Stratified Background Research Articles

Compressible turbulent convection in highly stratified adiabatic background

Buoyancy-driven turbulent convection leads to a fully compressible flow with a prominent top-down asymmetry of first- and second-order statistics when the adiabatic equilibrium profiles of temperature, density and pressure change very strongly across the convection layer. The growth of this asymmetry and the formation of an increasingly thicker stabilized sublayer with a slightly negative mean convective heat flux$J_c(z)$at the top of the convection zone is reported here by a series of highly resolved three-dimensional direct numerical simulations beyond the Oberbeck–Boussinesq and anelastic limits for dimensionless dissipation numbers,$0.1 \le D\le 0.8$, at fixed Rayleigh number$Ra=10^6$and superadiabaticity$\epsilon =0.1$. The highly stratified compressible convection regime appears for$D > D_{crit}\approx 0.65$, when density fluctuations collapse to those of pressure; it is characterized by an up to nearly 50 % reduced global turbulent heat transfer and a sparse network of focused thin and sheet-like thermal plumes falling through the top sublayer deep into the bulk.

On the motion of hairpin filaments in the atmospheric boundary layer

A recent work of Harikrishnan et al. [“Geometry and organization of coherent structures in stably stratified atmospheric boundary layers,” arXiv:2110.02253 (2021)] has revealed an abundance of hairpin-like vortex structures, oriented in a similar direction, in the turbulent patches of a stably stratified Ekman flow. In this study, hairpin-like structures are investigated by treating them as slender vortex filaments, i.e., a vortex filament whose diameter d is small when compared to its radius of curvature R. The corrected thin-tube model of Klein and Knio [“Asymptotic vorticity structure and numerical simulation of slender vortex filaments,” J. Fluid Mech. 284, 275 (1995)] is used to compute the motion of these filaments with the atmospheric boundary layer as a background flow. Our results suggest that the orientation of the hairpin filament in the spanwise direction is linked to its initial starting height under stable stratification, whereas no such dependency can be observed with the neutrally stratified background flow. An improved feature tracking scheme based on spatial overlap for tracking Q-criterion vortex structures on the direct numerical simulation data is also developed. It overcomes the limitation of using a constant threshold in time by dynamically adjusting the thresholds to accommodate the growth or deterioration of a feature. A comparison between the feature tracking and the filament simulation reveals qualitatively similar temporal developments. Finally, an extension of the asymptotic analysis of Callegari and Ting [“Motion of a curved vortex filament with decaying vortical core and axial velocity,” J. Appl. Math. 35, 148–175 (1978)] is carried out to include the effect of gravity. The results show that, in the regime considered here, a contribution from the gravity term occurs only when the tail of an infinitely long filament is tilted at an angle relative to the wall.

Assessing heterogeneity of electronic health-care databases: A case study of background incidence rates of venous thromboembolism.

Heterogeneous results from multi-database studies have been observed, for example, in the context of generating background incidence rates (IRs) for adverse events of special interest for SARS-CoV-2 vaccines. In this study, we aimed to explore different between-database sources of heterogeneity influencing the estimated background IR of venous thromboembolism (VTE). Through forest plots and random-effects models, we performed a qualitative and quantitative assessment of heterogeneity of VTE background IR derived from 11 databases from 6 European countries, using age and gender stratified background IR for the years 2017-2019 estimated in two studies. Sensitivity analyses were performed to assess the impact of selection criteria on the variability of the reported IR. A total of 54 257 284 subjects were included in this study. Age-gender pooled VTE IR varied from 5 to 421/100 000 person-years and IR increased with increasing age for both genders. Wide confidence intervals (CIs) demonstrated considerable within-data-source heterogeneity. Selecting databases with similar characteristics had only a minor impact on the variability as shown in forest plots and the magnitude of the I2 statistic, which remained large. Solely including databases with primary care and hospital data resulted in a noticeable decrease in heterogeneity. Large variability in IR between data sources and within age group and gender strata warrants the need for stratification and limits the feasibility of a meaningful pooled estimate. A more detailed knowledge of the data characteristics, operationalisation of case definitions and cohort population might support an informed choice of the adequate databases to calculate reliable estimates.

