarization of the pulsations depends on the hot beam temperature. The strong density increase of hot beam ions in these simulations is due to the steady injection of beam ions in a solar wind with an embedded field which is inclined relative to the solar wind direction. In the shock simulation the shock itself is the steady source of the hot backstreaming ions. These simulations suggest that upstream waves, shocklets, and short large-amplitude magnetic structures are all the same entity in different stages of their development and play a crucial role in re-forming oblique quasi-parallel shocks.

Numerical study of oblique shock-wave/boundary-layer interaction considering sidewall effects

Abstract: Large-eddy simulations are conducted to uncover physical aspects of sidewall-induced three-dimensionality for a moderately separated oblique shock-wave/boundary-layer interaction (SWBLI) at M=2.7. Simulations are run for three different aspect ratios of the interaction zone. The swept SWBLI on the sidewalls and the corner flow behaviour are investigated, along with the main oblique SWBLI on the bottom wall. As the aspect ratio decreases to unity, the separation and reattachment points on the central plane are observed to move upstream simultaneously, while the bubble length initially increases and then stabilizes to a length 30 % larger than for the infinite-span quasi-two-dimensional case. A distorted incident shock and a three-dimensional (3D) bottom-wall separation pattern are observed, with a patch of attached flow between the central and corner separations. The 3D flow structure is found to be induced by the swept SWBLI formed on the sidewalls. The location of the termination point of the incident shock near the sidewall is limited by a sweepback effect, allowing the definition of a penetration Mach number Mp that is shown to correlate well with the spanwise extent of the core flow. The structure and strength of the incident shock are modified significantly by the swept SWBLI on the sidewalls, along with a compression wave upstream and a secondary sidewall shock downstream, leading to a highly 3D pressure field in the main flow above the main SWBLI on the bottom wall. The reflection of the swept SWBLI from the bottom wall leads to a corner compression wave and strong transverse flow close to the bottom wall. A physical model based on the quasi-conical structure of the swept SWBLI on the sidewall is proposed to estimate the 3D SWBLI pattern on the bottom wall, in which the swept SWBLI features and the aspect ratio of the interaction zone are considered to be the critical factors

Shock waves for compressible navier‐stokes equations are stable

Abstract: It is shown that shock waves for the compressible Navier-Stokes equations are nonlinearly stable. A perturbation of a shock wave tends to the shock wave, properly translated in phase, as time tends to infinity. Through the consideration of conservation of mass, momentum and energy we obtain an a priori estimate of the amount of translation of the shock wave and the strength of the linear and nonlinear diffusion waves that arise due to the perturbation. Our techniques include the energy method for parabolic-hyperbolic systems, the decomposition of waves, and the energy-characteristic method for viscous conservation laws introduced earlier by the author.

Supersonic flow onto a solid wedge

Abstract: We consider the problem of two-dimensional supersonicflow onto a solid wedge, or equivalently in a concave corner formed by two solid walls. For mild corners, there are two possible steady state solutions, one with a strong and one with a weak shock emanating from the corner. The weak shock is observed in supersonic flights. A longstanding natural conjecture is that the strong shock is unstable in some sense. We resolve this issue by showing that a sharp wedge will eventually produce weak shocks at the tip when accelerated to a supersonic speed. More precisely, we prove that for upstream state as initial data in the entire domain, the timedependent solution is self-similar, with a weak shock at the tip of the wedge. We construct analytic solutions for self-similar potential flow, both isothermal and isentropic with arbitrary� � 1. In the process of constructing the self-similar solution, we develop a large number of theoretical tools for these elliptic regions. These tools allow us to establish large-data results rather than a small perturbation. We show that the wave pattern persists as long as the weak shock is supersonic-supersonic; when this is no longer true, numerics show a physical change of behavior. In addition, we obtain rather detailed information about the elliptic region, including analyticity as well as bounds for velocity components and shock tangents. c � 2007 Wiley Periodicals, Inc.

Numerical study on the rotational collapse of strongly magnetized cores of massive stars

Abstract: Hydrodynamics of the rotational collapse of strongly magnetized massive stellar cores has been studied numerically. Employing simplified microphysics and a two-dimensional nonrelativistic MHD code, we have performed a parametric research with respect to the strength of magnetic field and rotation, paying particular attention to the systematics of dynamics. We assume initially that the rotation is almost uniform and the magnetic field is constant in space and parallel to the rotation axis. The initial angular velocity and magnetic field strength span 1.7-6.8 rad s-1 and × 1012 G, respectively. We have found that the combination of rotation and magnetic field can lead to a jetlike prompt explosion in the direction of the rotational axis, which would not be produced by either of them alone. The range of the maximum angular velocity and field strength is 2.3 × 10-3 to 5.8 × 10-4 rad s-1 and 2.3 × 1015 to 5.6 × 1016 G, respectively, at the end of computations. Although the results appear to be consistent with those by LeBlanc & Wilson and Symbalisty, the magnetic fields behind the shock wave, not in the inner core, are the main driving factor of the jet in our models. The fields are amplified by the strong differential rotations in the region between the shock wave and the boundary of the inner and outer cores, enhanced further by the lateral matter motions induced either by an oblique shock wave (for a strong shock case) or possibly by the MRI (magnetorotational instability)-like instability (for a weak shock case). We have also calculated the gravitational wave forms in the quadrupole approximation. Although the wave form from a nonrotating magnetic core is qualitatively different from those from rotating cores, the amplitude is about an order of magnitude smaller. Otherwise, we have found no substantial difference in the first burst of gravitational waves among the magnetized and nonmagnetized models, since the bounce is mainly driven by the combination of the matter pressure and the centrifugal force.