Turbulent Heating Rates Research Articles

An Ensemble Study of Turbulence in Extended QSO Nebulae at z ≈ 0.5–1

Turbulent motions in the circumgalactic medium play a critical role in regulating the evolution of galaxies, yet their detailed characterization remains elusive. Using two-dimensional velocity maps constructed from spatially extended [O ii] and [O iii] emission, Chen et al. measured the velocity structure functions (VSFs) of four quasar nebulae at z ≈ 0.5–1.1. One of these exhibits a spectacular Kolmogorov relation. Here, we carry out an ensemble study using an expanded sample incorporating four new nebulae from three additional quasi-stellar object (QSO) fields. The VSFs measured for all eight nebulae are best explained by subsonic turbulence revealed by the line-emitting gas, which in turn strongly suggests that the cool gas (T ∼ 104 K) is dynamically coupled to the hot ambient medium. Previous work demonstrates that the largest nebulae in our sample reside in group environments with clear signs of tidal interactions, suggesting that environmental effects are vital in seeding and enhancing the turbulence within the gaseous halos, ultimately promoting the formation of the extended nebulae. No discernible differences are observed in the VSF properties between radio-loud and radio-quiet QSO fields. We estimate the turbulent heating rate per unit volume, Q turb, in the QSO nebulae to be ∼10−26–10−22 erg cm−3 s−1 for the cool phase and ∼10−28–10−25 erg cm−3 s−1 for the hot phase. This range aligns with measurements in the intracluster medium and star-forming molecular clouds but is ∼103 times higher than the Q turb observed inside cool gas clumps on scales ≲1 kpc using absorption-line techniques. We discuss the prospect of bridging the gap between emission and absorption studies by pushing the emission-based VSF measurements to below ≈10 kpc.

NIRwave: A wave-turbulence-driven solar wind model constrained by PSP observations

Aims. We generate a model description of the solar wind based on an explicit wave-turbulence-driven heating mechanism, and constrain our model with observational data. Methods. We included an explicit coronal heating source term in the general 3D magnetohydrodynamic code NIRVANA to simulate the properties of the solar wind. The adapted heating mechanism is based on the interaction and subsequent dissipation of counter-propagating Alfvén waves in the solar corona, accounting for a turbulent heating rate Qp. The solar magnetic field is assumed to be an axisymmetric dipole with a field strength of 1 G. Our model results are validated against observational data taken by the Parker Solar Probe (PSP). Results. Our NIRwave solar wind model reconstructs the bimodal structure of the solar wind with slow and fast wind speeds of 410 km s−1 and 650 km s−1 respectively. The global mass-loss rate of our solar wind model is 2.6 × 10−14 M⊙ yr−1. Despite implementing simplified conditions to represent the solar magnetic field, the solar wind parameters characterising our steady-state solution are in reasonable agreement with previously established results and empirical constraints. The number density from our wind solution is in good agreement with the derived empirical constraints, with larger deviations for the radial velocity and temperature. In a comparison to a polytropic wind model generated with NIRVANA, we find that our NIRwave model is in better agreement with the observational constraints that we derive.

Polytropic Behavior in the Structures of Interplanetary Coronal Mass Ejections

The polytropic process characterizes the thermodynamics of space plasma particle populations. The polytropic index, γ, is particularly important as it describes the thermodynamic behavior of the system by quantifying the changes in temperature as the system is compressed or expanded. Using Wind spacecraft plasma and magnetic field data during 1995 February–2015 December, we investigate the thermodynamic evolution in 336 interplanetary coronal mass ejection (ICME) events. For each event, we derive the index γ in the sheath and magnetic ejecta structures, along with the pre- and post-event regions. We then examine the distributions of all γ indices in these four regions and derive the entropic gradient of each, which is indicative of the ambient heating. We find that in the ICME sheath region, where wave turbulence is expected to be highest, the thermodynamics takes longest to recover into the original quasi-adiabatic process, while it recovers faster in the quieter ejecta region. This pattern creates a thermodynamic cycle, featuring a near adiabatic value γ ∼ γ a (=5/3) upstream of the ICMEs, γ a − γ ∼ 0.26 in the sheaths, γ a − γ ∼ 0.13 in the ICME ejecta, and recovers again to γ ∼ γ a after the passage of the ICME. These results expose the turbulent heating rates in the ICME plasma: the lower the polytropic index from its adiabatic value and closer to its isothermal value, the larger the entropic gradient, and thus, the rate of turbulent heating that heats the ICME plasma.

