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1
Vuorinen, Laura, Rami Vainio, Heli Hietala, and Terry Z. Liu. "Monte Carlo Simulations of Electron Acceleration at Bow Waves Driven by Fast Jets in the Earth’s Magnetosheath." Astrophysical Journal 934, no. 2 (August 1, 2022): 165. http://dx.doi.org/10.3847/1538-4357/ac7f42.
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Abstract The shocked solar wind flows around the Earth’s magnetosphere in the magnetosheath downstream of the Earth’s bow shock. Within this region, faster flows of plasma, called magnetosheath jets, are frequently observed. These jets have been shown to sometimes exhibit supermagnetosonic speeds relative to the magnetosheath flow and to develop bow waves or shocks of their own. Such jet-driven bow waves have been observed to accelerate ions and electrons. We model electron acceleration by magnetosheath jet-driven bow waves using test-particle Monte Carlo simulations. Our simulations suggest that the energy increase of electrons with energies of a few hundred eV to 10 keV can be explained by a collapsing magnetic trap forming between the bow wave and the magnetopause with shock drift acceleration at the moving bow wave. Our simulations allow us to estimate the efficiency of acceleration as a function of different jet and magnetosheath parameters. Electron acceleration by jet-driven bow waves can increase the total acceleration in the parent shock environment, most likely also at shocks other than the Earth’s bow shock.
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Czaykowska, A., T. M. Bauer, R. A. Treumann, and W. Baumjohann. "Magnetic field fluctuations across the Earth’s bow shock." Annales Geophysicae 19, no. 3 (March 31, 2001): 275–87. http://dx.doi.org/10.5194/angeo-19-275-2001.
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Abstract. We present a statistical analysis of 132 dayside (LT 0700-1700) bow shock crossings of the AMPTE/IRM spacecraft. We perform a superposed epoch analysis of low frequency, magnetic power spectra some minutes up-stream and downstream of the bow shock. The events are devided into categories depending on the angle θBn between bow shock normal and interplanetary magnetic field, and on plasma-β. In the foreshock upstream of the quasi-parallel bow shock, the power of the magnetic fluctuations is roughly 1 order of magnitude larger (δB ~ 4 nT for frequencies 0.01–0.04 Hz) than upstream of the quasi-perpendicular shock. There is no significant difference in the magnetic power spectra upstream and downstream of the quasi-parallel bow shock; only at the shock itself, is the magnetic power enhanced by a factor of 4. This enhancement may be due to either an amplification of convecting upstream waves or to wave generation at the shock interface. On the contrary, downstream of the quasi-perpendicular shock, the magnetic wave activity is considerably higher than upstream. Down-stream of the quasi-perpendicular low-β bow shock, we find a dominance of the left-hand polarized component at frequencies just below the ion-cyclotron frequency, with amplitudes of about 3 nT. These waves are identified as ion-cyclotron waves, which grow in a low-β regime due to the proton temperature anisotropy. We find a strong correlation of this anisotropy with the intensity of the left-hand polarized component. Downstream of some nearly perpendicular (θBn ≈ 90°) high-β crossings, mirror waves are identified. However, there are also cases where the conditions for mirror modes are met downstream of the nearly perpendicular shock, but no mirror waves are observed.Key words. Interplanetary physics (plasma waves and turbulence) – Magnetospheric physics (magnetosheath; plasma waves and instabilities)
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ZHONG, XIAOLIN. "Leading-edge receptivity to free-stream disturbance waves for hypersonic flow over a parabola." Journal of Fluid Mechanics 441 (August 15, 2001): 315–67. http://dx.doi.org/10.1017/s0022112001004918.
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The receptivity of hypersonic boundary layers to free-stream disturbances, which is the process of environmental disturbances initially entering the boundary layers and generating disturbance waves, is altered considerably by the presence of bow shocks in hypersonic flow fields. This paper presents a numerical simulation study of the generation of boundary layer disturbance waves due to free-stream waves, for a two-dimensional Mach 15 viscous flow over a parabola. Both steady and unsteady flow solutions of the receptivity problem are obtained by computing the full Navier–Stokes equations using a high-order-accurate shock-fitting finite difference scheme. The effects of bow-shock/free-stream-sound interactions on the receptivity process are accurately taken into account by treating the shock as a discontinuity surface, governed by the Rankine-Hugoniot relations. The results show that the disturbance waves generated and developed in the hypersonic boundary layer contain both first-, second-, and third-mode waves. A parametric study is carried out on the receptivity characteristics for different free-stream waves, frequencies, nose bluntness characterized by Strouhal numbers, Reynolds numbers, Mach numbers, and wall cooling. In this paper, the hypersonic boundary-layer receptivity is characterized by a receptivity parameter defined as the ratio of the maximum induced wave amplitude in the first-mode-dominated region to the amplitude of the free-stream forcing wave. It is found that the receptivity parameter decreases when the forcing frequency or nose bluntness increase. The results also show that the generation of boundary layer waves is mainly due to the interaction of the boundary layer with the acoustic wave field behind the bow shock, rather than interactions with the entropy and vorticity wave fields.
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Знаменская, И. А., Д. С. Наумов, Н. Н. Сысоев, and В. А. Черников. "Исследование динамических процессов, реализующихся при генерации плазмоидных образований в сверхзвуковом потоке." Журнал технической физики 89, no. 6 (2019): 856. http://dx.doi.org/10.21883/jtf.2019.06.47631.349-18.
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An analysis of plasma dynamic processes and shock waves interactions in supersonic jet at plasma spherical formation initiation was made using the high-speed digital image recording. The dynamics of the spherical plasmoid which creates discontinuities, affecting the bow shock wave in front of the model was investigated with a high temporal resolution. It was shown that during the time of plasmoid electric current (about 100-130 microseconds) the structure of supersonic flow around the model changes: the shock layer is transformed, bow shock wave detached distance on the symmetry axis is significantly increased due to a change of oncoming flow parameters and structure.
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JIANG, QINGFANG, and RONALD B. SMITH. "V-waves, bow shocks, and wakes in supercritical hydrostatic flow." Journal of Fluid Mechanics 406 (March 10, 2000): 27–53. http://dx.doi.org/10.1017/s0022112099007636.
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The structure of the bow shock, V-wave, and the related wave drag and wake in supercritical ambient flow are investigated for homogeneous hydrostatic single-layer flow with a free surface over an isolated two-dimensional (i.e. h(x, y)) obstacle. The two control parameters for this physical system are the ratio of obstacle height to fluid depth and the Froude number F = U/√gH. Based on theoretical analysis and numerical modelling, a steady-state regime diagram is constructed for supercritical flow. This study suggests that supercritical flow may have an upstream bow shock with a transition from the supercritical state to the subcritical state near the centreline, and a V-shock in the lee without a state transition. Unlike subcritical flow, neither a flank shock nor a normal lee shock is observed, due to the local supercritical environment. Both the bow shock and V-shock are dissipative and reduce the Bernoulli constant, but the vorticity generation is very weak in comparison with subcritical ambient flow. Thus, in supercritical flow, wakes are weak and eddy shedding is absent.Formulae for V-wave shape and V-wave drag are given using linear theory. Both formulae compare well with numerical model runs for small obstacles.These results can be applied to air flow over mountains, river hydraulics and coastal ocean currents with bottom topographies.
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Kosinov, Aleksandr, Maxim Golubev, and Alexey Pavlov. "On Determination Of The Mechanism Of Mach Wave / Bow-Shock Interaction." Siberian Journal of Physics 12, no. 2 (June 1, 2017): 20–27. http://dx.doi.org/10.54362/1818-7919-2017-12-2-20-27.
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The work presents the results of investigation of interaction of outer couple weak shock waves with a bow shock produced by a triangle plate at Mach number M = 2. The couple of waves were generated by a two-dimensional roughness on the wall of the test section of supersonic tunnel. Hotwire measurements showed generated to free flow perturbations to correspond to N-wave. Optical visualization was done applying schlieren technique and interferometric method using adaptive visualizing transparencies based on absorption saturation. Qualitative coincidence of hotwire and interference data was obtained. Inclination angle of weak waves passed through the bow shock was observed to change.
