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Showing papers on "Oblique shock published in 1984"


Journal ArticleDOI
TL;DR: In this article, a statistical study on the proton energy spectra in the range of 35-1600 keV during the one-hour interval centered on the time of arrival of the shock front at the spacecraft of 75 interplanetary shocks that cover the period from August 1978 until December 1980, using the low-energy proton experiment on ISEE 3.
Abstract: We present the results of a statistical study on the proton energy spectra in the range of 35–1600 keV during the one-hour interval centered on the time of arrival of the shock front at the spacecraft of 75 interplanetary shocks that cover the period from August 1978 until December 1980, using the low-energy proton experiment on ISEE 3. The strength of the shocks was determined by calculating the ratio of the downstream to upstream plasma density by using the ion data obtained by the Los Alamos solar wind instrument. The shock events were sub-divided into four different classes based on the behavior of their low-energy (35–238 keV) spectral index. The signatures of the shock events and their spectral index-time profiles in the different classes are (1) smooth profiles associated with oblique, strong, and fast shocks, which roughly corresponds with predictions following from diffusive shock acceleration theory; (2) irregular profiles mainly associated with quasi-perpendicular shocks and (3) spikelike profiles associated with quasi-perpendicular shock spike events, where the properties within both classes point at predominant shock drift acceleration; (4) flat profiles, mainly associated with weak shocks accompanied by little or no shock-accelerated particles. Strong and fast oblique shocks are found to be the most effective particle accelerators. The spectrum at the shock can generally be described by two power laws with a breakpoint energy near 250 keV. For only 15% of the events the spectrum followed a power law over the full energy range. We found that the low-energy spectral index, measured immediately downstream of shocks associated with clear flux enhancements, is related to the shock strength according to predictions from first-order Fermi acceleration, irrespective of the assigned diffusive or drift character of the event.

136 citations


Journal ArticleDOI
TL;DR: In this paper, a numerical scheme is developed which automatically locates the angle at which a shock might be expected to cross the computing grid then constructs separate finite difference formulas for the flux components normal and tangential to this direction.

127 citations


Journal ArticleDOI
TL;DR: In this paper, the authors used ISEE 1 and 2 spacecraft magnetic field data to determine the scale lengths of various elements of shock structure, as well as wavelengths and wave polarizations, in a study of structural elements which include shock ramps and precursor wave trains over a series of oblique, low Mach number terrestrial bow shocks.
Abstract: ISEE 1 and 2 spacecraft magnetic field data are used to determine the scale lengths of various elements of shock structure, as well as wavelengths and wave polarizations, in a study of structural elements which include shock ramps and precursor wave trains over a series of oblique, low Mach number terrestrial bow shocks. Dissipative processes are reflected in the damping of the precursors, and dissipative scale lengths are of 200-800 km, or several times greater than shock thicknesses. The source of dissipation in the shocks does not appear to be the wave-wave decay of the whistlers, for which no evidence is found. The interaction of the whistler itself with upstream electrons is suggested as a simple and self-consistent explanation for the observed wave train damping.

121 citations


Journal ArticleDOI
TL;DR: In this paper, the shape of diffracting waves is calculated by modifying Whitham's theory for the calculation of the shape and the flow pattern of diffracted waves in gases.

104 citations


Patent
24 Jul 1984
TL;DR: In this article, an essentially planar shock wave is generated with the assistance of a shock wave tube via a magnetic dynamic effect, which is focussed by an acoustic convergent lens, whereby the calculus to be pulverized is placed at the focal point (F) of the convergence lens.
Abstract: The utilization of the apparatus fundamentally lies in the medical sector. An essentially planar shock wave is generated with the assistance of a shock wave tube via a magnetic dynamic effect. This shock wave is focussed by an acoustic convergent lens, whereby the calculus to be pulverized is placed at the focal point (F) of the convergent lens. In order to couple the shock wave to the patient, the space that the shock wave traverses is filled with a coupling agent, for example water. The shock wave tube, the convergent lens and a fine adjustment for the displacement of the convergent lens relative to the shock wave tube are attached to a mounting stand so as to be pivotable in all directions. This disintegration facility comprising a shock wave tube has high operating reliability with respect to high voltage, requires low maintenance, and has only negligible imaging or focussing errors resulting from the shock wave producing membrane and the convergent lens.

