Compressible Turbulence Research Articles

Influence of Intermittency on the Quasi-perpendicular Scaling in Three-dimensional Magnetohydrodynamic Turbulence

Abstract Solar wind fluctuations reveal the ubiquity of intermittency, which is believed to affect the spectral signatures of turbulence. In this work, based on simulation of driven compressible MHD turbulence, we apply the wavelet technique to the magnetic field and velocity to identify intermittency, and we analyze the influence of the intermittency on the quasi-perpendicular scaling in the inertial range. The numerical results show that the original magnetic and velocity fluctuations are anisotropic, and have a power anisotropy with a spectral index approaching the Iroshnikov–Kraichnan scaling in the direction quasi-perpendicular to the local mean magnetic field. As in observations of the solar wind fluctuations, as the scale decreases in the simulation, the calculated probability distribution functions (pdfs) of the wavelet coefficients become extended on both tails of the non-Gaussian distribution, with a rapid increase in flatness. After intermittency has been removed from the driven turbulence, at each scale, the pdfs approach a Gaussian distribution, with the flatness being ∼3. Meanwhile, the quasi-perpendicular scaling for both fluctuations becomes steeper and close to a Kolmogorov scaling, which may be a result of the stronger intermittency in the quasi-perpendicular direction and at the smaller scales. These results suggest that there is intermittency superposed on the “background” turbulence that seems to have the Kolmogorov scaling, whereby the overall slope is getting flatter with the involvement of intermittency.

Review of experimental Richtmyer–Meshkov instability in shock tube: From simple to complex

Richtmyer–Meshkov (RM) instability is regarded as a central role for understanding the hydrodynamic processes involved in inertial confinement fusion, supersonic combustion and supernova explosion. Because of its academic implication and engineering applications, the RM instability has received much attention since it was proposed. As an important tool for studying RM instability, shock tube experiment on shock–fluid interface interaction has been widely adopted and great progress has been achieved in past decades. The generation of a shock wave, the formation of an initial interface and the diagnostic of flow field are the three elements for studying the RM instability experimentally. This review surveys the advances in experimental investigations of RM instability in shock tube environment. Originating from a simple configuration as a planar shock interacting with a simple perturbed interface, the experimental study of RM instability approaches more complex situations like a convergent shock with a simple interface, or a planar shock with a complex interface. It is then expected that the experimental study on the real circumstance may be realized by using a complex shock with a complex interface. Finally, we propose the following issues for future study: (1) evolution of the RM instability induced by cylindrically converging shock waves; (2) effect of the three dimensions on the RM instability; (3) interaction of perturbed shock wave with an initially uniform or perturbed interface; and (4) formation and mixing mechanism of the compressible turbulence in the final stage of the RM instability.

Hybrid central–WENO scheme for the large eddy simulation of turbulent flows with shocks

ABSTRACTTo provide an effective numerical method for the large eddy simulation (LES) of turbulent flows with shocks, a hybrid scheme is developed in a finite volume framework based on the fourth-order central scheme and the third-order weighted essentially non-oscillatory (WENO) scheme. A total of six easy-to-implement and promising switch functions (SFs) are examined in the hybrid central–WENO scheme for the LES of compressible turbulent flows. Both the dissipation and dispersion of the developed hybrid central–WENO scheme are theoretically confirmed using the Fourier technique. Then, the effectiveness and accuracy of this scheme and the SFs are numerically tested by three problems: decaying compressible isotropic turbulence, inviscid, and turbulent transonic flow over a bump. The numerical results show the developed hybrid scheme, coupled with the SF based on local velocity divergence and pressure gradient, has excellent capabilities of capturing shocks and resolving turbulence.