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Du, J., C. Wang, T. L. Zhang, M. Volwerk, and C. Carr. "Mirror waves and mode transition observed in the magnetosheath by Double Star TC-1." Annales Geophysicae 27, no. 1 (January 22, 2009): 351–55. http://dx.doi.org/10.5194/angeo-27-351-2009.
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Abstract. The Double Star TC-1 magnetosheath pass on 26 February 2004 is used to investigate magnetic field fluctuations. Strong compressional signatures which last for more than an hour have been found near the magnetopause behind a quasi-perpendicular bow shock. These compressional structures are most likely mirror mode waves. There is a clear wave transition in the magnetosheath which probably results from the change of the interplanetary magnetic field (IMF) cone angle. The wave characteristics in the magnetosheath are strongly controlled by the type of the upstream bow shock.
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Mazelle, C., D. Le Quéau, and K. Meziane. "Nonlinear wave-particle interaction upstream from the Earth's bow shock." Nonlinear Processes in Geophysics 7, no. 3/4 (December 31, 2000): 185–90. http://dx.doi.org/10.5194/npg-7-185-2000.
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Abstract. Well-defined ring-like backstreaming ion distributions have been recently reported from observations made by the 3DP/PESA-High analyzer onboard the WIND spacecraft in the Earth's foreshock at large distances from the bow shock, which suggests a local production mechanism. The maximum phase space density for these distributions remains localized at a nearly constant pitch-angle value for a large number of gyroperiods while the shape of the distribution remains very steady. These distributions are also observed in association with quasi-monochromatic low frequency (~ 50 mHz) waves with substantial amplitude (δB/B>0.2). The analysis of the magnetic field data has shown that the waves are propagating parallel to the background field in the right-hand mode. Parallel ion beams are also often observed in the same region before the observation of both the ring-like distributions and the waves. The waves appear in cyclotron resonance with the ion parallel beams. We investigate first the possibility that the ion beams could provide the free energy source for driving an ion/ion instability responsible for the ULF wave occurrence. For that, we solve the wave dispersion relation with the observed parameters. Second, we show that the ring-like distributions could then be produced by a coherent nonlinear wave-particle interaction. It tends to trap the ions into narrow cells in velocity space centered on a well-defined pitch-angle, directly related to the saturation wave amplitude in the analytical theory. The theoretical predictions are in good quantitative agreement with the observations
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Dimmock, A. P., M. A. Balikhin, S. N. Walker, and S. A. Pope. "Dispersion of low frequency plasma waves upstream of the quasi-perpendicular terrestrial bow shock." Annales Geophysicae 31, no. 8 (August 9, 2013): 1387–95. http://dx.doi.org/10.5194/angeo-31-1387-2013.
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Abstract. Low frequency waves in the foot of a supercritical quasi-perpendicular shock front have been observed since the very early in situ observations of the terrestrial bow shock (Guha et al., 1972). The great attention that has been devoted to these type of waves since the first observations is explained by the key role attributed to them in the processes of energy redistribution in the shock front by various theoretical models. In some models, these waves play the role of the intermediator between the ions and electrons. It is assumed that they are generated by plasma instability that exist due to the counter-streaming flows of incident and reflected ions. In the second type of models, these waves result from the evolution of the shock front itself in the quasi-periodic process of steepening and overturning of the magnetic ramp. However, the range of the observed frequencies in the spacecraft frame are not enough to distinguish the origin of the observed waves. It also requires the determination of the wave vectors and the plasma frame frequencies. Multipoint measurements within the wave coherence length are needed for an ambiguous determination of the wave vectors. In the main multi-point missions such as ISEE, AMPTE, Cluster and THEMIS, the spacecraft separation is too large for such a wave vector determination and therefore only very few case studies are published (mainly for AMPTE UKS AMPTE IRM pair). Here we present the observations of upstream low frequency waves by the Cluster spacecraft which took place on 19 February 2002. The spacecraft separation during the crossing of the bow shock was small enough to determine the wave vectors and allowed the identification of the plasma wave dispersion relation for the observed waves. Presented results are compared with whistler wave dispersion and it is shown that contrary to previous studies based on the AMPTE data, the phase velocity in the shock frame is directed downstream. The consequences of this finding for both types of models that were developed to explain the generation of these waves are discussed.
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Clausen, L. B. N., T. K. Yeoman, R. C. Fear, R. Behlke, E. A. Lucek, and M. J. Engebretson. "First simultaneous measurements of waves generated at the bow shock in the solar wind, the magnetosphere and on the ground." Annales Geophysicae 27, no. 1 (January 22, 2009): 357–71. http://dx.doi.org/10.5194/angeo-27-357-2009.
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Abstract. On 5 September 2002 the Geotail satellite observed the cone angle of the Interplanetary Magnetic Field (IMF) change to values below 30° during a 56 min interval between 18:14 and 19:10 UT. This triggered the generation of upstream waves at the bow shock, 13 RE downstream of the position of Geotail. Upstream generated waves were subsequently observed by Geotail between 18:30 and 18:48 UT, during times the IMF cone angle dropped below values of 10°. At 18:24 UT all four Cluster satellites simultaneously observed a sudden increase in wave power in all three magnetic field components, independent of their position in the dayside magnetosphere. We show that the 10 min delay between the change in IMF direction as observed by Geotail and the increase in wave power observed by Cluster is consistent with the propagation of the IMF change from the Geotail position to the bow shock and the propagation of the generated waves through the bow shock, magnetosheath and magnetosphere towards the position of the Cluster satellites. We go on to show that the wave power recorded by the Cluster satellites in the component containing the poloidal and compressional pulsations was broadband and unstructured; the power in the component containing toroidal oscillations was structured and shows the existence of multi-harmonic Alfvénic continuum waves on field lines. Model predictions of these frequencies fit well with the observations. An increase in wave power associated with the change in IMF direction was also registered by ground based magnetometers which were magnetically conjunct with the Cluster satellites during the event. To the best of our knowledge we present the first simultaneous observations of waves created by backstreaming ions at the bow shock in the solar wind, the dayside magnetosphere and on the ground.
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Gorrell, Steven E., Theodore H. Okiishi, and William W. Copenhaver. "Stator-Rotor Interactions in a Transonic Compressor—Part 2: Description of a Loss-Producing Mechanism." Journal of Turbomachinery 125, no. 2 (April 1, 2003): 336–45. http://dx.doi.org/10.1115/1.1540120.
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A previously unidentified loss producing mechanism resulting from the interaction of a transonic rotor blade row with an upstream stator blade row is described. This additional loss occurs only when the two blade rows are spaced closer together axially. Time-accurate simulations of the flow and high-response static pressure measurements acquired on the stator blade surface reveal important aspects of the fluid dynamics of the production of this additional loss. At close spacing the rotor bow shock is chopped by the stator trailing edge. The chopped bow shock becomes a pressure wave on the upper surface of the stator that is nearly normal to the flow and that propagates upstream. In the reference frame relative to this pressure wave, the flow is supersonic and thus a moving shock wave that produces an entropy rise and loss is experienced. The effect of this outcome of blade-row interaction is to lower the efficiency, pressure ratio, and mass flow rate observed as blade-row axial spacing is reduced from far to close. The magnitude of loss production is affected by the strength of the bow shock and how much it turns as it interacts with the trailing edge of the stator. At far spacing the rotor bow shock degenerates into a bow wave before it interacts with the stator trailing edge and no significant pressure wave forms on the stator upper surface. For this condition, no additional loss is produced.
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Dimmock, A. P., Yu V. Khotyaintsev, A. Lalti, E. Yordanova, N. J. T. Edberg, K. Steinvall, D. B. Graham, et al. "Analysis of multiscale structures at the quasi-perpendicular Venus bow shock." Astronomy & Astrophysics 660 (April 2022): A64. http://dx.doi.org/10.1051/0004-6361/202140954.