Cloudy with a chance of rain: accretion braking of cold clouds

ABSTRACT Understanding the survival, growth, and dynamics of cold gas is fundamental to galaxy formation. While there has been a plethora of work on ‘wind tunnel’ simulations that study such cold gas in winds, the infall of this gas under gravity is at least equally important, and fundamentally different since cold gas can never entrain. Instead, velocity shear increases and remains unrelenting. If these clouds are growing, they can experience a drag force due to the accretion of low-momentum gas, which dominates over ram pressure drag. This leads to subvirial terminal velocities, in line with observations. We develop simple analytic theory and predictions based on turbulent radiative mixing layers. We test these scalings in 3D hydrodynamic simulations, both for an artificial constant background and a more realistic stratified background. We find that the survival criterion for infalling gas is more stringent than in a wind, requiring that clouds grow faster than they are destroyed ($t_{\rm grow} \lt 4\, t_{\rm cc}$). This can be translated to a critical pressure, which for Milky Way-like conditions is $P \sim 3000 \, {k}_\mathrm{ B} \, {\rm K}\, {\rm cm}^{-3}$. Cold gas that forms via linear thermal instability (tcool/tff < 1) in planar geometry meets the survival threshold. In stratified environments, larger clouds need only survive infall until cooling becomes effective. We discuss applications to high-velocity clouds and filaments in galaxy clusters.

Stability of the 2D anisotropic Boussinesq equations with mixed partial dissipation

Stability is an important property of solutions to many fluid flow equations. In this paper, we focus on the stability problem for two-dimensional Boussinesq equations with only vertical viscosity and horizontal thermal diffusion near a stratified, hydrostatic equilibrium in the domain Ω=T×R, where T=[−12,12] is a 1D periodic box. We are mainly concerned with the H2-stability of global solutions when the initial data are closed to an equilibrium state and sufficiently small. Due to the lack of horizontal viscosity in velocity equations and vertical thermal diffusion in temperature equation, this problem seems to be not trivial and becomes particularly difficult. In order to achieve our main goal, we divide the velocity field and temperature into two parts: the horizontal average and the remaining oscillation part. Besides, we fully exploit the Lt2Lx2-norm of ∂xu2 to help us dominate the nonlinear parts. Our result shows that with a small initial perturbation, there exists a unique global solution to the stated Boussinesq equations. In addition, the perturbation remains small for all time. In particular, our result also demonstrates the stabilizing effect of internal gravity waves, which are induced by the stratified background hydrostatic state.

A Taxonomy of Orchestral Grouping Effects Derived from Principles of Auditory Perception

The study of timbre and orchestration in symphonic music research is underexplored, and few theories attempt to explain strategies for combining and contrasting instruments and the resulting perception of orchestral structures and textures. An analysis of orchestration treatises and musical scores reveals an implicit understanding of auditory grouping principles by which many orchestration techniques give rise to predictable perceptual effects. We present a novel theory formalized in a taxonomy of devices related to auditory grouping principles that appear frequently in Western orchestration practices from a range of historical epochs. We develop three classes of orchestration analysis categories: concurrent grouping cues result in blended combinations of instruments; sequential grouping cues result in melodic lines, the integration of surface textures, and the segregation of melodies or stratified (foreground and background) layers based on acoustic (dis)similarities; segmental grouping cues contrast sequentially presented blocks of materials and contribute to the creation of perceptual boundaries. The theory predicts orchestration-based perceptual structuring in music and may be applied to music of any style, culture, or genre.