Multipoint analysis of compressive fluctuations in the fast and slow solar wind

AbstractCompressible turbulence in the solar wind is a topic of much recent debate. To understand the various compressive fluctuations at scales comparable to proton characteristic lengths, we use multipoint magnetic field and density data (derived from spacecraft potential which allows higher time resolution than is typically possible than with particle instruments) from the Cluster spacecraft when they were in undisturbed intervals of slow and fast solar wind. The application of the multipoint signal resonator technique is performed for the first time, to the analysis of scalar time series. Fluctuations in the measurements of electron density and in magnitude of the magnetic field (used as a proxy for compressible magnetic fluctuations) are used as inputs in addition to the traditional vector components of the magnetic field. This analysis is performed on two streams of solar wind, one which can be classed as a slow stream and one which can be classed as a fast stream to investigate the difference in the compressible components in the two types of wind. The recovered plasma frame frequencies for the incompressible component show low propagation speed in the plasma frame consistent with previous applications of the method, while the compressible components are more scattered, some with very high phase speeds. Based on these results, we propose a picture of compressive solar wind turbulence as a mixed state of (1) linear modes such as kinetic Alfvén, kinetic slow, and ion Bernstein modes; (2) coherent structures with very small intrinsic frequencies; and (3) nonlinear or sideband modes.

The Origin of Compressible Magnetic Turbulence in the Very Local Interstellar Medium

Abstract Voyager 1 observed compressible magnetic turbulence in the very local interstellar medium (VLISM). We show that inner heliosheath (IHS) fast- and slow-mode waves incident on the heliopause (HP) generate VLISM fast-mode waves only that propagate into the VLISM. We suggest that this is the origin of compressible turbulence in the VLISM. We show that fast- and slow-mode waves transmitted across a tangential discontinuity such as the HP are strongly refracted on crossing the HP and subsequently propagate at highly oblique angles to the VLISM magnetic field. Thus, fast-mode waves in the VLISM contribute primarily to the compressible and not the transverse components of the VLISM fluctuating magnetic field variance since and . If the fast- and slow-mode waves in the IHS exhibit a Kolmogorov-like power spectral density, as appears to be observed by Voyager 1, then the corresponding transmitted spectral density in the VLISM forms an amplified power law. Consequently, the HP “radiates” fast-mode fluctuations into the VLISM, and the heliosphere therefore mediates the character of turbulence in the VLISM. In particular, we predict the form of the VLISM magnetic turbulence power spectral density to be a superposition of the background pristine interstellar turbulence spectrum and the fast-mode spectrum generated by the interaction of fast- and slow-mode IHS waves with the HP, i.e., a power law with an enhanced feature or “bump” corresponding to the contribution by fast-mode turbulence radiated by the HP. We note the applicability of these results to the generation of compressible turbulence in the local interstellar medium surrounding the asterospheres of stars.

Compressible Turbulence Model Consistency for Separated High-Speed Flow Regimes

Fluid compressibility can remarkably modify the behavior of turbulent flow with respect to the incompressible case. The presence of strong pressure-induced density changes adds to the turbulence phenomenology new specific processes and mechanisms, such as new pathways for energy exchanges and a strong coupling between momentum and energy exchanges, significantly altering the flow behavior. Many research groups are working on methods to include these compressibility effects in conventional turbulence models to predict the flowfield for compressible conditions more realistically. This work aims at the assessment and validation of several compressible corrections to an in-house hypersonic multigrid reactive Navier–Stokes code within the “baseline” Spalart–Allmaras turbulence model. The base pressure enhancement for supersonic afterbody flow computations is first addressed. Then, the shock/turbulent boundary-layer interaction at the junction of a cone/flare configuration is dealt with. The analysis of the numerical results and their comparison with the experimental data show that, in most cases, the proposed corrections produce a significant simulation improvement. Finally, an in-house hypersonic wind-tunnel test campaign is performed on generic blunt-cone/flare configurations. The pressure distributions along the model as well as the forces and moments are used to calibrate the numerical calculations in the range of Mach numbers of 4.8 to 6.2.

Scaling and intermittency in compressible isotropic turbulence

Structure functions and PDFs of increments of the compressible velocity component and thermodynamic variables in compressible isotropic turbulence are studied. The relative scaling exponent of the structure functions saturates with increase of the order, due to the effect of shocklets.