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Context. Solar Orbiter is a European Space Agency mission with a suite of in situ and remote sensing instruments to investigate the physical processes across the inner heliosphere. During the mission, the spacecraft is expected to perform multiple Venus gravity assist maneuvers while providing measurements of the Venusian plasma environment. The first of these occurred on 27 December 2020, in which the spacecraft measured the regions such as the distant and near Venus magnetotail, magnetosheath, and bow shock. Aims. This study aims to investigate the outbound Venus bow shock crossing measured by Solar Orbiter during the first flyby. We study the complex features of the bow shock traversal in which multiple large amplitude magnetic field and density structures were observed as well as higher frequency waves. Our aim is to understand the physical mechanisms responsible for these high amplitude structures, characterize the higher frequency waves, determine the source of the waves, and put these results into context with terrestrial bow shock observations. Methods. High cadence magnetic field, electric field, and electron density measurements were employed to characterize the properties of the large amplitude structures and identify the relevant physical process. Minimum variance analysis, theoretical shock descriptions, coherency analysis, and singular value decomposition were used to study the properties of the higher frequency waves to compare and identify the wave mode. Results. The non-planar features of the bow shock are consistent with shock rippling and/or large amplitude whistler waves. Higher frequency waves are identified as whistler-mode waves, but their properties across the shock imply they may be generated by electron beams and temperature anisotropies. Conclusions. The Venus bow shock at a moderately high Mach number (∼5) in the quasi-perpendicular regime exhibits complex features similar to the Earth’s bow shock at comparable Mach numbers. The study highlights the need to be able to distinguish between large amplitude waves and spatial structures such as shock rippling. The simultaneous high frequency observations also demonstrate the complex nature of energy dissipation at the shock and the important question of understanding cross-scale coupling in these complex regions. These observations will be important to interpreting future planetary missions and additional gravity assist maneuvers.
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Savin, S., G. Pallocchia, C. Wang, and L. Legen. "COLLISIONLES INTERACTIONS: MAGNETOPAUSE COMMUNICATES WITH BOW SHOCK?" XXII workshop of the Council of nonlinear dynamics of the Russian Academy of Sciences 47, no. 1 (April 30, 2019): 111. http://dx.doi.org/10.29006/1564-2291.jor-2019.47(1).34.
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Our analysis of a sunward Poynting flux throughout magnetosheath and foreshock (directly measured byINTERBALL-1, CLUSTER-4 and DOUBLE STAR TC1), for the first time clearly demonstrates, how the resonances in the magnetospheric boundary layers are transmitted back wards the bow shock: the short pulses of the sunward Poynting flux initiate the strongest (>80%!) 3-wave interactions with the incident dynamic pressure. They start in the foreshock, regulate the bow shock position and oscillations, and then another near- magnetopause 3-wave strong interactions assist plasma flow extra deflections and acceleration downstream the magnetopause.
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Oliveira, G. N., M. G. Silva, and L. R. Carrocci. "PARAMETRIC SYSTEM IDENTIFICATION APPLIED TO THE BOW SHOCK WAVE SHAPE." Revista de Engenharia Térmica 12, no. 1 (June 30, 2013): 45. http://dx.doi.org/10.5380/reterm.v12i1.62029.
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In this paper it is addressed the prediction of form and location of detached shock waves ahead of two-dimensional and axially symmetric bodies at an zero angle of attack. As shown in Figs. 5 and 6, results show a very good agreement with experimental data. In this context an approximate method, based on a simplified form of the continuity relation, is developed to predict the location of detached shock waves ahead of two-dimensional and axially symmetric bodies. In order to reduce the problem to an equivalent onedimensional form, it is assumed that: (1) The form of the shock between its foremost point and its sonic point is adequately represented by a hyperbola asymptotic to tile free-stream Mach lines; and (2) the sonic line between the shock and the body is straight and inclined at a constant angle. Although the new methodology has some points of contact with earlier methodologies, the novelty here is that it is used Missile Datcom code as an aid to find out sonic point on body and also it is adopted Parametric System Identification (PSI) in the determination of bow shock shape which uses the Matlab® optimizer fmincon function and an active set strategy to minimize an error in a rms sense subject to simple constraint placed on the parameters by the user. The optimizer function calls a user written function which calculates the shape of the shock wave using the current parameters supplied by optimizer. Also for the shock distance L, the methodology presented here allows to select the value of the mentioned constant angle consistently based either in aerodynamics literature or through physical considerations. As the L value is previously known from measurements or aerodynamics literature, it was used an optimizer to minimize the error between predicted and known result varying a parameter which absorbs all inconsistencies that arise when it is used the basic Moeckel’s model considered here. Once the principal characteristics of the shock wave are calculated, an error value is returned to optimizer function based on the differences between predicted and known results.
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Chen, Kaiyi. "High Energy Cosmic Generation Form Collisionless Shock Wave Acceleration." Highlights in Science, Engineering and Technology 38 (March 16, 2023): 835–41. http://dx.doi.org/10.54097/hset.v38i.5967.
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The collision less shock wave one of the shock waves that is more likely to detect in the plasma that come from the magnetosphere, interplanetary space and so far. The most significance difference between other shock wave is the direct collision between particle is almost not exist. To be specific, the bow shock wave that occur by the interact of magnetosphere of an astrophysical object and solar wind is one of the collisions less shock wave. The collision-less shock wave in the universe could accelerate the particle in to high energy and form cosmic rays. In this essay, the basic reorganization of collision-less shock wave will be illustrated. On this basis, this paper is going to analysis a few mechanism of how the collision-less shock wave accelerate the particle and the recent experiment about the shock wave. According to the analysis, lots of state-of-art observations can be explained. These results shed light on guiding further exploration of high energy cosmic ray.
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Hanusch, Adrian, Tatyana V. Liseykina, and Mikhail A. Malkov. "Electron energization in quasi-parallel shocks." Astronomy & Astrophysics 642 (October 2020): A47. http://dx.doi.org/10.1051/0004-6361/202038915.
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Context. In situ observations of energetic particles at the Earth’s bow-shock that are attainable by the satellite missions have fostered the opinion for a long time that electrons are most efficiently accelerated in a quasi-perpendicular shock geometry. However, shocks that are deemed to be responsible for the production of cosmic ray electrons and their radiation from sources such as supernova remnants are much more powerful and larger than the Earth’s bow-shock. Their remote observations and also in situ measurements at Saturn’s bow shock, that is, the strongest shock in the Solar System, suggest that electrons are accelerated very efficiently in the quasi-parallel shocks as well. Aims. In this paper we investigate the possibility that protons that are accelerated to high energies create sufficient wave turbulence, which is necessary for the electron preheating and subsequent injection into the diffusive shock acceleration in a quasi-parallel shock geometry. Methods. An additional test-particle-electron population, which is meant to be a low-density addition to the electron core-distribution on which the hybrid simulation operates, is introduced. Our purpose is to investigate how these electrons are energized by the “hybrid” electromagnetic field. The reduced spatial dimensionality allowed us to dramatically increase the number of macro-ions per numerical cell and achieve the converged results for the velocity distributions of test electrons. Results. We discuss the electron preheating mechanisms, which can make a significant part of thermal electrons accessible to the ion-driven waves observed in hybrid simulations. We find that the precursor wave field supplied by ions has a considerable potential to preheat the electrons before they are shocked at the subshock. Our results indicate that a downstream thermal equilibration of the hot test electrons and protons does not occur. Instead, the resulting electron-to-proton temperature ratio is a decreasing function of the shock Mach number, MA, which has a tendency for a saturation at high MA.
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Kamaletdinov, S. R., I. Y. Vasko, A. V. Artemyev, R. Wang, and F. S. Mozer. "Quantifying electron scattering by electrostatic solitary waves in the Earth's bow shock." Physics of Plasmas 29, no. 8 (August 2022): 082301. http://dx.doi.org/10.1063/5.0097611.
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The electrostatic fluctuations are always present in the Earth's bow shock at frequencies above about 100 Hz, but the effects of this wave activity on electron dynamics have not been quantified yet. In this paper, we quantify electron pitch-angle scattering by electrostatic solitary waves, which make up a substantial part of the electrostatic fluctuations in the Earth's bow shock and were recently shown to be predominantly ion holes. We present analytical estimates and test-particle simulations of electron pitch-angle scattering by ion holes typical of the Earth's bow shock and conclude that this scattering can be rather well quantified within the quasi-linear theory. We use the observed distributions of ion hole parameters to estimate pitch-angle scattering rates by the ensemble of ion holes typical of the Earth's bow shock. We use the recently proposed theory of stochastic shock drift acceleration to show that pitch-angle scattering of electrons by the electrostatic fluctuations can keep electrons in the shock transition region long enough to support acceleration of thermal electrons by a factor of a few tens, that is up to a few hundred eV. Importantly, the electrostatic fluctuations can be more efficient in pitch-angle scattering of [Formula: see text] keV electrons, than typically observed whistler waves.