Turbulent Proton Heating Rate in the Solar Wind from 5–45 R ⊙

Abstract Various remote sensing observations have been used so far to probe the turbulent properties of the solar wind. Using the recently reported density modulation indices that are derived using angular broadening observations of Crab Nebula during 1952–2013, we measured the solar wind proton heating using the kinetic Alfvén wave dispersion equation. The estimated heating rates vary from ≈1.58 × 10−14 to 1.01 × 10−8 erg cm−3 s−1 in the heliocentric distance range of 5–45 R ⊙. Further, we found that heating rates vary with the solar cycle in correlation with density modulation indices. The models derived using in situ measurements (for example, electron/proton density, temperature, and magnetic field) that the recently launched Parker Solar Probe observations (planned closest perihelia 9.86 R ⊙ from the center of the Sun) are useful in the estimation of the turbulent heating rate precisely. Further, we compared our heating rate estimates with the one derived using previously reported remote sensing and in situ observations.

Estimation of Turbulent Heating of Solar Wind Protons at 1 au

Abstract The paper presents a new method for deriving turbulent heating of the solar wind using plasma moments and magnetic field data. We develop the method and then apply it to compute the turbulent heating of the solar wind proton plasma at 1 au. The method employs two physical properties of the expanding solar wind plasma, the wave-particle thermodynamic equilibrium, and the transport of entropic rate. We analyze plasma moments and field data taken from Wind S/C, in order to compute (i) the fluctuating magnetic energy, (ii) the corresponding correlation length, and (iii) the turbulent heating rate. We identify their relationships with the solar wind speed, as well as the variation of these relationships relative to solar wind and interplanetary coronal mass ejection plasma.

Identifying Active Kelvin–Helmholtz Vortices on Saturn's Magnetopause Boundary

AbstractFor Cassini magnetopause encounters, we analyse plasma and magnetic fields. The boundary can be unstable to the Kelvin–Helmholtz instability (KHI), which can drive large‐scale flows identifiable in plasma measurements. Bulk flow reversed from the expected direction near the magnetopause can indicate vorticity associated with active KH, and events are found dominantly in the dawn–subsolar region. KHIs are also responsible for magnetic field fluctuations, and hybrid simulations indicate heating, and transport is significant in an actively growing vortex. Cassini observations are filtered for disturbed magnetic fields near the magnetopause, similar to the signatures from hybrid simulations, with significant fluctuation and current sheet crossings. We also find that these occur most frequently in the dawn–subsolar region. A turbulent heating rate density and mass diffusion coefficient are calculated for these disturbed events and compared with the hybrid simulation to test whether enhanced values for these quantities can identify active KH events.

Reflection-driven magnetohydrodynamic turbulence in the solar atmosphere and solar wind

We present three-dimensional direct numerical simulations and an analytic model of reflection-driven magnetohydrodynamic (MHD) turbulence in the solar wind. Our simulations describe transverse, non-compressive MHD fluctuations within a narrow magnetic flux tube that extends from the photosphere, through the chromosphere and corona and out to a heliocentric distance $r$of 21 solar radii $(R_{\odot })$. We launch outward-propagating ‘$\boldsymbol{z}^{+}$fluctuations’ into the simulation domain by imposing a randomly evolving photospheric velocity field. As these fluctuations propagate away from the Sun, they undergo partial reflection, producing inward-propagating ‘$\boldsymbol{z}^{-}$fluctuations’. Counter-propagating fluctuations subsequently interact, causing fluctuation energy to cascade to small scales and dissipate. Our analytic model incorporates dynamic alignment, allows for strongly or weakly turbulent nonlinear interactions and divides the$\boldsymbol{z}^{+}$fluctuations into two populations with different characteristic radial correlation lengths. The inertial-range power spectra of$\boldsymbol{z}^{+}$and$\boldsymbol{z}^{-}$fluctuations in our simulations evolve toward a$k_{\bot }^{-3/2}$scaling at$r>10R_{\odot }$, where$k_{\bot }$is the wave-vector component perpendicular to the background magnetic field. In two of our simulations, the$\boldsymbol{z}^{+}$power spectra are much flatter between the coronal base and$r\simeq 4R_{\odot }$. We argue that these spectral scalings are caused by: (i) high-pass filtering in the upper chromosphere; (ii) the anomalous coherence of inertial-range$\boldsymbol{z}^{-}$fluctuations in a reference frame propagating outwards with the$\boldsymbol{z}^{+}$fluctuations; and (iii) the change in the sign of the radial derivative of the Alfvén speed at$r=r_{\text{m}}\simeq 1.7R_{\odot }$, which disrupts this anomalous coherence between$r=r_{\text{m}}$and$r\simeq 2r_{\text{m}}$. At$r>1.3R_{\odot }$, the turbulent heating rate in our simulations is comparable to the turbulent heating rate in a previously developed solar-wind model that agreed with a number of observational constraints, consistent with the hypothesis that MHD turbulence accounts for much of the heating of the fast solar wind.

