Turbulent Shock Research Articles

Interstellar Turbulence II: Implications and Effects

▪ Abstract Interstellar turbulence has implications for the dispersal and mixing of the elements, cloud chemistry, cosmic ray scattering, and radio wave propagation through the ionized medium. This review discusses the observations and theory of these effects. Metallicity fluctuations are summarized, and the theory of turbulent transport of passive tracers is reviewed. Modeling methods, turbulent concentration of dust grains, and the turbulent washout of radial abundance gradients are discussed. Interstellar chemistry is affected by turbulent transport of various species between environments with different physical properties and by turbulent heating in shocks, vortical dissipation regions, and local regions of enhanced ambipolar diffusion. Cosmic rays are scattered and accelerated in turbulent magnetic waves and shocks, and they generate turbulence on the scale of their gyroradii. Radio wave scintillation is an important diagnostic for small-scale turbulence in the ionized medium, giving information about the power spectrum and amplitude of fluctuations. The theory of diffraction and refraction as well as the main observations and scintillation regions are reviewed.

Time accurate numerical study of turbulent supersonic jets

A time accurate numerical study is presented of an over-expanded Mach 2 circular turbulent jet in which the flow is assumed axisymmetric. The focus of this investigation is on the jet screech phenomenon resulting from the interaction between the large-scale turbulent mixing region instabilities and the regular spacing of the shock wave-expansion system, (shock cells), in the over-expanded jet. The solution is obtained of the “short” time-dependent Reynolds averaged Navier–Stokes equations (TRANS), using a two-equation, k– ω, turbulence model. The time accurate method was first calibrated for the given model geometry when the flow was fully expanded, and the resulting mean flow characteristics were compared with experimental data. The results were in broad agreement for the first 10 diameters of the jet downstream of the exit. Further downstream the time-averaged axial velocity decayed at a slightly faster rate than in the experiments. In an ideal inviscid fully expanded jet no shock cells would be present but in the turbulent jet calculations weak shock cells appeared which gradually died out beyond about 10 diameters from the nozzle exit. The calculated non-dimensional time-averaged transverse velocity profiles showed self-similarity, when allowance was made for the false origin of the shear layer, in agreement with the measured results. In the calculations for the over-expanded jet it was found, in agreement with experimental data, that the interaction between shock cell modulated instability waves and the shock-expansion system generated jet screech. It was found, as part of the screech phenomenon, that the shocks and the shock cells oscillated over a small distance which increased from the axis to a maximum within the shear layer. This shock unsteadiness resulted in the shocks being smeared when viewed in the equivalent steady flow calculations.

Variable Density Fluid Turbulence. Fluid Mechanics and its Applications, Vol 69

Variable Density Fluid Turbulence. Fluid Mechanics and its Applications, Vol 69

Extraplanar Emission‐Line Gas in Edge‐on Spiral Galaxies. II. Optical Spectroscopy

The results from deep long-slit spectroscopy of nine edge-on spiral galaxies with known extraplanar line emission are reported. Emission from Hα, [N II] λλ6548, 6583, and [S II] λλ6716, 6731 is detected out to heights of a few kiloparsecs in all of these galaxies. Several other fainter diagnostic lines such as [O I] λ6300, [O III] λλ4959, 5007, and He I λ5876 are also detected over a smaller scale. The relative strengths, centroids, and widths of the various emission lines provide constraints on the electron density, temperature, reddening, source(s) of ionization, and kinematics of the extraplanar gas. In all but one galaxy, photoionization by massive OB stars alone has difficulties explaining all of the line ratios in the extraplanar gas. Hybrid models that combine photoionization by OB stars and another source of ionization such as photoionization by turbulent mixing layers or shocks provide a better fit to the data. The (upper limits on the) velocity gradients measured in these galaxies are consistent with the predictions of the galactic fountain model to within the accuracy of the measurements.