Viscosity, pressure and support of the gas in simulations of merging cool-core clusters

Major mergers are considered to be a significant source of turbulence in clusters. We performed a numerical simulation of a major merger event using nested-grid initial conditions, adaptive mesh refinement, radiative cooling of primordial gas, and a homogeneous ultraviolet background. By calculating the microscopic viscosity on the basis of various theoretical assumptions and estimating the Kolmogorov length from the turbulent dissipation rate computed with a subgrid-scale model, we are able to demonstrate that most of the warm-hot intergalactic medium can sustain a fully turbulent state only if the magnetic suppression of the viscosity is considerable. Accepting this as premise, it turns out that ratios of turbulent and thermal quantities change only little in the course of the merger. This confirms the tight correlations between the mean thermal and non-thermal energy content for large samples of clusters in earlier studies, which can be interpreted as second self-similarity on top of the self-similarity for different halo masses. Another long-standing question is how and to which extent turbulence contributes to the support of the gas against gravity. From a global perspective, the ratio of turbulent and thermal pressures is significant for the clusters in our simulation. On the other hand, a local measure is provided by the compression rate, i.e. the growth rate of the divergence of the flow. Particularly for the intracluster medium, we find that the dominant contribution against gravity comes from thermal pressure, while compressible turbulence effectively counteracts the support. For this reason it appears to be too simplistic to consider turbulence merely as an effective enhancement of thermal energy.

Direct numerical simulations of supersonic turbulent channel flows of dense gases

The influence of dense-gas effects on compressible wall-bounded turbulence is investigated by means of direct numerical simulations of supersonic turbulent channel flows. Results are obtained for PP11, a heavy fluorocarbon representative of dense gases, the thermophysics properties of which are described by using a fifth-order virial equation of state and advanced models for the transport properties. In the dense-gas regime, the speed of sound varies non-monotonically in small perturbations and the dependency of the transport properties on the fluid density (in addition to the temperature) is no longer negligible. A parametric study is carried out by varying the bulk Mach and Reynolds numbers, and results are compared to those obtained for a perfect gas, namely air. Dense-gas flow exhibits almost negligible friction heating effects, since the high specific heat of the fluids leads to a loose coupling between thermal and kinetic fields, even at high Mach numbers. Despite negligible temperature variations across the channel, the mean viscosity tends to decrease from the channel walls to the centreline (liquid-like behaviour), due to its complex dependency on fluid density. On the other hand, strong density fluctuations are present, but due to the non-standard sound speed variation (opposite to the mean density evolution across the channel), the amplitude is maximal close to the channel wall, i.e. in the viscous sublayer instead of the buffer layer like in perfect gases. As a consequence, these fluctuations do not alter the turbulence structure significantly, and Morkovin’s hypothesis is well respected at any Mach number considered in the study. The preceding features make high Mach wall-bounded flows of dense gases similar to incompressible flows with variable properties, despite the significant fluctuations of density and speed of sound. Indeed, the semi-local scaling of Patelet al.(Phys. Fluids, vol. 27 (9), 2015, 095101) or Trettel & Larsson (Phys. Fluids, vol. 28 (2), 2016, 026102) is shown to be well adapted to compare results from existing surveys and with the well-documented incompressible limit. Additionally, for a dense gas the isothermal channel flow is also almost adiabatic, and the Van Driest transformation also performs reasonably well. The present observations open the way to the development of suitable models for dense-gas turbulent flows.

Parallel Compatible Transition Closure Model for High-Speed Transitional Flow

A single-point transition closure model that incorporates analytical results by stability theory in a reasonably wide range of Mach numbers has been formulated for supersonic/hypersonic boundary-layer flows, which includes two transport equations to specify the transition onset locations: one for the eddy-viscosity coefficient of laminar fluctuations and another for intermittency factor. The effects of compressibility are modeled through solutions of laminar self-similar boundary layer at subsonic and supersonic conditions with a totally local closure. Then, to form a complete transition turbulence model, the proposed transition model is coupled with the compressible shear-stress transport turbulence model. In the end, several sets of well-documented flow cases are chosen to validate the present transition model, and the results are in satisfactory accord with experimental data. Proven by the numerical tests, the present model is capable of predicting well the supersonic/hypersonic transition onset that is dominated by the first and second Mack instability modes and laminar separation mode.

