Oblique shock

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

Convection of a pattern of vorticity through a shock wave

Abstract: An arbitrary weak spatial distribution of vorticity can be represented in terms of plane sinusoidal shear waves of all orientations and wave lengths (Fourier integral). The analysis treats the passage of a single representative weak shear wave through a plane shock and shows refraction and modification of the shear wave with simultaneous generation of an acoustically intense sound wave. Applications to turbulence and to noise in supersonic wind tunnels are indicated.

Detonation structures behind oblique shocks

Abstract: Detonation structures generated by wedge‐induced, oblique shocks in hydrogen–oxygen–nitrogen mixtures were investigated by time‐dependent numerical simulations. The simulations show a multidimensional detonation structure consisting of the following elements: (1) a nonreactive, oblique shock, (2) an induction zone, (3) a set of deflagration waves, and (4) a ‘‘reactive shock,’’ in which the shock front is closely coupled with the energy release. In a wide range of flow and mixture conditions, this structure is stable and very resilient to disturbances in the flow. The entire detonation structure is steady on the wedge when the flow behind the structure is completely supersonic. If a part of the flow behind the structure is subsonic, the entire structure may become detached from the wedge and move upstream continuously.

The Interaction of an Oblique Shock Wave with a Laminar Boundary Layer

Abstract: The results of some experimental and theoretical studies of the interaction of oblique shock waves with laminar boundary layers are presented. Detailed measurements of pressure distribution, shear distribution, and velocity profiles were made during the interaction of oblique shock waves with laminar boundary layers on a flat plate. From these measurements a model was derived to predict the pressure levels characteristic of separation and the length of the separated region.

The profile of a steady plane shock wave

Abstract: Introduction The physical problem of the propagation of small disturbances (sound waves) corresponds to linearization of the equations in the appropriate mathematical formulation. In an inviscid fluid this leads to plane waves which can be either compressive or rarefactive and which propagate at a constant speed (the sound speed) which is a property of the medium. Since differential equations inherently assume the differentiability of solutions, the propagation of discontinuous wave fronts requires special treatment. This is accomplished by the simple expedient of approximating an initially discontinuous wave front by a sequence of continuous initial functions. The corresponding sequence of continuous solutions of the differential equations is observed to converge to a discontinuous wave front propagating at the same sound speed. This serves to extend the manifold of solutions of the differential equations to include discontinuities which propagate unaltered whether they are compressive or rarefactive. If dissipation is introduced into the mathematical formulation, it is observed that initial discontinuities are wiped out, and all disturbances tend to broaden with time. On the other hand, it is a classical result that the propagation of non-dissipative waves of finite amplitude is no longer symmetric, compressive fronts tending to steepen and rarefactive ones to broaden. In particular, a compressive front will steepen until it attains a vertical slope, after which it becomes multiple-valued and can no longer represent a physical quantity. Furthermore, if it is attempted to approximate an initially discontinuous compressive wave by a sequence of smooth initial functions, the time of breakdown of each succeeding smooth wave will approach the initial instant, so that no limit exists which could be termed propagation of the initial discontinuity. By contrast, successive approximations of this sort do converge if the initial discontinuity is rarefactive, but it is found that the initial discontinuity is immediately wiped out and propagates as a broadening rarefaction wave. 1

On the formation of auroral arcs and acceleration of auroral electrons

Abstract: It is suggested that the highly structured auroral arc is caused by a current-driven laminar electrostatic shock oblique to the geomagnetic field. Electrons are accelerated by the potential jump associated with the shock. The shock is assumed to be confined to a plane. Self-consistent solutions to the Poisson-Vlasov systems are calculated for the electrostatic potential. Adiabatic theory is used to calculate the ion number density in terms of the electrostatic potential and its derivatives. The electrons are assumed to be highly magnetized so they can only move parallel to the magnetic field. Solutions are exhibited for two plasma models: (1) streaming electrons and a two-temperature distribution of ions and (2) streaming electrons and ions and thermal electrons and ions. In the latter model, solutions can be obtained for an arbitrary potential jump across the shock. The shock is identified with the linear electrostatic ion cyclotron wave, and stability of these waves is examined to determine conditions for the formation of oblique shocks. Finally, the theory is discussed in the context of the magnetosphere, and possible model shocks are exhibited and discussed in terms of auroral arc formation.