Scale Turbulence Research Articles

A numerical study on the feasibility of predicting the resistance of a full-scale ship using a virtual fluid

In general, the resistance of a real ship is estimated using an extrapolation method after doing experimental tests or numerical simulations with a model scale ship. Since the only Froude similarity is applied in the model test and simulation, the flow characteristics between the model and real ships could be different due to the inconsistency of Reynolds number. However, in the Computational Fluid Dynamics (CFD), the Froude and Reynolds numbers can be satisfied simultaneously because a fluid with virtual properties can be applied. This study investigated the effect of turbulence models and scales for a flat plate. And then the hydrodynamic feasibility of using a virtual fluid was investigated through numerical analysis. The resistance performance and flow structure of the ship were analysed by applying the virtual fluid, and they were confirmed how well these values and flow characteristics simulate the full-scale with a real fluid. This study shows that the results of a full-scale can be obtained at model scale by applying a virtual fluid instead of full-scale numerical simulations that require more computational resources.

Dark Matter Minihalos from Primordial Magnetic Fields.

Primordial magnetic fields (PMF) can enhance baryon perturbations on scales below the photon mean free path. However, a magnetically driven baryon fluid becomes turbulent near recombination, thereby damping out baryon perturbations below the turbulence scale. In this Letter, we show that the initial growth in baryon perturbations gravitationally induces growth in the dark matter perturbations, which are unaffected by turbulence and eventually collapse to form 10^{-11}-10^{3}M_{⊙} dark matter minihalos. If the magnetic fields purportedly detected in the blazar observations are PMFs generated after inflation and have a Batchelor spectrum, then such PMFs could potentially produce dark matter minihalos.

Toward high-fidelity Numerical Wave Tank development: Scale resolving Partially-Averaged Navier–Stokes simulations of dam-break flow

Numerical Wave Tanks (NWTs) based on Navier–Stokes equations are emerging as valuable tools for simulating various ocean and coastal engineering flows. By capturing essential hydrodynamic non-linearities, including turbulent processes, these Navier–Stokes based NWTs can potentially provide high-accuracy data to complement traditional experimental wave basins for design and development applications. Many NWT approaches currently use the RANS (Reynolds Averaged Navier–Stokes) method. For many coastal resiliency and wave-energy converter applications, a higher fidelity turbulence treatment may be needed. In this work, we explore the applicability of the scale-resolving Partially-Averaged Navier–Stokes (PANS) technique for NWT computation. The PANS model is employed to study the dam-break benchmark case which is an important benchmark case for seawall and wave energy converter hydrodynamics analysis. Computations using RANS are also provided as a reference for accuracy and computational effort. The objectives are to: (i) investigate the effect of enhancing turbulence scale resolution on the pressure field, wave elevation and three-dimensional effects within the tank; and (ii) examine the influence of initial kinetic energy and grid resolution on the results. It is shown that, the early transient behavior is reasonably insensitive to scale resolution or initial turbulence level. Indeed, RANS and PANS of different scale resolutions yield similar results in the early stages as the flow physics is dominated by quasi-linear flow processes. The differences between RANS and PANS appear at later times. The so-called second pressure peak, standing wave amplitude and three-dimensional effects are better captured with increasing scale resolution for the same grid resolution. Overall, the results indicate that PANS is a viable model for NWT applications, with more detail being captured at a similar computational cost compared to RANS.

Numerical Testing of Mirror Diffusion of Cosmic Rays

The tension between recent observations and theories on cosmic-ray (CR) diffusion necessitates exploration of new CR diffusion mechanisms. We perform the first numerical study on the mirror diffusion of CRs that is recently proposed by Lazarian & Xu. We demonstrate that the perpendicular superdiffusion of turbulent magnetic fields and magnetic mirroring that naturally arise in magnetohydrodynamic (MHD) turbulence are the two essential physical ingredients for the mirror diffusion to happen. In supersonic, subsonic, and incompressible MHD turbulence, with the pitch angles of CRs repeatedly crossing 90° due to the mirror reflection, we find that the mirror diffusion strongly enhances the confinement of CRs, and their pitch-angle-dependent parallel mean free path can be much smaller than the injection scale of turbulence. With the stochastic change of pitch angles due to gyroresonant scattering, CRs stochastically undergo slow mirror diffusion at relatively large pitch angles and fast scattering diffusion at smaller pitch angles, resulting in a Lévy-flight-like propagation.