90 citations


Journal ArticleDOI
TL;DR: In this article, the experimental results from a detailed investigation of the turbulent flowfields in supersonic shockwave/boundary-layer interactions at Af=2.25 were reported.
Abstract: This paper reports the experimental results from a detailed investigation of the turbulent flowfields in supersonic shock-wave/boundary-layer interactions at Af=2.25. The interactions were produced by twodimensional compression corners having angles of 8, 13, and 18 deg, the flows being respectively attached, incipiently separated, and separated. Turbulence data from a laser velocimeter and a constant-temperature, hotwire anemometer are presented along with a mean flow survey from wall and pitot-static pressures. Qualitative aspects of the turbulence deduced from spectral analysis and high-speed schlieren pictures are also discussed. It is shown that a large amount of the turbulent energy is contained in large-scale structures that are still observed downstream of the interacting region, despite the severe pressure gradient. The lateral extent of these structures is of the order of one boundary-layer thickness and is roughly half of their longitudinal scale. A low-frequency unsteadiness is associated with the existence of a separation bubble, but does not affect the rest of the flow. The Reynolds shear stress is reduced in the vicinity of the separation bubble where the spatial derivatives of the normal stresses become significant.

87 citations


Journal ArticleDOI
TL;DR: In this article, high-resolution magnetic field measurements adjacent to the boundary of the distant magnetotail plasma sheet have been analyzed, and the nature of the changes in the field between the lobe and the plasma sheet is consistent with the boundary being a slow mode shock.
Abstract: High time-resolution magnetic field measurements adjacent to the boundary of the distant magnetotail plasma sheet have been analyzed. The nature of the changes in the field between the lobe and the plasma sheet is consistent with the boundary being a slow mode shock. The crossing times are relatively long (about 30 sec), implying a shock thickness estimated to be approximately 2000 km. An increase in the entropy of the electrons is consistent with dissipation at the shock. Reasonable shock-normal directions are derived, and may be used to determine the location of the spacecraft relative to the reconnection or merging region. It is suggested that a foreshock exists in which upstream wave and particle phenomena are occurring.

85 citations



Journal ArticleDOI
TL;DR: In this article, a high speed camera was used to measure the induced impulsive pressure induced by gas bubble interaction with a solid wall by a shock wave, and the effects of number and configuration of gas bubbles on the collapsing process and the impulsive pressures were clarified.
Abstract: The problem of bubble‐bubble interaction is studied experimentally. The motions of multiple gas bubbles attached to a solid wall by a shock wave are observed by using a high speed camera, and the induced impulsive pressures are measured. On the basis of these results, the effects of number and configuration of gas bubbles on the collapsing process and the impulsive pressure are clarified. The maximum impulsive pressure quickly decreases with reducing the interval beteween bubbles due to significant interaction. The direction of a liquid jet formed within a bubble is determined as a resultant of effects such as shock direction, shock strength, and interactions between bubbles and between a bubble and a solid wall.

45 citations


Journal ArticleDOI
TL;DR: In this paper, the interaction of solar wind thermal ions with the earth's bow shock was investigated using test particle trajectories in a simplified model of a supercritical, oblique, collisionless shock.
Abstract: Using test particle trajectories in a simplified model of a supercritical, oblique, collisionless shock, we investigate the interaction of solar wind thermal ions with the earth's bow shock. We present results for shocks with shock angle (θBn) between 35° and 60° and show that their velocity space signatures are consistent with observations of many upstream ion events, particularly gyrating ions and field-aligned ion beams. The shock is modeled as a finite, planar discontinuity in the magnetic field and in the electrostatic potential, which is also given an overshoot at the shock. We find that the shock can produce backstreaming ions by reflecting a small fraction of the incident distribution. The reflected particle trajectories are of three types: specularly reflected, multiple traversal, and multiple bounce. All backstreaming reflected ions are found to suffer specular reflection on their first encounter with the shock surface; their subsequent behavior is determined by the angle θBn and their initial conditions.

39 citations


Journal ArticleDOI
TL;DR: In this article, a method is given to determine θ Bn and M A and their estimated errors for all types of shocks without knowing the shock normals, where the only measured quantities needed to determine the parameters are the plasma density and magnetic field on both sides of the shock.