Scaling of energy spectra in weakly compressible turbulence

We find an asymptotic expression for the characteristic timescales of decorrelation processes in weakly compressible and isothermal turbulence. This result is used in the Eddy-Damped Quasi-Normal Markovian equation to derive the scalings of compressible energy spectra: (1) if the acoustic waves are dominant, the compressible energy spectra exhibit $$-7/3$$ scaling; (2) if local eddy straining is dominant, the compressible energy spectra are scaled as $$-3$$ . Meanwhile, the energy spectra of incompressible components display the same scaling of $$-5/3$$ as those in incompressible turbulence. The direct numerical simulations of weakly compressible turbulence are used to examine the scaling.

Scaling laws of compressible turbulence

Spatial scaling laws of velocity kinetic energy spectra for the compressible turbulence flow and the density-weighted counterparts are formulated in terms of the wavenumber, dissipation rate, and Mach number by using a dimensional analysis. We apply the Barenblatt’s incomplete similarity theory to both kinetic and density-weighted energy spectra. It shows that, within the initial subrange, both energy spectra approach the –5/3 and –2 power laws of the wavenumber when the Mach number tends to unity and infinity, respectively.

Resolution and Energy Dissipation Characteristics of Implicit LES and Explicit Filtering Models for Compressible Turbulence

Solving two-dimensional compressible turbulence problems up to a resolution of 16, 3842, this paper investigates the characteristics of two promising computational approaches: (i) an implicit or numerical large eddy simulation (ILES) framework using an upwind-biased fifth-order weighted essentially non-oscillatory (WENO) reconstruction algorithm equipped with several Riemann solvers, and (ii) a central sixth-order reconstruction framework combined with various linear and nonlinear explicit low-pass spatial filtering processes. Our primary aim is to quantify the dissipative behavior, resolution characteristics, shock capturing ability and computational expenditure for each approach utilizing a systematic analysis with respect to its modeling parameters or parameterizations. The relative advantages and disadvantages of both approaches are addressed for solving a stratified Kelvin-Helmholtz instability shear layer problem as well as a canonical Riemann problem with the interaction of four shocks. The comparisons are both qualitative and quantitative, using visualizations of the spatial structure of the flow and energy spectra, respectively. We observe that the central scheme, with relaxation filtering, offers a competitive approach to ILES and is much more computationally efficient than WENO-based schemes.

A Lower Bound on Adiabatic Heating of Compressed Turbulence for Simulation and Model Validation

Abstract The energy in turbulent flow can be amplified by compression, when the compression occurs on a timescale shorter than the turbulent dissipation time. This mechanism may play a part in sustaining turbulence in various astrophysical systems, including molecular clouds. The amount of turbulent amplification depends on the net effect of the compressive forcing and turbulent dissipation. By giving an argument for a bound on this dissipation, we give a lower bound for the scaling of the turbulent velocity with the compression ratio in compressed turbulence. That is, turbulence undergoing compression will be enhanced at least as much as the bound given here, subject to a set of caveats that will be outlined. Used as a validation check, this lower bound suggests that some models of compressing astrophysical turbulence are too dissipative. The technique used highlights the relationship between compressed turbulence and decaying turbulence.

Comparative statistics of selected subgrid-scale models in large-eddy simulations of decaying, supersonic magnetohydrodynamic turbulence.