Constraints on star formation from the close packing of protostars in clusters

The mm-wave continuum sources (MCS) in Ophiuchus have mutual collision rates less than their collapse rates by a factor of 10 to 100, suggesting most will form stars without further interactions. However, this ratio of rates would have exceeded unity in the past if the MCS were 2.5 times larger than they are now. Such a high previous ratio was not likely, suggesting that the MCS grew from smaller sizes at a constant high density, possible behind turbulent shocks. Proximity constraints are even more important in massive clusters, where massive stars with the same or greater space density are more strongly interacting than the Ophiuchus MCS. As a result, the density contrast for MCS must be larger in massive clusters than it is in Ophiuchus, or significant coalescence will occur in the protostellar phase, possible forming a massive black hole. A proportionality to the second power of the Mach number allows the MCS cores to collapse independently. These results suggest that stars in dense clusters generally form on a dynamical time by the continuous collection and rapid collapse of turbulence-shocked gas. Implications of proximity constraints on the initial stellar mass function are also discussed.

Large Eddy Simulation of Unsteady Interaction between Supersonic Turbulent Boundary Layer and Shock Wave at a Compression Corner

Large eddy simulation (LES) of compression ramp flow with a shock wave was successfully performed at a free-stream Mach number of 2.9 and a Reynolds number of 10 6 based on the boundary layer thickness. A compressible Smagorinsky-type eddy viscosity model was employed. It was shown that the present LES predicts not only the time-averaged quantities but also fluctuations such as pressure deviation and shock motion near the compression corner. Also, the present simulation predicts the three-dimensional structure of shock/turbulent boundary interaction, which is difficult to simulate by using Reynolds averaged Navier-Stokes equations (RANS)

Shock Orientations, Magnetic Turbulence and Forbush Decreases

We have studied the effects of quasi-parallel and quasi-perpendicular shocks on the transient modulation of cosmic-ray intensity. Interplanetary magnetic field strength, its variance and solar wind velocity during their passage have also been considered for the analysis in this work. It has been demonstrated that magnetically turbulent quasi-parallel shocks are much more effective in producing Forbush decreases in cosmic-ray intensity than the non-turbulent quasi-perpendicular shocks. From these results it is inferred that turbulence in the shock environment is an important factor in causing Forbush decreases by scattering particles due to magnetic field fluctuations. Results presented in this study provide more specific information about structures responsible for Forbush decreases, physical processes mainly responsible for this phenomenon and the possibility of predicting the likely occurrence of Forbush decreases from observations in space.

Two‐dimensional simulations of a curved shock: Self‐consistent formation of the electron foreshock

A collisionless curved shock is analyzed in a supercritical regime with the help of a two‐dimensional electromagnetic full particle code. Curvature effects are included self‐consistently and allow one to follow continuously the transition from a narrow and step‐like strictly perpendicular shock to a wider and more turbulent oblique shock within the quasi‐perpendicular range 65° < θBn < 90°. Present results reproduce the formation of the electron foreshock without any simplifying assumptions. In agreement with experimental data, local bump‐on‐tail parallel distribution functions are well recovered in the foreshock region and correspond to electrons backstreaming along the magnetic field lines. Present detailed analysis shows that local back‐streaming distributions have two components: (i) a high parallel energy component corresponding to back‐streaming electrons characterized by a field‐aligned bump‐in‐tail or beam signature, and (ii) a low‐energy parallel component characterized by a loss cone signature (mirrored electron). Two types of bump‐in‐tail patterns, broad and narrow, are identified at short and large distances from the curved shock, respectively, and are due to different contributions of these two components according to the local impact of the time‐of‐flight effects. Present results allow one to identify more clearly the nature of the bump‐in‐tail pattern evidenced experimentally (narrow type). These also confirm that mirroring electrons make the dominant contribution to the bump‐in‐tail pattern in the total distribution in agreement with previous studies. Results suggest that low and high parallel energy populations are intimately related and may contribute together to the upstream wave turbulence.