Numerical study on the aerothermodynamics of different heatshield configurations for Mars entry capsules

Aeroheating predictions play an important role in the heatshield design of Mars entry capsule. This paper numerically investigates the effects of sphere-cone angle on the aerothermodynamic performances of heatshield configurations. Three-dimensional Navier-Stokes equations with chemical non-equilibrium models are employed to simulate the flowfield around the capsule. The laminar and turbulent heating rates of different heatshield configurations are compared and analyzed in detail. A novel correlation for turbulent heating augmentation in terms of laminar momentum thickness Reynolds number is developed to provide a guidance for engineering design and application. The proposed correlation can be more accurate and applicable due to its consideration of the sphere-cone angle effects. Finally, the laminar and turbulent maximum heat flux and total heat load along the flight trajectory are investigated for all the configurations. The numerical study is expected to illustrate the aeroheating characteristics of different heatshield configurations and provide an insight into the rational configuration design for future Mars entry capsules.

Substructures associated with the sloshing cold front in the Perseus cluster

X-ray substructures in clusters of galaxies provide indirect clues about the microphysical properties of the intracluster medium (ICM), which are still not very well known. In order to investigate X-ray substructures in detail, we studied archival $\sim$1~Msec Chandra data of the core of the Perseus cluster, focusing on the substructures associated with the sloshing cold front. In the east half of the cold front, we found a Kelvin-Helmholtz instability (KHI) layer candidate. The measured width-to-azimuthal extension ratio and the thermodynamic properties are all consistent with it being a KHI layer currently developing along the sloshing cold front. We found a thermal pressure deficit of the order of 10$^{-2}~\mathrm{keV~cm^{-3}}$ at the KHI layer. Assuming that turbulent pressure fully supports the pressure deficit, we estimated the turbulent strength at several hundred km~s$^{-1}$, which translates into the turbulent heating rate of $Q_\mathrm{turb}\sim 10^{-26}~\mathrm{erg~cm^{-3}~s^{-1}}$. This value agrees within an order of magnitude with the previous estimation derived from the surface brightness fluctuations, and can balance the radiative cooling at this radius. In the west half of the cold front, we found feather-like structures which are similar to the structures observed in recent numerical simulations of the gas sloshing of magnetized plasma. Their thermodynamic properties are consistent with one of the feathers being a projected gas depletion layer induced by the amplified magnetic field whose strength is $B\sim$30$~\mathrm{\mu G}$.

What fraction of the density fluctuations in the Perseus cluster core is due to gas sloshing rather than AGN feedback?

Deep Chandra observations of the core of the Perseus cluster show a plethora of complex structure. It has been found that when the observed density fluctuations in the intracluster medium are converted into constraints on AGN induced turbulence, the resulting turbulent heating rates are sufficient to balance cooling locally throughout the central 220kpc. However while the signatures of AGN feedback (inflated bubbles) dominate the central 60kpc in X-ray images, beyond this radius the intracluster medium is increasingly shaped by the effects of gas sloshing, which can also produce subtle variations in X-ray surface brightness. We use mock Chandra observations of gas sloshing simulations to investigate what fraction of the observed density fluctuations in the core of the Perseus galaxy cluster may originate from sloshing rather than AGN induced feedback. Outside 60kpc, we find that the observed level of the density fluctuations is broadly consistent with being produced by sloshing alone. If this is the case, AGN-generated turbulence is likely to be insufficient in combating cooling outside 60kpc.