Large-eddy simulations (LES) are a powerful tool in understanding processes that are inaccessible by direct simulations due to their complexity, for example, in the highly turbulent regime. However, their accuracy and success depends on a proper subgrid-scale (SGS) model that accounts for the unresolved scales in the simulation. We evaluate the applicability of two traditional SGS models, namely the eddy-viscosity (EV) and the scale-similarity (SS) models, and one recently proposed nonlinear (NL) SGS model in the realm of compressible magnetohydrodynamic (MHD) turbulence. Using 209 simulations of decaying, supersonic (initial sonic Mach number M_{s}≈3) MHD turbulence with a shock-capturing scheme and varying resolution, SGS model, and filter, we analyze the ensemble statistics of kinetic and magnetic energy spectra and structure functions. Furthermore, we compare the temporal evolution of lower- and higher-order statistical moments of the spatial distributions of kinetic and magnetic energy, vorticity, current density, and dilatation magnitudes. We find no statistical influence on the evolution of the flow by any model if grid-scale quantities are used to calculate SGS contributions. In addition, the SS models, which employ an explicit filter, have no impact in general. On the contrary, both the EV and NL models change the statistics if an explicit filter is used. For example, they slightly increase the dissipation on the smallest scales. We demonstrate that the nonlinear model improves higher-order statistics already with a small explicit filter, i.e., a three-point stencil. The results of, e.g., the structure functions or the skewness and kurtosis of the current density distribution are closer to the ones obtained from simulations at higher resolution. In addition, no additional regularization to stabilize the model is required. We conclude that the nonlinear model with a small explicit filter is suitable for application in more complex scenarios when higher-order statistics are important.

Suitability of artificial viscosity discontinuous Galerkin method for compressible turbulence

A discontinuous Galerkin method based on an artificial viscosity model is investigated in the context of the simulation of compressible turbulence. The effects of artificial viscosity on shock capturing ability, broadband accuracy and under-resolved instability are examined combined with various orders and mesh resolutions. For shock-dominated flows, the superior accuracy of high order methods in terms of discontinuity resolution are well retained compared with lower ones. For under-resolved simulations, the artificial viscosity model is able to enhance stability of the eighth order discontinuous Galerkin method despite of detrimental influence for accuracy. For multi-scale flows, the artificial viscosity model demonstrates biased numerical dissipation towards higher wavenumbers. Capability in terms of boundary layer flows and hybrid meshes is also demonstrated. It is concluded that the fourth order artificial viscosity discontinuous Galerkin method is comparable to typical high order finite difference methods in the literature in terms of accuracy for identical number of degrees of freedom, while the eighth order is significantly better unless the under-resolved instability issue is raised. Furthermore, the artificial viscosity discontinuous Galerkin method is shown to provide appropriate numerical dissipation as compensation for turbulent kinetic energy decaying on moderately coarse meshes, indicating good potentiality for implicit large eddy simulation.

Damping numerical oscillations in hybrid solvers through detection of Gibbs phenomenon

SummaryA Gibbs phenomenon detector that is useful in damping numerical oscillations in hybrid solvers for compressible turbulence is proposed and tested. It is designed to function in regions away from discontinuities where commonly used discontinuity sensors are ineffective. Using this Gibbs phenomenon detector in addition to a discontinuity sensor for combining central and shock capturing schemes provides an integrated way of dealing with numerical oscillations generated by shock waves and contact lines that are normal to the flow. When complete suppression of numerical oscillations is not possible, they are sufficiently localized. Canonical tests and large eddy simulations show that inclusion of the proposed detector does not cause additional damping of ‘well‐resolved’ physical oscillations. Copyright © 2017 John Wiley & Sons, Ltd.

Research advances in the influence of temperature on the sequential transportation in product pipeline