Spectra scaling of velocity components and pressure–strain correlations for hypersonic boundary layers at a range of wall-to-recovery temperatures

Flow similarity is one of the most desirable features for turbulence under different conditions. For hypersonic boundary layers, different wall temperatures are known to change the turbulence evolution by influencing the intercomponent energy transfer, while the flow similarity has received less attention. Based on direct numerical simulations, this work investigates the spectral distribution of velocity components and pressure–strain correlations for hypersonic boundary layers at Mach 6 and wall-to-recovery temperature ratios equal to 0.3, 0.5, 0.76, and 1. The wall-normal evolution of turbulent structures is compared by the spectra peak scale λSP, wall-normal location ySP, and the vertical profiles of peak scale λP. For all cases, the peak scale profiles exhibit linear increases with a height of 0.1≤y/δ≤0.25. The linear growth of the turbulence scale in the logarithmic region indicates the existence of self-similar structures, and the agreement of peak scales in the outer scaling suggests the flow similarity under different wall temperatures. Likewise, the streamwise pressure–strain term has the peak scale profile linearly dependent on the height for the same vertical range 0.1≤y/δ≤0.25 with velocity components, while the wall-normal and spanwise terms exhibit both linear and constant vertical dependence depending on the wall temperatures. With the increase in wall temperature, the peak scale exhibits broader constant vertical dependence and narrower linear vertical dependence. The cospectral analysis further confirms that the pressure–strain correlations are maximized at different spanwise-vertical aspect ratios of turbulence structures.

Experimental investigation of aerodynamic sound radiated from flow around an airfoil placed in the turbulent flow generated by active turbulence generator

Sound generated aerodynamically from a flow around an airfoil subjected to inflow turbulence is investigated experimentally to identify the dominant source of the sound. The test airfoil has NACA0012 wing section. The wind speed is set to 30 m/s, which results in an airfoil Reynolds number of 300000. Its lift and drag coefficient are 0.78 and 0.06 when the angle of attack is 9 degrees. Wind tunnel experiments are conducted with Active Turbulence Generator (ATG) set at the nozzle exit. The ATG is controlled by the swing angles and rotation speeds of the stepping motors to control the turbulence intensity and the eddy scale of the inflow turbulence, independently. The former is varied from 10 % to 20 % while the latter is varied from 300 mm to 1600 mm. As a result, we have found that the pressure fluctuation near the leading edge of the airfoil is remarkably high, and therefore, it is most likely the cause of the considerable increase in the sound generated from the airfoil. Therefore, the higher the turbulence intensity, the higher the sound, and the higher the correlation between the power of the flow velocity fluctuation and the sound pressure level at each frequency.

Low Mach number aeroacoustic computations of airfoils in application with Pierce's wave equation

The airflows generated by drones are fairly different from those arising for conventional aeronautical architectures. They are low Mach number, relatively low Reynolds number and transient regimes play a dominant role. The goals of this work are twofold. This study firstly seeks to present an aeroacoustic model built on Pierce's wave equation, which is adapted to the specificity of this physic, and which is consistent and robust. The second part of this contribution then focuses on the use and the validation of a high-order highly scalable solver relying on an open source C++ library to solve the large scales of the flow turbulence by means of an explicit filtering. The flow corresponding to a benchmarked Re = 5 · 104 airfoil in full stall is computed and results are briefly discussed.

Stochastic modeling of turbulent mixing based on a hierarchical swapping of fluid parcels

AbstractTurbulent mixing is an omnipresent phenomenon that constantly affects our everyday life and plays an important role in a variety of industrial applications. The simulation of turbulent mixing poses great challenges, since the full resolution of all relevant length and time scales is associated with an immense computational effort. This limitation can be overcome by only resolving the large‐scale effects and completely model the sub‐grid scales. The development of an accurate sub‐grid mixing model is therefore a key challenge to capture all interactions in the sub‐grid scales. At this place, the hierarchical parcel‐swapping (HiPS) model formulated by A.R. Kerstein [J. Stat. Phys. 153, 142–161 (2013)] represents a computationally efficient and scale‐resolving turbulent mixing model. HiPS mimics the effects of turbulence on time‐evolving, diffusive scalar fields. In HiPS, the diffusive scalar fields or a state space is interpreted as a binary tree structure, which is an alternative approach compared to the most common mixing models. Every level of the tree represents a specific length and time scale, which is based on turbulence inertial range scaling. The state variables are only located at the base of the tree and are treated as fluid parcels. The effects of turbulent advection are represented by stochastic swaps of sub‐trees at rates determined by turbulent time scales associated with the sub‐trees. The mixing only takes places between adjacent fluid parcels and at rates consistent with the prevailing diffusion time scales. In this work, the HiPS model formulation for the simulation of passive scalar mixing is detailed first. Preliminary results for the mean square displacement, passive scalar probability density function (PDF) and scalar dissipation rate are given and reveal the strengths of the HiPS model considering the reduced order and computational efficiency. These model investigations are an important step of further HiPS advancements. The integrated auxiliary binary tree structure allows HiPS to satisfy a large number of criteria for a good mixing model. From this point of view, HiPS is an attractive candidate for modeling the mixing in transported PDF methods.