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Liu, Yanming, Hong Zhang, and Pingchao Liu. "Flow control in supersonic flow field based on micro jets." Advances in Mechanical Engineering 11, no. 1 (January 2019): 168781401882152. http://dx.doi.org/10.1177/1687814018821526.
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The flow field around supersonic aircraft is usually accompanied by complex flow phenomena, such as shock wave and shock wave/boundary layer interaction, which cause some adverse effects on aircraft performance. Seeking effective flow control methods has been a hot topic for many researchers. As an important method to improve the flow characteristics in supersonic flows, micro jet technology and its control mechanism have been paid much attention. In this article, we used compression corner calculation model and conducted detailed numerical investigations in the supersonic flow field with different injection pressure ratios, various actuation positions, and different nozzle types. The interaction between the micro jets and supersonic upstream flows generates complex flow structures, which contain bow shocks, barrel shocks, Mach disk, counter-rotating vortex pairs, and so on. The flow characteristics with micro jet schemes are superior to those in the no-control case. The controlling performance of micro jet is mainly determined by the following aspects. First, the downwash effect of counter-rotating vortex pairs can bring high-energy fluid into the bottom of the boundary layer to activate low-energy fluid and then strengthen the ability of resisting the flow separations. Second, the bow shock, which is generated upstream of the micro jet, significantly decelerates the downstream flows. Thus, the shock intensity at the corner is weakened and the characteristic of shock wave/boundary layer interaction is improved. In addition, the effective function range of MJ, that is, the distance between the counter-rotating vortex pair and the wall surface, is also an important factor. When both the counter-rotating vortex pairs and the bow shock are further from the wall, the flow characteristics around the corner in a larger area can be improved. Research shows that the micro jet scheme with Laval nozzle gives better controlling effect on shock wave/boundary layer interaction when the injection pressure radio is set to be 0.6, with the actuation location being 20 times the jet outlet diameter upstream of the corner.
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Shi, Xiaofei, Terry Liu, Anton Artemyev, Vassilis Angelopoulos, Xiao-Jia Zhang, and Drew L. Turner. "Intense Whistler-mode Waves at Foreshock Transients: Characteristics and Regimes of Wave−Particle Resonant Interaction." Astrophysical Journal 944, no. 2 (February 1, 2023): 193. http://dx.doi.org/10.3847/1538-4357/acb543.
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Abstract Thermalization and heating of plasma flows at shocks result in unstable charged-particle distributions that generate a wide range of electromagnetic waves. These waves, in turn, can further accelerate and scatter energetic particles. Thus, the properties of the waves and their implication for wave−particle interactions are critically important for modeling energetic particle dynamics in shock environments. Whistler-mode waves, excited by the electron heat flux or a temperature anisotropy, arise naturally near shocks and foreshock transients. As a result, they can often interact with suprathermal electrons. The low background magnetic field typical at the core of such transients and the large wave amplitudes may cause such interactions to enter the nonlinear regime. In this study, we present a statistical characterization of whistler-mode waves at foreshock transients around Earth’s bow shock, as they are observed under a wide range of upstream conditions. We find that a significant portion of them are sufficiently intense and coherent (narrowband) to warrant nonlinear treatment. Copious observations of background magnetic field gradients and intense whistler wave amplitudes suggest that phase trapping, a very effective mechanism for electron acceleration in inhomogeneous plasmas, may be the cause. We discuss the implications of our findings for electron acceleration in planetary and astrophysical shock environments.
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BINGHAM, R., R. BAMFORD, B. J. KELLETT, and V. D. SHAPIRO. "Electron energization in lunar magnetospheres." Journal of Plasma Physics 76, no. 6 (August 20, 2010): 915–18. http://dx.doi.org/10.1017/s0022377810000462.
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AbstractThe interaction of the solar wind with lunar surface magnetic fields produces a bow shock and a magnetosphere-like structure. In front of the shock wave energetic electrons up to keV energies are produced. This paper describes how resonant interactions between plasma turbulence in the form of lower-hybrid waves and electrons can result in field aligned electron acceleration. The turbulent wave fields close to the lower-hybrid resonant frequency are excited most probably by the modified two-stream instability, driven by the solar wind ions that are reflected and deflected by the low shock.
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Ocker, Stella Koch, James M. Cordes, Shami Chatterjee, and Timothy Dolch. "An In Situ Study of Turbulence near Stellar Bow Shocks." Astrophysical Journal 922, no. 2 (December 1, 2021): 233. http://dx.doi.org/10.3847/1538-4357/ac2b28.
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Abstract Stellar bow shocks are observed in a variety of interstellar environments and shaped by the conditions of gas in the interstellar medium (ISM). In situ measurements of turbulent density fluctuations near stellar bow shocks are only achievable with a few observational probes, including Hα-emitting bow shocks and the Voyager Interstellar Mission (VIM). In this paper, we examine density variations around the Guitar Nebula, an Hα bow shock associated with PSR B2224+65, in tandem with density variations probed by VIM near the boundary of the solar wind and ISM. High-resolution Hubble Space Telescope observations of the Guitar Nebula taken between 1994 and 2006 trace density variations over scales from hundreds to thousands of au, while VIM density measurements made with the Voyager 1 Plasma Wave System constrain variations from thousands of meters to tens of au. The power spectrum of density fluctuations constrains the amplitude of the turbulence wavenumber spectrum near the Guitar Nebula to log 10 C n 2 = − 0.8 ± 0.2 m−20/3 and for the very local ISM probed by Voyager to log 10 C n 2 = − 1.57 ± 0.02 m−20/3. Spectral amplitudes obtained from multiepoch observations of four other Hα bow shocks also show significant enhancements from values that are considered typical for the diffuse, warm ionized medium, suggesting that density fluctuations near these bow shocks may be amplified by shock interactions with the surrounding medium or selection effects that favor Hα emission from bow shocks embedded in denser media.
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Princet, S. A., and N. Qin. "Mechanism of windward vortex shocks about supersonic slender bodies." Aeronautical Journal 106, no. 1063 (September 2002): 507–19. http://dx.doi.org/10.1017/s0001924000092368.
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AbstractA detailed numerical study has been performed to investigate the origin and mechanism of the formation of windward shocks that have been observed on inclined slender bodies at supersonic speeds inside the bow shock wave around the body. It is shown that the feature is associated with the virtual double cone-like deflection of the supersonic stream by the primary vortices and, as such, can be named the ‘vortex shock’.
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Kononov, D. A., D. V. Bisikalo, V. B. Puzin, and A. G. Zhilkin. "Transient Processes in a Binary System with a White Dwarf." Acta Polytechnica CTU Proceedings 2, no. 1 (February 23, 2015): 46–49. http://dx.doi.org/10.14311/app.2015.02.0046.
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Using the results of 3D gas dynamic numerical simulations we propose a mechanism that can explain the quiescent multihumped shape of light curves of WZ Sge short-period cataclysmic variable stars. Analysis of the obtained solutions shows that in the modeled system an accretion disk forms. In the outer regions of the disk four shock waves occur: two arms of the spiral tidal shock; “hot line”, a shock wave caused by the interaction of the circum-disk halo and the stream from the inner Lagrangian point; and the bow-shock forming due to the supersonic motion of the accretor and disk in the gas of the circum-binary envelope. In addition, in our solutions we observe a spiral precessional density wave in the disk. This wave propagates from inside the disk down to its outer regions and almost rests in the laboratory frame in one orbital period. As a results every next orbital period each shock wave passes through the outer part of the density wave. Supplying these shocks with extra-density the precessional density wave amplifies them, which leads to enhanced energy release at each shock and may be observed as a brightening (or hump) in the light curve. Since the velocity of the retrograde precession is a little lower that the orbital velocity of the system, the same shock wave at every next orbital cycle interacts with the density wave later than at the previous cycle. This causes the observed shift of the humps over binary phases. The number of the shock waves, interacting with the density wave determines the largest number of humps that may be observed in one orbital period of a WZ Sge type star.