Sequential transportation is the main way of long-distance transportation for the oil product, whose essence is a coupling process of flow, mass transfer and heat transfer. Thus, like the pressure gradient and the concentration gradient, the heat gradient is one main power source of the mentioned coupling process as well. The previous related study done by researchers both at home and abroad mainly focus on the aspects including the making scheduling plans for batches in the oil product pipeline, the oil batch interface tracking as well as simulation, the scheme optimization for activating pumps, the mechanism of forming mixed oil and the detection of oil leakage. However, all of these works have failed to take the proper factor of temperature into consideration. As for the researches on experiments, the majority of them concentrate on factors such as the flow patterns, the categories of the oil product, and the parameters of the pipeline and on those factors’ influence upon the total amount of the mixed oil. They all have been irrespective of the effect of temperature and corresponding mechanism. Most of the researches regard the pipeline as an isothermal body, which is a postulated condition in their papers. In the background of digital pipeline system and intelligentized management transportation system, both of a better accuracy and reliability are required for the model to deal with the problem mentioned above. Thus, the classical theory regarding mixed oil, coupling of flow and heat transfer, scheduling plans, separation of mixed oil and leakage detection cannot keep up with the pace the development of the pipeline system. At present, researches of the following aspects are in a fledging period: the smearing phenomenon of mixed oil, the scheduling plans making considering nonlinear factors, the scheduling plan optimization considering coupling of hydraulic and thermal factors, the batch interface tracking regarding the oil quality and the three-dimensional transient flow simulation in long-distance pipeline, which need to make a further study shedding light on the detailed mechanism concerning the temperature’s influence. Thus, firstly in the paper, the correlated researches on mixed oil, scheduling plans, heated oil pipelines and batch interface tracking without taking temperature’s influence into account have been summarized and the corresponding defect has been discussed. Next, current status of researches about the temperature’s influence on the mechanism of mixed oil and on the process of mass transfer as well as heat transfer are analyzed and commented, including the related experimental research. The influences are embodied in the change of transport capacity, the vaporization of oil, the decreasing quality of oil, the low accuracy of batch interface tracking, the high risk of mixed oil cutting and the large pressure drop after pipeline shutdown. Correspondingly, the relevant theoretical and experimental studies are not perfect and sufficient. And the empirical formulae or modified coefficient methods presented in these studies are not suitable enough for the industrial applications. At the end of the paper, it is pointed out that based on the development requirements of the pipeline system, the scheduling plan combined with thermal as well as hydraulic factors, the abnormal diffusion considering temperature between different batches, the three-dimensional simulation of compressible multi-phase turbulence and the batch interface tracking in complex pipelines are the major research directions and key issues in the research field.

DNS of turbulent flows of dense gases

The influence of dense gas effects on compressible turbulence is investigated by means of numerical simulations of the decay of compressible homogeneous isotropic turbulence (CHIT) and of supersonic turbulent flows through a plane channel (TCF). For both configurations, a parametric study on the Mach and Reynolds numbers is carried out. The dense gas considered in these parametric studies is PP11, a heavy fluorocarbon. The results are systematically compared to those obtained for a diatomic perfect gas (air). In our computations, the thermodynamic behaviour of the dense gases is modelled by means of the Martin-Hou equation of state. For CHIT cases, initial turbulent Mach numbers up to 1 are analyzed using mesh resolutions up to 5123. For TCF, bulk Mach numbers up to 3 and bulk Reynolds numbers up to 12000 are investigated. Average profiles of the thermodynamic quantities exhibit significant differences with respect to perfect-gas solutions for both of the configurations. For high-Mach CHIT, compressible structures are modified with respect to air, with weaker eddy shocklets and stronger expansions. In TCF, the velocity profiles of dense gas flows are much less sensitive to the Mach number and collapse reasonably well in the logarithmic region without any special need for compressible scalings, unlike the case of air, and the overall flow behaviour is midway between that of a variable-property liquid and that of a gas.

Compressibility effect on coherent structures, energy transfer, and scaling in magnetohydrodynamic turbulence

Compressible magnetohydrodynamic (MHD) turbulence, a model often used to study space and astrophysical plasmas, differs from incompressible magnetohydrodynamic and hydrodynamic (HD) turbulence in many ways. Here direct numerical simulations of mechanically forced compressible MHD turbulence are used to study the degree to which some turbulence theories proposed in the incompressible case remain applicable in the compressible one. Several aspects of compressible turbulence are studied: (i) Intermittency in the compressible case is studied by addressing flows driven with varying forcing mechanisms; these display different features, such as compression and coherent structures. The more compressive simulation is characterized by sheet-like current density structures and shocks, which lead to saturated scaling exponents of high order structure functions of density and compressive velocity. (ii) Further investigations employing conditional averages of different energy transfer fluxes reveal that the influence of shocks (or compressions) makes differences in energy cascade and magnetic amplification. (iii) Cascade is also studied by examining the validity of Yaglom-type relations that verify the scale invariant property within the inertial range, where the transfer is relatively free of the effect of pressure dilation.