01 Jul 1984
TL;DR: In this paper, the effects of crossflow on the scale and properties of attached and separated region induced over a flate plate at the base of skewed/oblique shocks were examined.
Abstract: : This report describes results from 3 experimental studies designed to examine the aerothermal characteristics of regions of three-dimensional shock wave/boundary layer interaction in high-speed flow over non-adiabatic surfaces. The objectives were: (1) to explore the basic mechanisms associated with 3D boundary layer separation in high-speed flows with special emphasis on the large heat transfer rates and gradients developed in the separation and reattachment regions of these flows; and (2) to obtain detailed sets of experimental measurements with which to extend the simple semi-empirical prediction methods to the hypersonic/cooled wall regime where no previous data existed. These studies were conducted at mach 11 for Reynolds number of up to 40 million in Calspan's 96-Inch Shock Tunnel. In the first study we examined the effects of crossflow on the scale and properties of attached and separated region induced over a flate plate at the base of skewed/oblique shocks. Analysis of the detailed heat transfer and pressure measurements together with flow visualization demonstrated that, for sweep angles of up to 45 deg, crossflow had little effect on the size or characteristics of the interaction regions. In the second study the swept-shock was induced normal to the flat plate boundary layer by a shock generator mounted perpendicular to the flat plate. Our corner flow measurements demonstrated that, in highly-cooled hypersonic flows, the pressure rise to induce incipient separation is significantly larger than predicted by the semi-empirical methods.

Journal ArticleDOI
TL;DR: In this paper, the reflection of oblique shock waves in air in pseudo-stationary flow was investigated analytically and numerically, and the transition boundaries between the four types of shock-wave reflection (regular RR, single Mach SMR, complex Mach CMR and double Mach DMR) were established up to an initial shock Mach number MS = 20 for both frozen (perfect) and imperfect air in thermodynamic equilibrium (rotation-vibration coupling, vibrational excitation, dissociation, electronic excitation and ionization).

Journal ArticleDOI
TL;DR: In this paper, a numerical study of the conical, supersonic, inviscid flow about circular slender cones at large incidence is presented, and separation and an accompanying spiral are found.
Abstract: A numerical study of the conical, supersonic, inviscid flow about circular slender cones at large incidence is presented. Although the flow is assumed inviscid, separation and an accompanying spiral are found. This phenomenon is shown to be a valid solution to Euler's equations, i.e., valid in the sense of being independent of any numerical viscosity. The separation and spiral are caused solely by the vorticity produced by a cross-flow shock. The resulting separated flowfields are compared to full potential calculations and to experimental data.

Journal ArticleDOI
TL;DR: In this article, a theory concerning turbulent boundary-layer development behind a shock moving with uniform speed was used to obtain numerical results for turbulent boundary layer properties in air, and the results were tabulated for shock propagation at Mach numbers in the range 1.01
Abstract: A theory, previously presented by the author, concerning turbulent boundary-layer development behind a shock moving with uniform speed is used to obtain numerical results for turbulent boundary-layer properties in air. Numerical results are tabulated for shock propagation at Mach numbers in the range 1.01

01 Jan 1984
TL;DR: In this article, the structure of the bow shock wave was analyzed by analyzing satellite observations and comparing them with generalized results of laboratory experiments, and it was shown that the bow wave fronts of a laminar type is similar to that of a transverse and oblique shock observed in a laboratory plasma.
Abstract: In this paper, by analyzing satellite observations and comparing them with generalized results of laboratory experiments a study is made of the structure of the bow shock wave and of the nature of the mechanisms that shape it up. It is shown that the structure of bow shock fronts of a laminar type is similar to that of a transverse and oblique shock observed in a laboratory plasma. The quasilaminar and turbulent (for not very large 0 < β1 ≲ 3) structures of the bow shock with “subshock” are similar to the shock with an isomagnetic jump in the laboratory plasma.

Journal ArticleDOI
TL;DR: The results of a test-particle simulation studying the movement of a lithium tracer ion injected upstream of the bow shock are reported in this paper, showing that even a moderate level of wave activity can substantially change the results obtained in the absence of waves.
Abstract: The results of a test-particle simulation studying the movement of a lithium tracer ion injected upstream of the bow shock are reported. Wave activity consists of parallel and antiparallel propagating Alfven waves characterized by a frequency power spectrum within a frequency or range of amplitudes defined separately in the upstream and downstream regions. The results show that even a moderate level of wave activity can substantially change the results obtained in the absence of waves. Among the effects observed are: (1) increased ion transmission; (2) both the average energy gain and spread about the average are increased for transmitted and reflected particles; (3) the average final pitch angle for transmitted particles tends to 90 deg, and the spread of reflected particles is reduced; and (4) the spatial dispersion of the ions on the bow shock after a single encounter is increased.

Journal ArticleDOI
TL;DR: In this paper, an overview of previous studies of ion thermalization at the Prognoz-8 quasi-perpendicular bow shock crossing on 11 February 1981 is considered for which high-time resolution data on plasma and ELF electric field fluctuations are available.