Gravity-driven filamentary flow in molecular clouds

ABSTRACT We present a numerical study of the gravity-driven filamentary flow arising in the presence of elongated perturbations embedded in a globally gravitationally unstable medium. We perform idealized simulations of the gravitational collapse of a moderate filamentary perturbation with a central enhancement (a core) embedded in either a uniform or a stratified background. Both simulations maintain the filamentary structure during the collapse, developing a hierarchical accretion flow from the cloud to the filament, and from the filament to the core. Only the stratified simulation produces a flat central density profile of filaments, best matching the observed Plummer-like profiles, supporting suggestions that molecular clouds may be preferentially flattened. The flow changes direction smoothly from the cloud to the filament, with no density divergence nor a shock developing at the filament’s axis during the prestellar evolution. The drainage of material by the filament-to-core accretion slows down the growth of the filament, causing the ratio of the core’s central density to the filament’s axial density to increase in time, and to diverge at the time when a singularity (protostar) forms in the core. We argue that the system should evolve towards a stationary state in which the filament-to-core accretion balances the cloud-to-filament one, and search for it in the simulations, but find no unambiguous evidence. However, we find that, after a period of accelerated increase, the filament’s linear mass density reaches a linear growth rate. The stationary state may be approached during the protostellar stage.

A field experiment characterizing variable detection rates during plant surveys.

Surveys aimed at finding threatened and invasive species can be challenging due to individual rarity and low and variable individual detection rates. Detection rate in plant surveys typically varies due to differences among observers, among the individual plants being surveyed (targets), and across background environments. Interactions among these 3 components may occur but are rarely estimated due to limited replication and control during data collection. We conducted an experiment to investigate sources of variation in detection of 2 Pilosella species that are invasive and sparsely distributed in the Alpine National Park, Australia. These species are superficially similar in appearance to other yellow‐flowered plants occurring in this landscape. We controlled the presence and color of flowers on target Pilosella plants and controlled their placement in plots, which were selected for their variation in cover of non‐target yellow flowers and dominant vegetation type. Observers mimicked Pilosella surveys in the plots and reported 1 categorical and 4 quantitative indicators of their survey experience level. We applied survival analysis to detection data to model the influence of both controlled and uncontrolled variables on detection rate. Orange‐ and yellow‐flowering Pilosella in grass‐ and heath‐dominated vegetation were detected at a higher rate than nonflowering Pilosella. However, this detection gain diminished as the cover of other co‐occurring yellow‐flowering species increased. Recent experience with Pilosella surveys improved detection rate. Detection experiments are a direct and accessible means of understanding detection processes and interpreting survey data for threatened and invasive species. Our detection findings have been used for survey planning and can inform progress toward eradication. Interaction of target and background characteristics determined detection rate, which enhanced predictions in the Pilosella eradication program and demonstrated the difficulty of transferring detection findings into untested environments.

Observational Signatures of Planets in Protoplanetary Disks: Temperature Structures in Spiral Arms

Abstract High-resolution imaging of protoplanetary disks has unveiled a rich diversity of spiral structure, some of which may arise from disk-planet interaction. Using 3D hydrodynamics with β cooling to a vertically stratified background, as well as radiative-transfer modeling, we investigate the temperature rise in planet-driven spirals. In rapidly cooling disks, the temperature rise is dominated by a contribution from stellar irradiation, 0.3%–3% inside the planet radius but always < 0.5% outside. When cooling time equals or exceeds dynamical time, however, this is overwhelmed by hydrodynamic PdV work, which introduces a ∼10%–20% perturbation within a factor of ∼2 from the planet’s orbital radius. We devise an empirical fit of the spiral amplitude Δ ( T ) = ( M p / M th ) c ( f PdV e − t arm / t c + f rad ) to take into account both effects. Where cooling is slow, we find also that temperature perturbations from buoyancy spirals—a strictly 3D, nonisothermal phenomenon—become nearly as strong as those from Lindblad spirals, which are amenable to 2D and isothermal studies. Our findings may help explain observed thermal features in disks like TW Hydrae and CQ Tauri, and underscore that 3D effects have a qualitatively important effect on disk structure.