Turbulent adiabatic shock waves and diffusive particle acceleration

We investigate the properties of turbulent adiabatic shock waves resulting from the self-consistent inclusion of finite Alfvén-wave pressure in the shock balance equations. We demonstrate (i) the absence of a switch-on shock; (ii) the existence of two separated domains where the Mach number is greater than unity that have gas compression, and an associated domain where the gas compression ratio is less than unity (i.e. a rarefaction domain); (iii) the difference between the scattering-centre compression ratio and the gas compression ratio for all upstream wave cross-helicity values except for the isolated case of zero helicity; (iv) the presence of anomalous domains where the cosmic-ray particle spectral index can be negative. All of these results are brought about by including the upstream and downstream turbulent wave energies in the shock balance structure. Without the waves, none of the effects persists.

Large Eddy Simulation of Unsteady Interaction between Supersonic Turbulent Boundary Layer and Shock Wave at a Compression Corner.

Large eddy simulation (LES) of compression ramp flow including shock wave was successfully performed at a free stream Mach number of 2.9 and a Reynolds number of 106 based on the boundary layer thickness. A compressible Smagorinsky-type eddy viscosity model was employed. It was shown that the present LES predicts not only the time-averaged quantities but fluctuations such as pressure deviation at compression corner. Also, the present simulation predicts three dimensional structure of shock/turbulent boundary interaction, which is essentially difficult to simulate by using Reynolds averaged Navier-Stokes equations (RANS).

Shock Wave—Turbulence Interactions

▪ Abstract The idealized interactions of shock waves with homogeneous and isotropic turbulence, homogeneous sheared turbulence, turbulent jets, shear layers, turbulent wake flows, and two-dimensional boundary layers have been reviewed. The interaction between a shock wave and turbulence is mutual. A shock wave exhibits substantial unsteadiness and deformation as a result of the interaction, whereas the characteristic velocity, timescales and length scales of turbulence change considerably. The outcomes of the interaction depend on the strength, orientation, location, and shape of the shock wave, as well as the flow geometry and boundary conditions. The state of turbulence and the compressibility of the incoming flow are two additional parameters that also affect the interaction.

A two-time-scale turbulence model for compressible flows: Turbulence dominated by mean deformation interaction

The multiple-time-scale concept is applied to develop a turbulence model for compressible flows. Transport equations for the turbulent kinetic energies and the energy transfer rates are linked to each domain of the turbulent spectrum. The model coefficients are calibrated, with respect to simple flows, by using a new method which takes advantage of the spectral character of the model. One innovation of this method is to use, as a component, the CG model [V. M. Canuto and I. Goldman, Phys. Rev. Lett. 54, 430 (1985)] which gives the large scale spectrum as a function of the instability-generating turbulence. Then, the two-time-scale model, with its complete set of coefficients, has been successfully applied to the simulation of plane mixing layers and homogeneous shear flows. A significant issue of this work is the study of the behavior of the two-time-scale model when a shock wave interacts with a homogeneous turbulence. We first compare model results with experimental data for a 2.8 Mach number interaction [D. Alem, Ph.D. thesis, Université de Poitiers, 1995]. The decrease of the integral length scale, predicted by the linear analysis, is reproduced with the two-time-scale model, which, moreover, recovered the rate of reduction measured by Alem. The amplification of the turbulence level through the shock wave is also consistent with the measurements. Then, we confront our results with a direct numerical simulation of the shock–turbulence interaction at M=1.2 [S. Lee et al., J. Fluid Mech. 251, 533 (1993)]. The spectrum of the turbulence injected in the inflow region of the direct numerical simulation appeared to be far from the freely decaying state. The two-time-scale model, which accounts for the spectral nonequilibrium effects, is able to recover the spatial decrease of turbulence in the inflow region whereas a single-time-scale model fails. Moreover, the profiles for the turbulent kinetic energy and its dissipation rate over all the calculation domain are much better reproduced with the two-time-scale model than with the primary k–ε model.