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Pushkar, E. A., and A. S. Korolev. "Collision of a solar wind shock wave with the Earth’s bow shock. Wave flow pattern." Proceedings of the Steklov Institute of Mathematics 281, no. 1 (July 2013): 189–203. http://dx.doi.org/10.1134/s0081543813040160.
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Krasnoselskikh, V. V., T. Dudok de Wit, and S. D. Bale. "Determining the wavelength of Langmuir wave packets at the Earth's bow shock." Annales Geophysicae 29, no. 3 (March 28, 2011): 613–17. http://dx.doi.org/10.5194/angeo-29-613-2011.
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Abstract. The propagation of Langmuir waves in plasmas is known to be sensitive to density fluctuations. Such fluctuations may lead to the coexistence of wave pairs that have almost opposite wave-numbers in the vicinity of their reflection points. Using high frequency electric field measurements from the WIND satellite, we determine for the first time the wavelength of intense Langmuir wave packets that are generated upstream of the Earth's electron foreshock by energetic electron beams. Surprisingly, the wavelength is found to be 2 to 3 times larger than the value expected from standard theory. These values are consistent with the presence of strong inhomogeneities in the solar wind plasma rather than with the effect of weak beam instabilities.
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Smith, Charles W., Melvyn L. Goldstein, and Hung K. Wong. "Whistler wave bursts upstream of the Uranian bow shock." Journal of Geophysical Research 94, A12 (1989): 17035. http://dx.doi.org/10.1029/ja094ia12p17035.
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Lobzin, V. V., V. V. Krasnoselskikh, K. Musatenko, and T. Dudok de Wit. "On nonstationarity and rippling of the quasiperpendicular zone of the Earth bow shock: Cluster observations." Annales Geophysicae 26, no. 9 (September 23, 2008): 2899–910. http://dx.doi.org/10.5194/angeo-26-2899-2008.
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Abstract. A new method for remote sensing of the quasiperpendicular part of the bow shock surface is presented. The method is based on analysis of high frequency electric field fluctuations corresponding to Langmuir, upshifted, and downshifted oscillations in the electron foreshock. Langmuir waves usually have maximum intensity at the upstream boundary of this region. All these waves are generated by energetic electrons accelerated by quasiperpendicular zone of the shock front. Nonstationary behavior of the shock, in particular due to rippling, should result in modulation of energetic electron fluxes, thereby giving rise to variations of Langmuir waves intensity. For upshifted and downshifted oscillations, the variations of both intensity and central frequency can be observed. For the present study, WHISPER measurements of electric field spectra obtained aboard Cluster spacecraft are used to choose 48 crossings of the electron foreshock boundary with dominating Langmuir waves and to perform for the first time a statistical analysis of nonstationary behavior of quasiperpendicular zone of the Earth's bow shock. Analysis of hidden periodicities in plasma wave energy reveals shock front nonstationarity in the frequency range 0.33 fBi<f<fBi, where fBi is the proton gyrofrequency upstream of the shock, and shows that the probability to observe such a nonstationarity increases with Mach number. The profiles observed aboard different spacecraft and the dominating frequencies of the periodicities are usually different. Hence nonstationarity and/or rippling seem to be rather irregular both in space and time rather than resembling a quasiregular wave propagating on the shock surface.
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Znamenskaya, Irina, Vladimir Chernikov, and Olga Azarova. "Dynamics of Shock Structure and Frontal Drag Force in a Supersonic Flow Past a Blunt Cone under the Action of Plasma Formation." Fluids 6, no. 11 (November 4, 2021): 399. http://dx.doi.org/10.3390/fluids6110399.
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The paper is devoted to the experimental and CFD investigation of a plasma formation impact on the supersonic flow over a body “blunt cone-cylinder”. In the experiments, a series of schlieren pictures of bow shock wave–blast waves non-stationary interaction was obtained with the use of high speed shadowgraphy. The accompanying calculations are based on the system of Euler equations. The freestream Mach number is 3.1. The plasmoid is modeled by the instantaneous release of energy into a bounded volume of gas, increasing the pressure in the volume. The research of the dynamics of a shock wave structure caused by the bow shock wave and blast flow interaction has been conducted. The significant value of energy released to a supersonic flow (500J) allowed constructing a diagram of the generation and dynamics of the resulting shock waves and contact discontinuities, as well as obtaining a significant drop in the drag force and stagnation pressure (up to 80%). The dynamics of a low density and high gas temperature zone, which becomes the main factor reducing the frontal body drag force, was researched. The dynamics of the front surface drag forces have been studied for different values of the plasmoid energy as well. Qualitative agreement of the numerical flow patterns with the experiment ones has been obtained.
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Lin, Mingyue, Fan Yang, Zongmin Hu, Chun Wang, and Zonglin Jiang. "Transitional criterion and hysteresis of multiple shock–shock interference." Physics of Fluids 35, no. 4 (April 2023): 046110. http://dx.doi.org/10.1063/5.0146200.
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In this study, oblique-shock/bow-shock interference is theoretically and numerically studied with two incident shock waves. The transition criteria between the two modes of multiple shock–shock interference, i.e., the concomitant-jet (CJ) and dual-jet (DJ) modes, are given. The oblique shock relationship and shock polar analysis are utilized to obtain the analytical solution of the transition condition. The theoretical results indicate the existence of a dual solution interval (DSI) that widens with increasing Mach number and narrows with increasing deflection angle induced by the first incident shock wave. The DSI obtained by numerical simulation is considerably narrower than that theoretically predicted due to the advanced CJ→DJ and DJ→CJ transitions. The analysis reveals that the transitions are advanced due to the downstream disturbance and secondary waves in the flow field.
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Zhang, Bo, Quan Hong, Yun Bai, Jiquan Li, and Honghu Ji. "Numerical investigation of heat transfer in film layer under supersonic condition of convergent-divergent transition." Thermal Science 24, no. 3 Part B (2020): 2279–88. http://dx.doi.org/10.2298/tsci190401310z.
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The distribution of film cooling effectiveness in supersonic mainstream of circle-rectangular Convergent-Divergent transition has been numerically investigated under different pressure ratios. The shock wave exerted superior influence on film cooling. In supersonic main flow, extra compression waves formed in upstream of the film holes, resulted by the obstruction of the multiple cooling jets. This exerted extra pressure to the boundary-layer, induced adverse pressure gradient, and led to weakening of the film flow attachment ability and decreasing of local cooling effectiveness. Bow oblique shock wave occurred in front of holes, the two oblique bow shaped low pressure zones formed on both sides of the hole, and low cooling effectiveness zones appeared accordingly. The inefficient region at the leading edge of the hole destroyed the film developing between holes, decreased the cooling effectiveness accumulation in the rear part. The decrease of hole incline angle caused an increase of cooling effectiveness, which reduced reverse velocity gradient caused by shock wave in the boundary-layer and improved film attachment. The influence of main flow pressure ratio to film cooling was also investigated, and found with increasing of the ratio, the influence will became even significant.
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Guicking, L., K. H. Glassmeier, H. U. Auster, M. Delva, U. Motschmann, Y. Narita, and T. L. Zhang. "Low-frequency magnetic field fluctuations in Venus' solar wind interaction region: Venus Express observations." Annales Geophysicae 28, no. 4 (April 15, 2010): 951–67. http://dx.doi.org/10.5194/angeo-28-951-2010.