Heating of accretion-disk coronae and jets by general relativistic magnetohydrodynamic turbulence

Turbulence in an accretion disk launches Alfvén waves (AWs) that propagate away from the disk along magnetic-field lines. Because the Alfvén speed varies with distance from the disk, the AWs undergo partial non-WKB reflection, and counter-propagating AWs subsequently interact, causing AW energy to cascade to small scales and dissipate. To investigate this process, we introduce an Elsasser-like formulation of general relativistic magnetohydrodynamics (GRMHD) and develop the theory of general relativistic reduced MHD in an inhomogeneous medium. We then derive a set of equations for the mean-square AW amplitude $M_{+}$and turbulent heating rate $Q$under the assumption that, in the plasma rest frame, AWs propagating away from the disk are much more energetic than AWs propagating toward the disk. For the case in which the background flow is axisymmetric and time independent, we solve these equations analytically to determine$M_{+}$and $Q$as functions of position. We find that, for an idealized thin disk threaded by a large-scale poloidal magnetic field, the AW energy flux is${\sim}(\unicode[STIX]{x1D70C}_{\text{b}}/\unicode[STIX]{x1D70C}_{\text{d}})^{1/2}\unicode[STIX]{x1D6FD}_{\text{net,d}}^{-1/2}$times the disk’s radiative flux, where$\unicode[STIX]{x1D70C}_{\text{b}}$and$\unicode[STIX]{x1D70C}_{\text{d}}$are the mass densities at the coronal base and disk midplane, respectively, and$\unicode[STIX]{x1D6FD}_{\text{net,d}}$is the ratio (evaluated at the disk midplane) of plasma-plus-radiation pressure to the pressure of the average vertical magnetic field. This energy flux could have a significant impact on disk coronae and outflows. To lay the groundwork for future global simulations of turbulent disk coronae and jets, we derive a set of averaged GRMHD equations that account for reflection-driven AW turbulence using a sub-grid model.

The ion cyclotron turbulence generated by a low frequency kinetic Alfvén wave and turbulent heating of ions

The ion cyclotron instability driven by a strong kinetic Alfvén wave is investigated as a possible source of anisotropic heating of ions in the sun's corona. We present a novel model of a plasma with coupled inhomogeneous current and shearing flow, which results from the particle's motion in the electric field of the kinetic Alfvén wave of finite wavelength. The investigation is performed employing the non-modal kinetic theory grounded on the shearing mode approach. The solution of the governing linear integral equation for the perturbed potential displays that the flow velocity shear, which for the corona conditions may be above the growth rate of the ion cyclotron instability in the plasma with steady current, changes the exponential growth of the ion cyclotron potential on the power function of time, that impedes the growth of the unstable ion cyclotron wave and reduces the turbulent heating rate of ions across the magnetic field.

Sensitivity analysis of geometric parameters upon the aerothermodynamic performances of Mars entry vehicle

Aerothermodynamic environment predictions play an important role in the heatshield design of Mars entry vehicle. This article investigates and presents the influences of geometric parameters of the heatshield on its aerothermodynamic performances. The three-dimensional coupled implicit compressible Reynolds Averaged Navier–Stokes (RANS) equations and perfect gas model with the specified effective specific heat ratio have been applied to numerically simulate the flow fields around the vehicle. Menter’s shear stress transport (SST) turbulence model with compressible correction is implemented to take account of the turbulent effect. The laminar and turbulent heating rates are demonstrated and analyzed in detail. Furthermore, a non-intrusive polynomial chaos (NIPC) method with Latin hypercube sampling (LHS) is utilized to establish the functional relationship between the aerothermodynamics and geometric parameters. In addition, Sobol indices as global sensitivity metrics have been introduced to investigate the relative contribution of each geometric parameter. The results show that for the maximum heat flux, the value of the cone angle (αc) with a high index is the top contributor to the both laminar and turbulent flow state, thus the geometric parameter αc should be considered firstly in the material design process of thermal protection system. Moreover, in the most region of MSL heatshield, cone angle (αc) also became the major influence factor. However, in a relatively small region, aerothermodynamics exhibits a great sensitivity to the change of nose radius (Rn). In all regions of heatshield, the parameter of shoulder radius (Rs) is always at a low level of Sobol index.