A parallel, implicit, multi-dimensional upwind, residual distribution method for the Navier-Stokes equations on unstructured grids

A multi-dimensional cell-vertex upwind discretization technique for the Navier-Strokes equations on unstructured grids is presented. The grids are composed of linear triangles in two and linear tetrahedra in three space dimensions. The nonlinear upwind schemes for the inviscid part can be viewed as a multi-dimensional generalization of the Roe-scheme, but also as a special class of Petrov-Galerkin schemes. They share with these schemes a compact Galerkin stencil, and are in addition monotonic by construction. The Petrov-Galerkin interpretation of the discretization technique allows a straightforward extension to the Navier-Strokes equations. For linear elements this boils down to a Galerkin discretization for the viscous terms. Compared to standard finite-volume methods on these grids, the method shows an increased accuracy, which becomes comparable with structured grid algorithms. The spatially discretized set of equations is integrated in time using the Backward Euler time integration method. The full Jacobian matrix is computed, either numerically by finite differences or approximated analytically, and stored. The resulting set of linear equations is solved by a Block MILU(0) preconditioned Krylov subspace method. For this purpose the Aztec library of SANDIA National Laboratories is used, which also takes care of the parallelization process and completely hides the details for the user. Results are presented for a two-dimensional turbulent shock wave boundary layer interaction in a nozzle and the turbulent flow over an ogive cylinder. All computations have been performed on the Cray T3E of the Technical University of Delft.

A method for separating shock wave motion and turbulence in LDV measurements

Two-component laser Doppler velocimetry (LDV) measurements were made in a planar, two-dimensional flow containing an unsteady oblique shock wave formed by the convergence of two supersonic streams past a thick plate. High-speed wall pressure measurements locate the shock wave and, consequently, allow separation of the effects of shock wave motion from the turbulence fluctuations in the LDV measurements of the shock-separated free shear layer. In the current flow isolating the large-scale changes in the position of the shock from the turbulence primarily reduces the experimental scatter rather than significantly changing the shapes or magnitudes of the turbulent stress profiles. Changes in the direction of shock motion do not significantly affect the mean velocity, but do affect the turbulent stresses.

Low-Dissipative High-Order Shock-Capturing Methods Using Characteristic-Based Filters

An approach which closely maintains the non-dissipative nature of classical fourth- or higher-order spatial differencing away from shock waves and steep gradient regions while being capable of accurately capturing discontinuities, steep gradient, and fine scale turbulent structures in a stable and efficient manner is described. The approach is a generalization of the method of Gustafsson and Olsson and the artificial compression method (ACM) switch of Harten. Spatially non-dissipative fourth- or higher-order compact and non-compact spatial differencings are used as the base schemes. Instead of applying a scalar filter as in Gustafsson and Olsson, an ACM switch is used to signal the appropriate amount of second- or third-order total variation diminishing (TVD) or essentially non-oscillatory (ENO) types of characteristic based numerical dissipation. This term acts as a characteristic filter to minimize numerical dissipation for the overall scheme. For time-accurate computations, time discretizations with low dissipation are used. Numerical experiments on 2-D vortical flows, vortex–shock interactions, and compressible spatially and temporally evolving mixing layers showed that the proposed schemes have the desired property with only a 10% increase in operations count over standard second-order TVD schemes. Aside from the ability to accurately capture shock–turbulence interaction flows, this approach is also capable of accurately preserving vortex convection. Higher accuracy is achieved with fewer grid points when compared to that of standard second-order TVD, positive, or ENO schemes.

Generation of Ternary Pr−Mo−O Oxides by Solid State Reactions between Oxide Powders under Ultrasonic Stirring

Time-of-flight secondary ion mass spectrometry (ToF-SIMS) and scanning electron microscopy are used to prove that the ultrasound used for the preparation of molybdenum- and praseodymium-based heterogeneous multiphase catalysts can induce solid-state reactions at room. temperature between the binary oxides Pr6O11 and MoO3. Turbulent flows and shock waves produced by the ultrasonic cavitation are thought to cause particles to collide into one another and to generate local temperatures which are sufficiently high far inducing interparticle melting. Unequivocal evidence is provided by ToF-SIMS that the ultrasonic dispersion leads to the surface formation of the praseodymium molybdate phase Pr2Mo3O12.