Journal ArticleDOI
TL;DR: In this paper, the local interaction of an oblique shock wave with an unseparated turbulent boundary layer at a shallow two-dimensional compression corner is described by asymptotic expansions for small values of the non-dimensional friction velocity and the flow turning angle.
Abstract: The local interaction of an oblique shock wave with an unseparated turbulent boundary layer at a shallow two-dimensional compression corner is described by asymptotic expansions for small values of the non-dimensional friction velocity and the flow turning angle. It is assumed that the velocity-defect law and the law of the wall, adapted for compressible flow, provide an asymptotic representation of the mean velocity profile in the undisturbed boundary layer. Analytical solutions for the local mean-velocity and pressure distributions are derived in supersonic, hypersonic and transonic small-disturbance limits, with additional intermediate limits required at distances from the corner that are small in comparison with the boundary-layer thickness. The solutions describe small perturbations in an inviscid rotational flow, and show good agreement with available experimental data in most cases where effects of separation can be neglected. Calculation of the wall shear stress requires solution of the boundary-layer momentum equation in a sublayer which plays the role of a new thinner boundary layer but which is still much thicker than the wall layer. An analytical solution is derived with a mixing-length approximation, and is in qualitative agreement with one set of measured values.


Journal ArticleDOI
TL;DR: In this article, a model for the propagation of a solar flare and associated interplanetary shock wave is given, and a physical mechanism is described to calculate the probability that a weak shock which enters a turbulent solar wind region will degenerate into a MHD wave.

Journal Article
TL;DR: In this paper, an experimental investigation of sharp fin-induced shock/boundary layer interactions was carried out at a Mach number of 2.95, unit Reynolds numbers ranging from 1 to 4 million per inch, boundary layer thicknesses of 0.14 and 0.50 inches, and fin angles of attack between 12 and 22 degrees.
Abstract: : For this thesis an experimental investigation of sharp fin-induced shock/boundary layer interactions was carried out at a Mach number of 2.95, unit Reynolds numbers ranging from 1 to 4 million per inch, boundary layer thicknesses of 0.14 and 0.50 inches, and fin angles of attack between 12 and 22 degrees. Surface pressure and surface flow visualization data were collected. Results showed that high shock strength interactions were qualitatively similar to those at low shock strengths. When compared to two-dimensional test results, the present three-dimensional data were seen to have a similar dependence on Reynolds number but a different sort of dependence on shock strength. The data were also seen to possess conical similarity. As was the case at lower shock strengths, the interactions could be scaled using unit Reynolds number, boundary layer thickness, and normal Mach number. The appearance of the feature termed secondary separation was noted to depend on boundary layer thickness. Competing feature and turbulence scales were hypothesized to produce this dependence.

Journal ArticleDOI
TL;DR: In this paper, the authors derived the relation between the velocity of thermal shock wave propagation and the heat flux behind the wave and compared it with the theoretical approach of Lutset and co-workers (1981) and the experimental results of Cummings and coworkers (1978) and also comment on the remarks made by Turner (1981), concerning the observation of a critical velocity in shock wave experiments.
Abstract: When thermal shock waves propagate in helium II their velocity is related to the heat flux behind the wave. The authors derive this relation theoretically and compare it with the theoretical approach of Lutset and co-workers (1981) and the experimental results of Cummings and co-workers (1978). They also comment on the remarks made by Turner (1981) concerning the observation of a critical velocity in shock wave experiments.


Proceedings ArticleDOI
01 Jun 1984
TL;DR: In this article, a new method for solving the steady state Euler equations is presented, which is similar to streamline curvature methods but has a conserative finite volume formulation which ensures correct shock capturing.
Abstract: This paper presents a new method for solving the steady state Euler equations. The method is similar to streamline curvature methods but has a conserative finite volume formulation which ensures correct shock capturing. Either wall position or wall pressure may be prescribed as boundary conditions, permitting both direct and inverse calculations. In supersonic applications the solution is obtained by space-marching while in subsonic and transonic applications iterative relaxation methods are used. Numerical results are given for: (1) supersonic diffuser with oblique shocks (direct calculation); (2) supersonic jet entering still reservoir (inverse calculation); (3) subsonic bump in a channel with 25 percent blockage (direct and inverse); (4) subsonic high-work turbine cascade (direct); and (5) transonic bump in a channel with 12 percent blockage (direct calculation).