Invariance embedded physics-infused deep neural network-based sub-grid scale models for turbulent flows

In this paper, we present two novel physics-infused neural network (NN) architectures that satisfy various invariance conditions for constructing efficient and robust Deep Learning (DL)-based sub-grid scale (SGS) turbulence models for use in Large Eddy Simulation (LES) procedures widely used in various fluid engineering applications. The first architecture, called tensor basis neural networks (TBNN), recently proposed in the context of Reynolds-averaged Navier–Stokes (RANS) modeling, and introduced herein for SGS modeling of wall-bounded turbulence, embeds the analytical expansion of the SGS turbulence stresses into integrity basis tensors composed of the symmetric and anti-symmetric parts of the resolved velocity gradient tensor, thus incorporating the Galilean, rotational and reflectional invariances. In our second approach, a relatively simple yet powerful architecture, called Galilean Invariance embedded Neural Network (GINN) incorporates the Galilean invariance, and takes in as inputs the independent components of the integrity basis tensors in addition to the invariant inputs in a single input layer. Explicit filtering of data from direct simulations of the canonical channel flow at two friction Reynolds numbers Reτ≈395 and 590 provided accurate data for training and testing these models. Both sets of models are used to predict the SGS stresses for feature datasets generated with different filter widths, and at different Reynolds numbers. The GINN model yields less prediction error on test datasets (mean squared error ∼0.4) compared to the TBNN model (mean squared error ∼0.5). Upon comparison, it is revealed that GINN has better feature extraction capacity owing to its ability to establish relations between and extract information from cross-components of the integrity basis tensors and the SGS stresses. Based on their predictive performance, both models proposed herein have shown great promise for use in a posteriori actual LESs. The present work illustrates the significance of physics infusion as well as invariance embedding into NN architecture for constructing efficient and robust DL-based SGS turbulent models in achieving superior predictive efficacy.

Integral Turbulent Length and Time Scales of Higher Order Moments

Turbulent length and time scales represent a fundamental quantity for analysing and modelling turbulent flows. Although higher order statistical moments have been conveniently used for decades to describe the mean behaviour of turbulent fluid flow, the definition of the integral turbulent scales seems to be limited to the velocity or its fluctuation itself (i.e. the first moment). Higher order moments are characterized by smaller integral scales and a framework is proposed for estimating autocorrelation functions and integral turbulent length or time scales of higher order moments under the assumption that the probability distribution of the velocity field is Gaussian. The new relations are tested for synthetic turbulence as well as for DNS data of a turbulent plane jet at Reynolds number 10000. The present results in particular suggest that the length or time scales of higher order moments can be markedly smaller than those of the turbulent variable itself, which has implications for statistical uncertainty estimates of higher order moments.

Large Eddy Simulation of Soot Formation in a Real Aero-Engine Combustor Using Tabulated Chemistry and a Quadrature-Based Method of Moments

Abstract Considering the increasingly stringent targets for aircraft emissions, computational fluid dynamics (CFD) is becoming a viable tool for improving future aero-engine combustors. However, predicting pollutant formation remains challenging. In particular, directly solving the evolution of soot particles is numerically expensive. To reduce the computational cost but retain detailed physical modeling, quadrature-based moments methods can be efficiently employed to approximate the particle number density function (NDF). An example is the recently developed split-based extended quadrature method of moments (S-EQMOM), which enables a continuous description of the soot particles' NDF, essential to consider particle oxidation accurately. This model has shown promising results in laminar premixed flames up to turbulent laboratory scale configurations. However, the application to large-scale applications are still scarce. In this work, the S-EQMOM model is applied to the Rolls-Royce BR710 aero-engine combustor to investigate the soot evolution process in practically relevant configurations. For this, the soot model is embedded into a high-fidelity simulation framework, consisting of large eddy simulation for the turbulent flow and mixing and the flamelet-generated manifold method for chemistry reduction. An additional transport equation for polycyclic aromatic hydrocarbons is solved to model their slow chemistry and the transition from the gaseous phase to the solid phase. Simulations are performed for different operating conditions (idle, approach, climb, takeoff) to validate the model using experimental data. Subsequently, the results are analyzed to provide insights into the complex interactions of hydrodynamics, mixing, chemistry, and soot formation.