Full curvature effects of a collisionless shock

Curvature effects of a quasi-perpendicular collisionless shock in a super-critical regime are studied with the help of a 2 - D full particle electromagnetic simulation code, where both ions and electrons are treated as particles moving within self-consistent fields. The curved shock is initiated by using a cylindrical magnetic piston. Main characteristics of quasi-perpendicular collisionless shocks in the angular range 90° to 65° are fully recovered. Full curvature effects allow to follow continously the transition from a narrow and step-like strictly perpendicular shock to wider and more turbulent oblique shock waves. Present preliminary results emphasize the differences between planar and curved shock. For the first time to our knowledge, the formation of electron foreshock is fully recovered without any simplifying assumptions; moreover, loss cone distribution is also reproduced for high energy reflected electrons which is the signature of a dominant fast Fermi acceleration type process.

Direct Numerical Simulation of Turbulent Compression Ramp Flow

A numerical procedure for the direct numerical simulation of compressible turbulent flow and shock–turbulence interaction is detailed and analyzed. An upwind-biased finite-difference scheme with a compact centered stencil is used to discretize the convective part of the Navier–Stokes equations. The scheme has a uniformly high approximation order and allows for a spectral-like wave resolution while dissipating nonresolved wave numbers. When hybridized with an essentially nonoscillatory scheme near discontinuities, the scheme becomes shock–capturing and its resolution properties are preserved. Diffusive parts are discretized with symmetric compact finite differences and an explicit Runge–Kutta scheme is used for time-advancement. The peculiarities of efficient upwinding and coupling procedures are described and validation results are given. Using direct numerical simulation data, some aspects of turbulent supersonic compression ramp flow are studied to demonstrate the effectiveness of the simulation procedure.

Study of Passive Control in a Transonic Shock Wave/Boundary-Layer Interaction

Passive control applied to a turbulent shock wave/boundary-layer interaction has been investigated by considering a two-dimensional channel flow. The field has been probed in great detail by using a two-component laser Doppler velocimetry system to execute mean velocity and turbulence measurements. Four different perforated plates have been considered along with the solid wall reference case. These measurements have shown that passive control deeply modifies the inviscid flowfield structure, the single shock being replaced by a lambda shock system. This modified compression induces a substantial reduction of the wave drag associated with the interaction. On the other hand, the combined injection-suction effect taking place in the control region provokes an increase of the viscous drag, which nearly outbalances the reduction in wave drag. It was found that passive control induced a modest decrease of the total drag compared to the solid wall case. Moreover, the experimental wall transpiration velocity distribution in the control region is well represented by the usual laws

A basic experimental investigation of passive control applied to a transonic interaction

Passive control applied to a turbulent shock wave/boundary layer interaction has been investigated by considering a two-dimensional channel flow. The field resulting from application of passive control has been probed in great detail by using a two-component laser Doppler velocimetry system to execute mean velocity and turbulence measurements. Four different perforated plates have been considered, as also the solid wall reference case. The performed measurements have shown that passive control deeply modifies the inviscid flowfield structure, the unique strong shock being replaced by a lambda shock system. This fractionning of the compression induces a substantial reduction of the wave drag associated with the interaction. On the other hand, the combined injection-suction effect taking place in the control region provokes an important thickening of the boundary layer. There results an increase of the friction drag which nearly outbalances the gain in wave drag. A determination of the total drag in the control region was made. It was found that passive control induced a modest decrease of this drag compared to the solid wall case. Also, the rugosity of the holes is an important source of drag (excrescence drag) which contributes to compromise the potential benefit of the passive control technique.