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Abstract. We investigate wave properties of low-frequency magnetic field fluctuations in Venus' solar wind interaction region based on the measurements made on board the Venus Express spacecraft. The orbit geometry is very suitable to investigate the fluctuations in Venus' low-altitude magnetosheath and mid-magnetotail and provides an opportunity for a comparative study of low-frequency waves at Venus and Mars. The spatial distributions of the wave properties, in particular in the dayside and nightside magnetosheath as well as in the tail and mantle region, are similar to observations at Mars. As both planets do not have a global magnetic field, the interaction process of the solar wind with both planets is similar and leads to similar instabilities and wave structures. We focus on the spatial distribution of the wave intensity of the fluctuating magnetic field and detect an enhancement of the intensity in the dayside magnetosheath and a strong decrease towards the terminator. For a detailed investigation of the intensity distribution we adopt an analytical streamline model to describe the plasma flow around Venus. This allows displaying the evolution of the intensity along different streamlines. It is assumed that the waves are generated in the vicinity of the bow shock and are convected downstream with the turbulent magnetosheath flow. However, neither the different Mach numbers upstream and downstream of the bow shock, nor the variation of the cross sectional area and the flow velocity along the streamlines play probably an important role in order to explain the observed concentration of wave intensity in the dayside magnetosheath and the decay towards the nightside magnetosheath. But, the concept of freely evolving or decaying turbulence is in good qualitative agreement with the observations, as we observe a power law decay of the intensity along the streamlines. The observations support the assumption of wave convection through the magnetosheath, but reveal at the same time that wave sources may not only exist at the bow shock, but also in the magnetosheath.
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Beketaeva, Asel, Amr H. Abdalla, and Yekaterina Moisseyeva. "Investigation of Vortex Structures for Supersonic Jet Interaction Flowfield." Applied Mechanics and Materials 798 (October 2015): 546–50. http://dx.doi.org/10.4028/www.scientific.net/amm.798.546.
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The three-dimensional supersonic turbulent flow in presence of symmetric transverse injection of round jet is simulated numerically. The simulation is based on the Favre-averaged Navier-Stokes equations coupled with Wilcox’s turbulence model. The numerical solution is performed using ENO scheme and is validated with the experimental data that include the pressure distribution on the wall in front of the jet in the plane symmetry. The numerical simulation is used to investigate in detail the flow physics for a range of the pressure ratio . The well-known primary shock formations are observed (a barrel shock, a bow shock, and the system of λ-shock waves), and the vortices are identified (horseshoe vortex, an upper vortex, two trailing vortices formed in the separation region and aft of the bow shock wave, two trailing vortices that merge together into one single rotational motion). During the experiment the presence of the new vortices near the wall behind the jet for the pressure ratio is revealed.
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Battarbee, Markus, Xóchitl Blanco-Cano, Lucile Turc, Primož Kajdič, Andreas Johlander, Vertti Tarvus, Stephen Fuselier, et al. "Helium in the Earth's foreshock: a global Vlasiator survey." Annales Geophysicae 38, no. 5 (October 20, 2020): 1081–99. http://dx.doi.org/10.5194/angeo-38-1081-2020.
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Abstract. The foreshock is a region of space upstream of the Earth's bow shock extending along the interplanetary magnetic field (IMF). It is permeated by shock-reflected ions and electrons, low-frequency waves, and various plasma transients. We investigate the extent of the He2+ foreshock using Vlasiator, a global hybrid-Vlasov simulation. We perform the first numerical global survey of the helium foreshock and interpret some historical foreshock observations in a global context. The foreshock edge is populated by both proton and helium field-aligned beams, with the proton foreshock extending slightly further into the solar wind than the helium foreshock and both extending well beyond the ultra-low frequency (ULF) wave foreshock. We compare our simulation results with Magnetosphere Multiscale (MMS) Hot Plasma Composition Analyzer (HPCA) measurements, showing how the gradient of suprathermal ion densities at the foreshock crossing can vary between events. Our analysis suggests that the IMF cone angle and the associated shock obliquity gradient can play a role in explaining this differing behaviour. We also investigate wave–ion interactions with wavelet analysis and show that the dynamics and heating of He2+ must result from proton-driven ULF waves. Enhancements in ion agyrotropy are found in relation to, for example, the ion foreshock boundary, the ULF foreshock boundary, and specular reflection of ions at the bow shock. We show that specular reflection can describe many of the foreshock ion velocity distribution function (VDF) enhancements. Wave–wave interactions deep in the foreshock cause de-coherence of wavefronts, allowing He2+ to be scattered less than protons.
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Yu, Chunkai, Zhongwei Yang, Xinliang Gao, Quanming Lu, and Jian Zheng. "Electron Acceleration by Moderate-Mach-number Low-β Shocks: Particle-in-Cell Simulations." Astrophysical Journal 930, no. 2 (May 1, 2022): 155. http://dx.doi.org/10.3847/1538-4357/ac67df.
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Abstract Particle acceleration is ubiquitous at shock waves, occurring on scales ranging from supernova remnants in the universe to coronal-mass-ejection-driven shocks and planetary bow shocks in the heliosphere. The most promising mechanism responsible for the almost universally observed power-law spectra is diffusive shock acceleration (DSA). However, how electrons are preaccelerated by different shocks to the energy required by the DSA theory is still unclear. In this paper, we perform two-dimensional particle-in-cell plasma simulations to investigate how the magnetic field orientations, with respect to simulation planes, affect electron preacceleration in moderate-Mach-number low- β shocks. Simulation results show that instabilities can be different as the simulation planes capture different trajectories of particles. For magnetic fields perpendicular to the simulation plane, electron cyclotron drift instability dominates in the foot. Electrons can be trapped by the electrostatic wave and undergo shock-surfing acceleration. For magnetic fields lying in the simulation plane, whistler waves produced by modified two-stream instability dominate in the foot and scatter the electrons. In both cases, electrons undergo multistage acceleration in the foot, shock surface, and immediate downstream, during which process shock-surfing acceleration takes place as part of the preacceleration mechanism in moderate-Mach-number quasi-perpendicular shocks.
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Siti Aisyah Alimuddin, Iman Fitri Ismail, Akmal Nizam Mohammed, and Bambang Basuno. "The Influence of Limiters on Davis-Yee and Harten-Yee TVD Schemes." CFD Letters 14, no. 9 (September 30, 2022): 15–31. http://dx.doi.org/10.37934/cfdl.14.9.1531.
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TVD schemes have many selections of limiters, but the recommendation of limiters for specific cases is not available in the literature. This study focuses on incorporating two flux limiters as the extension of the TVD schemes proposed by Harten-Yee and Davis-Yee and extends the test case on external flows, blunt-body. The method used in this study is Harten-Yee Upwind TVD and Davis-Yee Symmetric TVD scheme with different limiter functions to simulate cases for two-dimensional compressible flow. The results show that all the limiter functions can capture shock waves when the flow passes through the geometry at Mach number . The flow features such as bow shock, oblique shock, shock wave reflection, interaction, and expansion wave can all be captured in the case of the bump in a channel and wedge. While in the case of the external supersonic flow passing through the blunt-body, the presence of a bow shock was captured. We discovered that Davis-Yee limiter number 2 performs significantly better than other proposed Davis-Yee and Harten-Yee limiters for the case in this study. Therefore, the Davis-Yee Upwind TVD method is recommended to be applied for the identical case on the expansion of this study
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Hou, Chuanpeng, Jiansen He, Die Duan, Xingyu Zhu, Wenya Li, Daniel Verscharen, Terry Liu, and Tieyan Wang. "Efficient Energy Conversion through Vortex Arrays in the Turbulent Magnetosheath." Astrophysical Journal 946, no. 1 (March 1, 2023): 13. http://dx.doi.org/10.3847/1538-4357/acb927.
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Abstract Turbulence is often enhanced when transmitted through a collisionless plasma shock. We investigate how the enhanced turbulent energy in the Earth's magnetosheath effectively dissipates via vortex arrays. This research topic is of great importance as it relates to particle energization at astrophysical shocks across the universe. Wave modes and intermittent coherent structures are the key candidate mechanisms for energy conversion in turbulent plasmas. Here, by comparing in-situ measurements in the Earth's magnetosheath with a theoretical model, we find the existence of vortex arrays at the transition between the downstream regions of the Earth's bow shock. Vortex arrays consist of quasi-orthogonal kinetic waves and exhibit both high volumetric filling factors and strong local energy conversion, thereby showing a greater dissipative energization than traditional waves and coherent structures. Therefore, we propose that vortex arrays are a promising mechanism for efficient energy conversion in the sheath regions downstream of astrophysical shocks.
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Skalsky, A., R. Grard, S. Klimov, C. M. C. Nairn, J. G. Trotignon, and K. Schwingenschuh. "The Martian bow shock: Wave observations in the upstream region." Journal of Geophysical Research: Space Physics 97, A3 (March 1, 1992): 2927–33. http://dx.doi.org/10.1029/91ja03078.