Assessing turbulence and mixing parameterizations in the gray-zone of multiscale simulations over mountainous terrain during the METEX21 field experiment

Multiscale numerical weather prediction models transition from mesoscale, where turbulence is fully parameterized, to microscale, where the majority of highly energetic scales of turbulence are resolved. The turbulence gray-zone is situated between these two regimes and multiscale models must downscale through these resolutions. Here, we compare three multiscale simulations which vary by the parameterization used for turbulence and mixing within the gray-zone. The three parameterizations analyzed are the Mellor-Yamada Nakanishi and Niino (MYNN) Level 2.5 planetary boundary layer scheme, the TKE-1.5 large eddy simulation (LES) closure scheme, and a recently developed three-dimensional planetary boundary layer scheme based on the Mellor-Yamada model. The simulation domain includes complex (i.e., mountainous) terrain in Nevada that was instrumented with meteorological towers, profiling and scanning lidars, a tethered balloon, and a surface flux tower. Simulations are compared to each other and to observations, with assessment of model skill at predicting wind speed, wind direction and TKE, and qualitative evaluations of transport and dispersion of smoke from controlled releases. This analysis demonstrates that microscale predictions of transport and dispersion can be significantly influenced by the choice of turbulence and mixing parameterization in the terra incognita, particularly over regions of complex terrain and with strong local forcing. This influence may not be apparent in the analysis of model skill, and motivates future field campaigns involving controlled tracer releases and corresponding modeling studies of the turbulence gray-zone.

Stochastic flutter analysis of a three-degree-of-freedom airfoil under vertical turbulence disturbance

This paper investigates the nonlinear stochastic dynamic response of a three-degree-of-freedom(3-DOF) airfoil with high substructural nonlinearity under vertical turbulent disturbances. Considering a two-dimensional flow field, the Dryden turbulence model is used to describe the vertical turbulent disturbance, and a nonlinear stochastic aerodynamic model based on the Theodorsen theory is established for the stochastic flutter problem of the wing. An analysis is conducted to reduce the dimensionality of the airfoil system and solve the critical flutter velocity of the system. The Monte-Carlo method is applied to analyze the stochastic P-bifurcation problem of the system, and the effects of parameters such as the incoming velocity, turbulence scale and intensity on the stochastic dynamics behavior of the system are clarified. It is shown that the amplitude of the steady-state oscillation of the system increases with the incoming velocity and turbulence intensity, whereas the critical flutter speed decreases with increases in these parameters.

Helical and non-helical large-scale dynamos in thin accretion discs

ABSTRACT The dynamics of accreting and outgoing flows around compact objects depends crucially on the strengths and configurations of the magnetic fields therein, especially of the large-scale fields that remain coherent beyond turbulence scales. Possible origins of these large-scale magnetic fields include flux advection and disc dynamo actions. However, most numerical simulations have to adopt an initially strong large-scale field rather than allow them to be self-consistently advected or amplified, due to limited computational resources. The situation can be partially cured by using sub-grid models where dynamo actions only reachable at high resolutions are mimicked by artificial terms in low-resolution simulations. In this work, I couple thin-disc models with local shearing-box simulation results to facilitate more realistic sub-grid dynamo implementations. For helical dynamos, detailed spatial profiles of dynamo drivers inferred from local simulations are used, and the non-linear quenching and saturation is constrained by magnetic helicity evolution. In the inner disc region, saturated fields have dipole configurations and the plasma β reaches ≃0.1 to 100, with correlation lengths ≃h in the vertical direction and ≃10 h in the radial direction, where h is the disc scale height. The dynamo cycle period is ≃40 orbital time scale, compatible with previous global simulations. Additionally, I explore two dynamo mechanisms which do not require a net kinetic helicity and have only been studied in shearing-box set-ups. I show that such dynamos are possible in thin accretion discs, but produce field configurations that are incompatible with previous results. I discuss implications for future general-relativistic magnetohydrodynamics simulations.