Turbulent shear layers in a uniformly stratified background: DNS at high Reynolds number

Abstract

On adiabatic oscillations of a stratified atmosphere on the flat earth

We consider the oscillations of the atmosphere around a stratified back ground density and entropy distribution under the gravitation on the flat Earth. The atmosphere is supposed to be an ideal gas, and the motion is supposed to be governed by the compressible Euler equations. The density distribution of the background equilibrium is supposed to touch the vacuum at the finite height of the stratosphere. Considering the linearized approximation for small perturbations, we show that time periodic oscillations with a sequence of time periods, which accumulate to infinity, say, slow and slow oscillations, so called “g-modes,” can appear when the square of the Brunt–Väisälä frequency is positive everywhere for the considered background equilibrium.

Investigation of LES models for a stratified shear layer

The performance of three large-eddy simulation (LES) models in predicting the evolution of a shear layer at moderate Reynolds number in a linearly stratified background is investigated. Results of the Dynamic Smagorinsky, Ducros, and Wall-Adapting Local Eddy Viscosity (WALE) models are compared against those of direct numerical simulation (DNS). Two levels of grid refinement are employed to assess the change in the models’ capabilities with varying resolution. Of particular interest is the ability of the models to capture the evolution of instabilities as well as accurately quantify turbulence statistics. Evolution of momentum thickness, local buoyancy flux, shear, and gradient Richardson number show good agreement of the LES models with the DNS. A comparison of the turbulent kinetic energy (TKE) and its budget indicates good capture of turbulence evolution in the LES models. There is a moderate over prediction of spatially integrated TKE during a short period when the integrated TKE is at its maximum. This feature is traced to the underestimate of turbulent dissipation rate in the LES. Coarsening grid resolution significantly increases the discrepancy in dissipation between the WALE model and the DNS while defects due to the coarser grid resolution are mild in the case of the Ducros model. All of the LES models overestimate the peak values of eddy viscosity and eddy diffusivity although the Ducros model produces the closest agreement with the DNS. Furthermore, the Ducros model is found to require fewer CPU hours than the DNS or other LES models.

TIV and PIV based natural convection study over a square flat plate under stable stratification

Natural convection over an isolated horizontal plate in a stably stratified background condition is fundamental and challenging in industrial, atmospheric, geographical, and oceanic environmental studies, which, however, is still lack of investigation. In this study, the water tank modelling experiment with two main techniques, Thermal Image Velocimetry (TIV) and Particle Image Velocimetry (PIV), was conducted to investigate large eddy structures, the mean velocity field and heat transfer over an idealized square heated surface under the stable stratification. Shirking, growing and twisting eddy structures were identified in this study. By measuring the velocity fields at different horizontal planes with varied heights, an asymmetric flow structure over a square urban area is suggested by the PIV method to be characterized as the main diagonal inflow at lower levels and as the side outflow (perpendicular to edges) at upper levels. The mean flow speeds measured by TIV and PIV were quantitatively compared and analyzed by using cross-correlation coefficients. The low-level (2 mm or less above) velocity field measured by TIV also well presents the similar characteristics of near-surface diagonal inflow observed in the PIV measurements. Consequently, the reliability of the TIV method in this study is well verified for resolving the near-surface convective flow fields. The stable stratification is found to significantly impair the heat transfer efficiency as results indicated that the heat transfer in a stable environment is significantly weaker than that in a neutral environment by 71%.

Using synchrotron emission modelling of relativistic hydrodynamic jet simulations to study the FR I/FR II dichotomy of active galactic nuclei radio jets

In this paper three dimensional relativistic hydrodynamic simulations of AGN jets are presented to investigate the FR I/FR II dichotomy. Three simulations are presented which illustrates the difference in morphology for high/low Lorentz factor injection as well as a stratified background medium. Lorentz factors of 10 and 1.0014 were used for the high and low Lorentz factor cases respectively. The hydrodynamic simulations show a division in the morphology of jets based on their initial injection luminosity. An additional simulation was set up to investigate the evolution of the low Lorentz factor jet if the mass injection was lowered after a certain time. A synchrotron emission model was applied to these simulations to reproduce intensity maps at radio frequencies (1.5GHz) which were compared to the observed emission structures of FR I/FR II radio galaxies. The effect of Doppler boosting on the intensity maps was also investigated for different polar angles. The intensity maps of both the high and low Lorentz factor cases reproduced emission structures that resemble those of FR II type radio galaxies with a dominant cocoon region containing time dependent hot spots and filaments. An FR I like structure was, however, produced for the low Lorentz factor case if the mass injection rate was lowered after a set time period.