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Dendy, R. O., and K. G. McClements. "Ion cyclotron wave emission at the quasi-perpendicular bow shock." Journal of Geophysical Research 98, A9 (1993): 15531. http://dx.doi.org/10.1029/93ja01386.
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Svetsov, V. "Vortical regime of the flow behind the bow shock wave." Shock Waves 11, no. 3 (September 2001): 229–44. http://dx.doi.org/10.1007/pl00004078.
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Papagiannis, Ilias, Asad Raheem, Altug Basol, Anestis Kalfas, Reza Abhari, Hisataka Fukushima, and Shigeki Senoo. "Unsteady flow mechanisms in the last stage of a transonic low pressure steam turbine—multistage effects and tip leakage flows." Journal of the Global Power and Propulsion Society 1 (July 20, 2017): F4IW8S. http://dx.doi.org/10.22261/f4iw8s.
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Abstract In this paper, an unsteady investigation of the last two stages of a low-pressure steam turbine with supersonic airfoils near the tip of the last stage’s rotor blade is presented. Goal is the investigation of multistage effects and tip leakage flow in the last stage of the turbine and to provide insight on the stator-rotor flow interaction in the presence of a bow-shock wave. This study is unique in a sense of combining experimental data for code validation and comparison with a numerical simulation of the last two stages of a real steam turbine, including tip-cavity paths and seals, steam modelling and experimental data used as inlet and outlet boundary conditions. Analysis of results shows high unsteadiness close to the tip of the last stage, due to the presence of a bow-shock wave upstream of the rotor blade leading edge and its interaction with the upstream stator blades, but no boundary layer separation on stator is detected at any instant in time. The intensity of the shock wave is weakest, when the axial distance of the rotor leading edge from the upstream stator trailing edge is largest, since it has more space available to weaken. However, a phase shift between the maximum values of static pressure along the suction side of the stator blade is identified, due to the shock wave moving with the rotor blades. Additionally, the bow-shock wave interacts with the blade shroud and the tip leakage flow. Despite the interaction with the incoming flow, the total tip leakage mass flow ingested in the tip-cavity shows a steady behaviour with extremely low fluctuations in time. Finally, traces of upstream stage’s leakage flow have been identified in the last stage, contributing to entropy generation in inlet and outlet of last stage’s stator blade, highlighting the importance of performing multistage simulations.
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Pfau-Kempf, Yann, Heli Hietala, Steve E. Milan, Liisa Juusola, Sanni Hoilijoki, Urs Ganse, Sebastian von Alfthan, and Minna Palmroth. "Evidence for transient, local ion foreshocks caused by dayside magnetopause reconnection." Annales Geophysicae 34, no. 11 (November 4, 2016): 943–59. http://dx.doi.org/10.5194/angeo-34-943-2016.
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Abstract. We present a scenario resulting in time-dependent behaviour of the bow shock and transient, local ion reflection under unchanging solar wind conditions. Dayside magnetopause reconnection produces flux transfer events driving fast-mode wave fronts in the magnetosheath. These fronts push out the bow shock surface due to their increased downstream pressure. The resulting bow shock deformations lead to a configuration favourable to localized ion reflection and thus the formation of transient, travelling foreshock-like field-aligned ion beams. This is identified in two-dimensional global magnetospheric hybrid-Vlasov simulations of the Earth's magnetosphere performed using the Vlasiator model (http://vlasiator.fmi.fi). We also present observational data showing the occurrence of dayside reconnection and flux transfer events at the same time as Geotail observations of transient foreshock-like field-aligned ion beams. The spacecraft is located well upstream of the foreshock edge and the bow shock, during a steady southward interplanetary magnetic field and in the absence of any solar wind or interplanetary magnetic field perturbations. This indicates the formation of such localized ion foreshocks.
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Langford, Matthew D., Andrew Breeze-Stringfellow, Stephen A. Guillot, William Solomon, Wing F. Ng, and Jordi Estevadeordal. "Experimental Investigation of the Effects of a Moving Shock Wave on Compressor Stator Flow." Journal of Turbomachinery 129, no. 1 (February 1, 2005): 127–35. http://dx.doi.org/10.1115/1.2370745.
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Linear cascade testing was performed to simulate the flow conditions experienced by stator blades in an axial compressor with supersonic relative Mach numbers at the inlet to the downstream embedded rotors. Experiments were conducted in a transonic blow-down wind tunnel with a nominal inlet Mach number of 0.65. A single moving normal shock introduced at the exit of the stator cascade simulated the bow shock from a downstream rotor. The shock was generated using a shock tube external to the wind tunnel. Pressure measurements indicated that the stator matched its design intent loading, turning, and loss under steady flow conditions. Effects of the passing shock on the stator flowfield were investigated using shadowgraph photography and digital particle image velocimetry (DPIV). Measurements were taken with three different shock strengths. In each case, the passing shock induced a vortex around the trailing edge of the stator. The size and strength of these vortices were directly related to the shock strength. A suction side separation on the trailing edge of the stator was observed and found to correlate with the vortex blockage.
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Comişel, H., M. Scholer, J. Soucek, and S. Matsukiyo. "Non-stationarity of the quasi-perpendicular bow shock: comparison between Cluster observations and simulations." Annales Geophysicae 29, no. 2 (February 3, 2011): 263–74. http://dx.doi.org/10.5194/angeo-29-263-2011.
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Abstract. We have performed full particle electromagnetic simulations of a quasi-perpendicular shock. The shock parameters have been chosen to be appropriate for the quasi-perpendicular Earth's bow shock observed by Cluster on 24 January 2001 (Lobzin et al., 2007). We have performed two simulations with different ion to electron mass ratio: run 1 with mi/me=1840 and run 2 with mi/me=100. In run 1 the growth rate of the modified two-stream instability (MTSI) is large enough to get excited during the reflection and upstream gyration of part of the incident solar wind ions. The waves due to the MTSI are on the whistler mode branch and have downstream directed phase velocities in the shock frame. The Poynting flux (and wave group velocity) far upstream in the foot is also directed in the downstream direction. However, in the density and magnetic field compression region of the overshoot the waves are refracted and the Poynting flux in the shock frame is directed upstream. The MTSI is suppressed in the low mass ratio run 2. The low mass ratio run shows more clearly the non-stationarity of the shock with a larger time scale of the order of an inverse ion gyrofrequency (Ωci): the magnetic field profile flattens and steepens with a period of ~1.5Ωci−1. This non-stationarity is different from reformation seen in previous simulations of perpendicular or quasi-perpendicular shocks. Beginning with a sharp shock ramp the large electric field in the normal direction leads to high reflection rate of solar wind protons. As they propagate upstream, the ion bulk velocity decreases and the magnetic field increases in the foot, which results in a flattening of the magnetic field profile and in a decrease of the normal electric field. Subsequently the reflection rate decreases and the whole shock profile steepens again. Superimposed on this 'breathing' behavior are in the realistic mass ratio case the waves due to the MTSI. The simulations lead us to a re-interpretation of the 24 January 2001 bow shock observations reported by Lobzin et al. (2007). It is suggested that the high frequency waves observed in the magnetic field data are due to the MTSI and are not related to a nonlinear phase standing whistler. Different profiles at the different spacecraft are due to the non-stationary behavior on the larger time scale.
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Wang, Dian Kai, Yan Ji Hong, and Jiang Bo Li. "Interaction of Laser Energy with Bow Shock in Mach 5 Flow." Applied Mechanics and Materials 313-314 (March 2013): 596–99. http://dx.doi.org/10.4028/www.scientific.net/amm.313-314.596.
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In order to develop a potential way to reduce the stagnation pressure and heat flux of the blunt body in hypersonic flow, single pulsed and high rated laser energy are deposited respectively to control the bow shock in Mach 5 flow. Process of the interaction of 100mJ single pulsed laser energy with bow shock is studied by schlieren experiment in Mach 5 shock tunnel. The results indicate that the schlieren photographs and stagnation pressure at different times fit well with the simulation. Bow shock is distorted by the laser induced blast wave. During a single laser pulse, the average stagnation pressure and temperature are reduced by 6.5% and 3.4%. High rated laser energy is used to sustain the low pressure and heat flux region to increase the control efficiency. With the power of 6.6% of the enthalpy flux, when the distance of deposition point and blunt body is 1.1 times of the diameter of the blunt body, the pressure and heat flux of the stagnation point is reduced to 49% and 75%, respectively. The mechanism of interaction of laser and bow shock is disclosed.