DissertationDOI
01 Jun 1984
TL;DR: In this article, an experimental investigation of the interaction of shock waves with discrete gas inhomogeneities is conducted in the GALCIT 15 cm diameter shock tube, where the gas volumes are cylindrical refraction cells of 5 cm diameter with a 0.5 µm thick membrane separating the test gas (helium or Freon 22) from the ambient air and large spherical soap bubbles containing the same gases.
Abstract: An experimental investigation of the interaction of shock waves with discrete gas inhomogeneities is conducted in the GALCIT 15 cm diameter shock tube. The gas volumes are cylindrical refraction cells of 5 cm diameter with a 0.5 µm thick membrane separating the test gas (helium or Freon 22) from the ambient air and large spherical soap bubbles containing the same gases. The incident wave Mach numbers are nominally 1.09 and 1.22. The wave pattern and the deformation of the gas volumes are documented by shadowgraphs. The transmitted and diffracted wave pressure profiles are recorded by pressure transducers at various distances behind the cylinders. The basic phenomena of acoustic wave refraction, reflection and diffraction by cylindrical acoustic lenses, with indices of refraction appropriate to the gases used in the experiments, are illustrated with computer-generated ray and wave-front diagrams. In the case of a Freon 22-filled cylinder, the wave diffracted externally around the body precedes the wave transmitted from the interior which goes through a focus just behind the cylinder, while in the case of the helium-filled cylinder the expanding transmitted wave runs ahead of the diffracted wave. Both sets of waves merge a few cylinder diameters downstream. The wave patterns inside the cylinder, showing initially the refracted waves and later the same waves reflected internally, present some interesting phenomena. The mechanisms by which the gas volumes are transformed into vertical structures by the shock motion are observed. The unique effect of shock acceleration and Rayleigh-Taylor instability on the spherical volume of helium leads to the formation of a strong vortex ring which rapidly separates from the main volume of helium. Measurements of the wave and gas-interface velocities are compared to values calculated for one-dimensional interactions and for a simple model of shock-induced Taylor instability. The behavior of thin liquid membranes accelerated by shocks under varying conditions is documented by high speed photography. In a related experiment, shock waves of Mach number between 1.005 and 1.36 interact with a dense random array of 2 mm diameter helium filled soap bubbles. Experimental results (based on shadowgraphs and pressure measurements) show that very weak shock waves (Ms ≤ 1.01) are strongly scattered by the array, which is left undisturbed by the shock, and that stronger shock waves, only locally disturbed by each bubble, maintain undisturbed pressure profiles because of nonlinear effects, while the array undergoes shock-induced mixing. A simple criterion for multiple scattering shows that the combined effect of many bubbles is necessary in order to produce important modifications on the shock wave pressure profile.

01 Jan 1984
TL;DR: In this paper, a method for analyzing shock coalescence which includes three dimensional effects was developed, based on an extension of the axisymmetric solution, with asymmetric effects introduced through an additional set of governing equations, derived by taking the second circumferential derivative of the standard shock equations in the plane of symmetry.
Abstract: A method for analyzing shock coalescence which includes three dimensional effects was developed. The method is based on an extension of the axisymmetric solution, with asymmetric effects introduced through an additional set of governing equations, derived by taking the second circumferential derivative of the standard shock equations in the plane of symmetry. The coalescence method is consistent with and has been combined with a nonlinear sonic boom extrapolation program which is based on the method of characteristics. The extrapolation program, is able to extrapolate pressure signatures which include embedded shocks from an initial data line in the plane of symmetry at approximately one body length from the axis of the aircraft to the ground. The axisymmetric shock coalescence solution, the asymmetric shock coalescence solution, the method of incorporating these solutions into the extrapolation program, and the methods used to determine spatial derivatives needed in the coalescence solution are described. Results of the method are shown for a body of revolution at a small, positive angle of attack.


Journal ArticleDOI
TL;DR: In this paper, the influence of the determining parameters on the size of the separation region formed when a normal shock wave impinges on a turbulent boundary layer in conical flows is analyzed.
Abstract: Published experimental data [1–5] are used to analyze the influence of the determining parameters on the size of the separation region formed when a normal shock wave impinges on a turbulent boundary layer in conical flows. Empirical dependences are proposed that make it possible to calculate the size of the region and its position relative to the incident shock wave or the direction of the undisturbed flow.

Journal ArticleDOI
M. M. Mellott1
TL;DR: In this paper, various collisionless dissipation mechanisms which can operate in weak shocks, taking into account the effects of different mechanisms on shock structure are investigated, and a restricted class of quasi-perpendicular low beta low Mach number shocks are traditionally called "laminar shocks".