The temporal evolution of the drift-cyclotron instability and anomalous ion heating in plasmas with transverse inhomogeneous electric field

The effect of the sheared flow across the magnetic field on drift-cyclotron turbulence is investigated with applications to anomalous ion heating in space plasmas employing the non-modal methodology of sheared modes. These modes are the waves that have a static spatial structure in the frame of the background flow and are the sheared modes in the laboratory frame. The analysis consists in the solution of the governing integral equation for the electrostatic potential in the time domain. It reveals that the instability experiences the non-modal temporal evolution in the sheared flow during which the unstable perturbation becomes very different from a canonical modal form. It displays that the growth rate of the drift-cyclotron instability and the turbulent ion heating rate decrease with time due to the shearing of ion cyclotron waves by the sheared flow. The effect of the quenching time of the drift-cyclotron instability and of the ion heating is confirmed also by the solution of the nonlinear integral equation, which accounts for the random scattering of the angle of ion gyro-motion due to the interaction of ions with an ensemble of sheared waves.

Laminar and turbulent heating predictions for mars entry vehicles

Laminar and turbulent heating rates play an important role in the design of Mars entry vehicles. Two distinct gas models, thermochemical non-equilibrium (real gas) model and perfect gas model with specified effective specific heat ratio, are utilized to investigate the aerothermodynamics of Mars entry vehicle named Mars Science Laboratory (MSL). Menter shear stress transport (SST) turbulent model with compressible correction is implemented to take account of the turbulent effect. The laminar and turbulent heating rates of the two gas models are compared and analyzed in detail. The laminar heating rates predicted by the two gas models are nearly the same at forebody of the vehicle, while the turbulent heating environments predicted by the real gas model are severer than the perfect gas model. The difference of specific heat ratio between the two gas models not only induces the flow structure's discrepancy but also increases the heating rates at afterbody of the vehicle obviously. Simple correlations for turbulent heating augmentation in terms of laminar momentum thickness Reynolds number, which can be employed as engineering level design and analysis tools, are also developed from numerical results. At the time of peak heat flux on the +3σ heat load trajectory, the maximum value of momentum thickness Reynolds number at the MSL's forebody is about 500, and the maximum value of turbulent augmentation factor (turbulent heating rates divided by laminar heating rates) is 5 for perfect gas model and 8 for real gas model.

Longitudinal and local time asymmetries of magnetospheric turbulence in Saturn's plasma sheet

AbstractBased on earlier studies that have shown Saturn's middle magnetosphere to contain turbulent magnetic field fluctuations, we analyze the spatial and temporal variations of the magnetic fluctuations and turbulent heating rate as a function of local time and magnetic phase. The region of study is Saturn's plasma sheet at a distance of 6–20 Rs, where Rs is Saturn's equatorial radius. The data set consists of magnetic field data measured during 92 orbits (revolutions) from the equatorial phases of Cassini covering 9 years from 2004 to 2012. We find asymmetries in the magnetosphere with enhanced fluctuations around noon. With respect to longitude we find increased fluctuations at 65° southern and 250° northern magnetic phase. This leads to an increased turbulent heating rate in these regions and is consistent with regions of increased plasma density and maximum downward field‐aligned currents according to the quasi‐dipolar perturbation fields. Analysis of single orbits reveals that the heating rate of 79% of all analyzed inbound and outbound legs is significantly (statistical error less than 1%) sinusoidally modulated. The modulation of the turbulent heating rate is predominantly observed during times when Cassini is located between dusk and midnight and additionally at dawn.