Statistical assessment of a Doppler radar model of TKE dissipation rate for low Richardson numbers

Abstract. The potential ability of VHF or UHF Doppler radars to measure turbulence kinetic energy (TKE) dissipation rate ε in the atmosphere is a major asset of these instruments because of the possibility to continuously monitor turbulence in the atmospheric column above the radars. Several models have been proposed over the past decades to relate ε to half the Doppler spectral width σ, corrected for non-turbulent contributions, but their relevance remains unclear. Recently, Luce et al. (2023) tested the performance of a new model expected to be valid for weakly stratified or strongly sheared conditions, i.e., for low Richardson (Ri) numbers. Its simplest expression is εS=CSσ2S, where CS∼0.64 and S=|dV/dz| is the vertical shear of the horizontal wind V. We assessed the relevance of this model with a UHF (1.357 GHz) wind profiler called WPR LQ-7, which is routinely operated at the Shigaraki Middle and Upper Atmosphere (MU) observatory (34.85∘ N, 136.10∘ E) in Japan. For this purpose, we selected turbulence events associated with Kelvin–Helmholtz (KH) billows, because their formation necessarily requires Ri<0.25 somewhere in the flow, a condition a priori favorable to the application of the model. Eleven years of WPR LQ-7 data were used for this objective. The assessment of εS was first based on its consistency with an empirical model εLout=σ3/Lout, where Lout has the dimension of an outer scale of turbulence. It was found to compare well in a KH layer with direct estimates of ε from in situ measurements for Lout≈70 m. Some degree of equivalence between εS and εLout was confirmed by statistical analysis of 192 KH layers found in the height range 0.3–5.0 km indicating that Lout≈LH/0.64, where LH=σ/S is the Hunt scale defined for neutral turbulence. The degree of equivalence is even significantly improved if Lout is not treated as a constant but depends on the depth D of the layer. We found Lout≈0.0875D or equivalently LH∼0.056D, which also means that σ is proportional to the apparent variation in the horizontal velocity (S×D) over the depth of the KH layer. Consequently, εS=0.64σ2S and εLout=σ3/0.0875D would express the same model for KH layers when Ri remains low. For such a condition, we provide a physical interpretation of εLout, which would be qualitatively identical to that for neutral boundary layers.

Anomalous Dissipation and Lack of Selection in the Obukhov–Corrsin Theory of Scalar Turbulence

The Obukhov–Corrsin theory of scalar turbulence [21, 54] advances quantitative predictions on passive-scalar advection in a turbulent regime and can be regarded as the analogue for passive scalars of Kolmogorov’s K41 theory of fully developed turbulence [47]. The scaling analysis of Obukhov and Corrsin from 1949 to 1951 identifies a critical regularity threshold for the advection-diffusion equation and predicts anomalous dissipation in the limit of vanishing diffusivity in the supercritical regime. In this paper we provide a fully rigorous mathematical validation of this prediction by constructing a velocity field and an initial datum such that the unique bounded solution of the advection-diffusion equation is bounded uniformly-in-diffusivity within any fixed supercritical Obukhov-Corrsin regularity regime while also exhibiting anomalous dissipation. Our approach relies on a fine quantitative analysis of the interaction between the spatial scale of the solution and the scale of the Brownian motion which represents diffusion in a stochastic Lagrangian setting. This provides a direct Lagrangian approach to anomalous dissipation which is fundamental in order to get detailed insight on the behavior of the solution. Exploiting further this approach, we also show that for a velocity field in Cα\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C^\\alpha $$\\end{document} of space and time (for an arbitrary 0≤α<1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0 \\le \\alpha < 1$$\\end{document}) neither vanishing diffusivity nor regularization by convolution provide a selection criterion for bounded solutions of the advection equation. This is motivated by the fundamental open problem of the selection of solutions of the Euler equations as vanishing-viscosity limit of solutions of the Navier-Stokes equations and provides a complete negative answer in the case of passive advection.