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Walker, S. N., M. A. Balikhin, H. St C. K. Alleyne, Y. Hobara, M. André, and M. W. Dunlop. "Lower hybrid waves at the shock front: a reassessment." Annales Geophysicae 26, no. 3 (March 26, 2008): 699–707. http://dx.doi.org/10.5194/angeo-26-699-2008.
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Abstract. The primary process occurring at a collisionless shock is the redistribution of the bulk upstream energy into other degrees of freedom. One part of this process results in the acceleration of electrons at the shock front. Accelerated electrons are observed at the terrestrial and other planetary shocks, comets, and their effects are observed in astrophysical phenomena such as supernova remnants and jets in the form of X-ray bremsstrahlung radiation. One of the physical models for electron acceleration at supercritical shocks is based on low-hybrid turbulence due to the presence of reflected ions in the foot region. Since lower hybrid waves propagate almost perpendicular to the magnetic field they can be simultaneously in resonance with both the unmagnetised ions (ω=Vik⊥) and magnetised electrons (ω=Vek||). In this paper, Cluster observations of the electric field are used to study the occurrence of lower hybrid waves in the front of the terrestrial bow shock. It is shown that the lower hybrid waves exist as isolated wave packets. However, the very low level of the observed lower hybrid turbulence is too small to impart significant energisation to the electron population.
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Pallocchia, G., A. A. Samsonov, M. B. Bavassano Cattaneo, M. F. Marcucci, H. Rème, C. M. Carr, and J. B. Cao. "Interplanetary shock transmitted into the Earth's magnetosheath: Cluster and Double Star observations." Annales Geophysicae 28, no. 5 (May 20, 2010): 1141–56. http://dx.doi.org/10.5194/angeo-28-1141-2010.
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Abstract. On day 7 May 2005, the plasma instruments on board Double Star TC1 and Cluster SC3 spacecraft register inside the magnetosheath, at 19:15:12 and 19:16:20 UT, respectively, a strong pressure pulse due to the impact of an interplanetary shock wave (IS) on the terrestrial bow shock. The analysis of this event provides clear and quantitative evidences confirming and strengthening some results given by past simulations and observational studies. In fact, here we show that the transmitted shock is slowed down with respect to the incident IS (in the Earth's reference frame) and that, besides the transmitted shock, the IS – bow shock interaction generates a second discontinuity. Moreover, supported also by a special set three-dimensional magnetohydrodynamic simulation, we discuss, as further effects of the interaction of the IS with the magnetosphere, other two interesting aspects of the present event, that is: the TC1 double crossing of the bow shock (observed few minutes after the impact of the IS) and the presence, only in the SC3 data, of a third discontinuity produced inside the magnetosheath.
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Miao, B., H. Kucharek, E. Möbius, C. Mouikis, H. Matsui, Y. C. M. Liu, and E. A. Lucek. "Remote sensing of local structure of the quasi-perpendicular Earth's bow shock by using field-aligned beams." Annales Geophysicae 27, no. 3 (March 2, 2009): 913–21. http://dx.doi.org/10.5194/angeo-27-913-2009.
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Abstract. Field-aligned ion beams (FABs) originate at the quasi-perpendicular Earth's bow shock and constitute an important ion population in the foreshock region. The bulk velocity of these FABs depends significantly on the shock normal angle, which is the angle between shock normal and upstream interplanetary magnetic field (IMF). This dependency may therefore be taken as an indicator of the local structure of the shock. Applying the direct reflection model to Cluster measurements, we have developed a method that uses proton FABs in the foreshock region for remote sensing of the local shock structure. The comparison of the model results with the multi-spacecraft observations of FAB events shows very good agreement in terms of wave amplitude and frequency of surface waves at the shock front.
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Kumar, Abhijeet, and Ben Thornber. "RANS Modelling of Shock-Wave Boundary Layer Interaction in a Mixed Compression Axisymmetric Hypersonic Intake." Applied Mechanics and Materials 846 (July 2016): 61–66. http://dx.doi.org/10.4028/www.scientific.net/amm.846.61.
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This work focuses on developing a design methodology for a mixed compression axisymmetric hypersonic intake and numerically computing flow around the designed intake using RANS methods to study shock/shock and shock wave/boundary layer interaction. The focus of the computational study is on the effect of increasing the blunt radius of the cowl lip on the resulting shock/shock interaction between the oblique shock emanating from the cone compression apex and the bow shock on the cowl lip; as well the resulting reflected oblique shock boundary layer interaction from the cowl tip onto the cone compression surface. Three (3) radii are tested: 2mm, 16mm and 32mm at Mach 2 and the study is extended to a nominal 16mm condition at Mach 5. It is found that with increasing cowl-lip radius the magnitude of the shock-wave/boundary layer interaction increases significantly. Separation on the cone compression surface is observed at the 16mm and 32mm case at the Mach 2 position and in the 16mm case at the Mach 5 position. In addition in the 16mm and 32mm cases at the Mach 2 position, a Mach stem is observed. The shock/shock interactions, however, are found to be less dramatic. Type III and IV phenomena are observed, however, there is limited interference with the bow shock.
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Lin, C. H., J. T. Lin, C. H. Chen, J. Y. Liu, Y. Y. Sun, Y. Kakinami, M. Matsumura, W. H. Chen, H. Liu, and R. J. Rau. "Ionospheric shock waves triggered by rockets." Annales Geophysicae 32, no. 9 (September 16, 2014): 1145–52. http://dx.doi.org/10.5194/angeo-32-1145-2014.
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Abstract. This paper presents a two-dimensional structure of the shock wave signatures in ionospheric electron density resulting from a rocket transit using the rate of change of the total electron content (TEC) derived from ground-based GPS receivers around Japan and Taiwan for the first time. From the TEC maps constructed for the 2009 North Korea (NK) Taepodong-2 and 2013 South Korea (SK) Korea Space Launch Vehicle-II (KSLV-II) rocket launches, features of the V-shaped shock wave fronts in TEC perturbations are prominently seen. These fronts, with periods of 100–600 s, produced by the propulsive blasts of the rockets appear immediately and then propagate perpendicularly outward from the rocket trajectory with supersonic velocities between 800–1200 m s−1 for both events. Additionally, clear rocket exhaust depletions of TECs are seen along the trajectory and are deflected by the background thermospheric neutral wind. Twenty minutes after the rocket transits, delayed electron density perturbation waves propagating along the bow wave direction appear with phase velocities of 800–1200 m s−1. According to their propagation character, these delayed waves may be generated by rocket exhaust plumes at earlier rocket locations at lower altitudes.
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Petrukovich, Anatoli A., Olga M. Chugunova, and Pavel I. Shustov. "Low-frequency magnetic variations at the high-<i>β</i> Earth bow shock." Annales Geophysicae 37, no. 5 (September 24, 2019): 877–89. http://dx.doi.org/10.5194/angeo-37-877-2019.
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Abstract. Observations of Earth's bow shock during high-β (ratio of thermal to magnetic pressure) solar wind streams are rare. However, such shocks are ubiquitous in astrophysical plasmas. Typical solar wind parameters related to high β (here β>10) are as follows: low speed, high density, and a very low interplanetary magnetic field of 1–2 nT. These conditions are usually quite transient and need to be verified immediately upstream of the observed shock crossings. In this report, three characteristic crossings by the Cluster project (from the 22 found) are studied using multipoint analysis, allowing us to determine spatial scales. The main magnetic field and density spatial scale of about a couple of hundred of kilometers generally corresponds to the increased proton convective gyroradius. Observed magnetic variations are different from those for supercritical shocks, with β∼1. Dominant magnetic variations in the shock transition have amplitudes much larger than the background field and have a frequency of ∼ 0.3–0.5 Hz (in some events – 1–2 Hz). The wave polarization has no stable phase and is closer to linear, which complicates the determination of the wave propagation direction. Spatial scales (wavelengths) of variations are within several tens to a couple of hundred of kilometers.