Onsager's symmetry relation and the residual parallel Reynolds stress in a magnetized plasma with electrostatic turbulence

The physics of the residual parallel Reynolds stress in a rotating plasma with electrostatic turbulence is explicitly identified by using the transport formulation of the gyrokinetic turbulence. It is clarified that the residual stress consists of four terms, among which are the cross terms due to the pressure gradient and the temperature gradient and the terms related to the turbulent acceleration impulse and the turbulent heating rate. The last two terms are identified for the first time, and are shown to cause analogous residual term in the heat flux. Meanwhile, the transport matrix reveals diffusion in the phase space. The transport matrix is demonstrated to satisfy the Onsager's symmetry relation.

Approximate Method for Computing Convective Heating on Hypersonic Vehicles Using Unstructured Grids

The ability to predict surface heating rates, as well as shear and pressure forces, is fundamental to the analysis and design of the thermal protection system for hypersonic vehicles. Approximate engineering codes that can be used to rapidly predict heating rates are extremely useful in the preliminary or conceptual design phase, whereas more detailed and expensive Navier–Stokes codes are generally used to provide more accurate heating rate predictions for final design. An earlier code has been used successfully in conjunction with inviscid flowfield codes computed on single-block structured grids. More recent inviscid codes have been developed that use unstructured grids, which greatly reduce grid generation time for complex configurations. A newer heating code had been used successfully with unstructured inviscid flowfield codes to compute laminar heating on general three-dimensional vehicles using unstructured grids and the heating rates over most of the vehicle have been shown to compare favorably with results from both boundary-layer and Navier–Stokes calculations. However, some anomalies were encountered in the stagnation region. This paper describes the newest version of the approximate heating code, which provides much better heating results in the stagnation region. The new code includes the capability to calculate both laminar and turbulent heating rates, for either perfect gas or equilibrium-air chemistry, with radiation-equilibrium or constant wall temperature boundary conditions. An approximate expression is implemented to account for the effect of velocity gradient on laminar heating. In addition, a new approximate method for computing the effect of finite wall catalysis on surface heating is included. A new improved axisymmetric analog method is developed to calculate inviscid surface streamlines and metric coefficients based on unstructured grids. Results are calculated and compared with both boundary-layer and Navier–Stokes solutions for a range of typical hypersonic vehicles. The new code is directed toward the development of more efficient and accurate approximate engineering methods for predicting heating on hypersonic vehicles and to better understand how these methods can be integrated with more detailed Navier–Stokes results to improve the overall vehicle and thermal design processes.

An Approximate Engineering Method for Aerodynamic Heating Solution around Blunt Body Nose

This paper is devoted to predict laminar and turbulent heating rates around blunt re-entry spacecraft at hypersonic conditions. Heating calculation of a hypersonic body is normally performed during the critical part of its flight trajectory. The procedure is of an inverse method, where a shock wave is assumed, and the body shape that supports this shock, as well as the flowfield between the shock and body, are calculated. For simplicity the normal momentum equation is replaced with a second order pressure relation; this simplification significantly reduces computation time. The geometries specified in this research, are parabola and ellipsoids which may have conical after bodies. An excellent agreement is observed between the results obtained in this paper and those calculated by others’ research. Since this method is much faster than Navier-Stokes solutions, it can be used in preliminary design, parametric study of hypersonic vehicles. Keywords—Aerodynamic Heating, Blunt Body, Hypersonic Flow, Laminar, Turbulent.

Magnetosphere-ionosphere coupling throughEregion turbulence: 2. Anomalous conductivities and frictional heating

[1] Global magnetospheric MHD codes using ionospheric conductances based on laminar models systematically overestimate the cross–polar cap potential during storm time by up to a factor of 2. At these times, strong DC electric fields penetrate to the E region and drive plasma instabilities that create turbulence. This plasma density turbulence induces nonlinear currents, while associated electrostatic field fluctuations result in strong anomalous electron heating. These two effects will increase the global ionospheric conductance. On the basis of the theory of nonlinear currents developed by Dimant and Oppenheim [2011], this paper derives the correction factors describing turbulent conductivities and calculates turbulent frictional heating rates. Estimates show that during strong geomagnetic storms the inclusion of anomalous conductivity can double the total Pedersen conductance. This may help explain the overestimation of the cross–polar cap potentials by existing MHD codes. The turbulent conductivities and frictional heating presented in this paper should be included in global magnetospheric codes developed for predictive modeling of space weather.