Rotating convective turbulence in moderate to high Prandtl number fluids

Rotating convective turbulence is ubiquitously found across geophysical settings, such as surface and subsurface oceans, planetary atmospheres, molten metal planetary cores, magma chambers, magma oceans, and basal magma oceans. Depending on the thermal and material properties of the system, buoyant convection can be driven thermally or compositionally, where a Prandtl number ( Pr = ν / κ i ) defines the characteristic diffusion properties of the system, with κ i = κ T representing thermal diffusion and κ i = κ C representing chemical diffusion. These numbers vary widely for geophysical systems; for example, the liquid iron undergoing thermal-compositional convection in Earth's core is defined by P r T ≈ 0.1 and P r C ≈ 100 , while a thermally-driven liquid silicate magma ocean is defined by P r T ≈ 100 . Currently, most numerical and laboratory data for rotating convective turbulent flows exists at Pr = O ( 1 ) ; high Pr rotating convection relevant to compositionally-driven core flow and other systems is less commonly studied. Here, we address this deficit by carrying out a broad suite of rotating convection experiments made over a range of Pr values, employing water and three different silicone oils as our working fluids ( Pr = 6, 41, 206, and 993). Using measurements of flow velocities (Reynolds, Re) and heat transfer efficiency (Nusselt, Nu), a baroclinic torque balance is found to describe the turbulence regardless of Prandtl number so long as Re is sufficiently large ( Re ≳ 10 ). Estimated turbulent scales are found to remain close to onset scales in all experiments, a result that may extrapolate to planetary settings. Lastly, we use our data to build Pr-dependent predictive nondimensional and dimensional scaling relations for rotating convective velocities that can be applied across a broad range of geophysical fluid dynamical settings.

Fluctuation relations at large scales in three-dimensional hydrodynamic turbulence

It has long been conjectured that, in three-dimensional turbulence, velocity modes at scales larger than the forcing scale follow equilibrium dynamics. Recent numerical and experimental evidence shows that such modes share the same mean energy and therefore support this claim, but equilibrium dynamics does not reduce to equipartition of energy. In this work, a large set of direct numerical simulations is carried out to investigate if fluctuation-dissipation relations and the fluctuation theorem also apply at these scales. These two results link out-of-equilibrium properties of a forced system with its behavior at equilibrium. Both relations are verified quantitatively by the results of our simulations, further supporting that large-scale modes display equilibrium dynamics. They provide new tools to characterize both the mean value and the fluctuations of the injected energy by a large-scale force acting on turbulence driven by small scale random noise.

Topology of turbulence within collisionless plasma reconnection

In near-collisionless plasmas, which are ubiquitous in astrophysics, entropy production relies on fully-nonlinear processes such as turbulence and reconnection, which lead to particle acceleration. Mechanisms for turbulent reconnection include multiple magnetic flux ropes interacting to generate thin current sheets which undergo reconnection, leading to mixing and magnetic merging and growth of coherent structures, unstable reconnection current layers that fragment and turbulent reconnection outflows. All of these processes act across, and encompass, multiple reconnection sites. We use Magnetospheric Multi Scale four-point satellite observations to characterize the magnetic field line topology within a single reconnection current layer. We examine magnetopause reconnection where the spacecraft encounter the Electron Diffusion Region (EDR). We find fluctuating magnetic field with topology identical to that found for dynamically evolving vortices in hydrodynamic turbulence. The turbulence is supported by an electron-magnetohydrodynamic (EMHD) flow in which the magnetic field is effectively frozen into the electron fluid. Accelerated electrons are found in the EDR edge where we identify a departure from this turbulent topology, towards two-dimensional sheet-like structures. This is consistent with a scenario in which sub-ion scale turbulence can suppress electron acceleration within the EDR which would otherwise be possible in the electric field at the X-line.

Assessment of heat transfer and Mach number effects on high-speed turbulent boundary layers

High-speed vehicles experience a highly challenging environment in which the freestream Mach number and surface temperature greatly influence aerodynamic drag and heat transfer. The interplay of these two parameters strongly affects the near-wall dynamics of high-speed turbulent boundary layers (TBLs) in a non-trivial way, breaking similarity arguments on velocity and temperature fields, typically derived for adiabatic cases. We present direct numerical simulations of flat-plate zero-pressure-gradient TBLs spanning three freestream Mach numbers $[2,4,6]$ and four wall temperature conditions (from adiabatic to very cold walls), emphasising the choice of the wall-cooling parameter to recover a similar flow organisation at different Mach numbers. We link qualitative observations on flow patterns to first- and second-order statistics to explain the decoupling of temperature–velocity fluctuations that occurs at reduced wall temperatures and high Mach numbers. For these cases, we discuss the formation of a secondary peak of thermal production in the viscous sublayer, which is in contrast with the monotonic behaviour of adiabatic profiles. We propose different physical mechanisms induced by wall-cooling and compressibility that result in apparently similar flow features, such as a higher peak in the streamwise velocity turbulence intensity, and distinct features, such as the separation of turbulent scales.