Dynamic mode decomposition for estimating vortices and lee waves in a stratified wake

Dynamic mode decomposition (DMD) is an analysis technique for extracting flow patterns and their dynamics from experimental or simulated velocity fields. Here, DMD is applied to experimental data in the vertical center-plane of wakes generated by a towed grid in a stably stratified background, at varying values of the dimensionless Froude and Reynolds Number. The primary goal was to identify dynamically important patterns and reveal the influence of stratification on their initiation and evolution. It is demonstrated that DMD captures lee wave and vortical modes with different length scales successfully. Further, one can construct a mode energy spectrum which shows a clear dependence on Froude Number, with energy transfer to larger scales in the near wake, as the initial shear-triggered Kelvin–Helmholtz roll-ups diffuse and pair with neighbors. Finally, this paper serves as a detailed example of the application of DMD to time-resolved particle imaging velocimetry data for a stratified flow. The results confirm its utility in objective identification of dynamics at different scales of complex fluid flows.

Statistical Enrichment of Epigenetic States Around Triplet Repeats that Can Undergo Expansions.

More than 30 human genetic diseases are linked to tri-nucleotide repeat expansions. There is no known mechanism that explains repeat expansions in full, but changes in the epigenetic state of the associated locus has been implicated in the disease pathology for a growing number of examples. A comprehensive comparative analysis of the genomic features associated with diverse repeat expansions has been lacking. Here, in an effort to decipher the propensity of repeats to undergo expansion and result in a disease state, we determine the genomic coordinates of tri-nucleotide repeat tracts at base pair resolution and computationally establish epigenetic profiles around them. Using three complementary statistical tests, we reveal that several epigenetic states are enriched around repeats that are associated with disease, even in cells that do not harbor expansion, relative to a carefully stratified background. Analysis of over one hundred cell types reveals that epigenetic states generally tend to vary widely between genic regions and cell types. However, there is qualified consistency in the epigenetic signatures of repeats associated with disease suggesting that changes to the chromatin and the DNA around an expanding repeat locus are likely to be similar. These epigenetic signatures may be exploited further to develop models that could explain the propensity of repeats to undergo expansions.

Thermal and non-thermal emission from reconnecting twisted coronal loops

Twisted magnetic fields should be ubiquitous in flare-producing active regions where the magnetic fields are strongly non-potential. It has been shown that reconnection in helical magnetic coronal loops results in plasma heating and particle acceleration distributed within a large volume, including the lower coronal and chromospheric sections of the loops. This scenario can be an alternative to the standard flare model, where particles are accelerated only in a small volume located in the upper corona. We use a combination of MHD simulations and test-particle methods, which describe the development of kink instability and magnetic reconnection in twisted coronal loops using resistive compressible MHD, and incorporate atmospheric stratification and large-scale loop curvature. The resulting distributions of hot plasma let us estimate thermal X-ray emission intensities. The electric and magnetic fields obtained are used to calculate electron trajectories using the guiding-centre approximation. These trajectories combined with the MHD plasma density distributions let us deduce synthetic HXR bremsstrahlung intensities. Our simulations emphasise that the geometry of the emission patterns produced by hot plasma in flaring twisted coronal loops can differ from the actual geometry of the underlying magnetic fields. The twist angles revealed by the emission threads (SXR) are consistently lower than the field-line twist present at the onset of the kink-instability. HXR emission due to the interaction of energetic electrons with the stratified background are concentrated at the loop foot-points in these simulations, even though the electrons are accelerated everywhere within the coronal volume of the loop. The maximum of HXR emission consistently precedes that of SXR emission, with the HXR light-curve being approximately proportional to the temporal derivative of the SXR light-curve.

Comprehensive numerical methodology for direct numerical simulations of compressible Rayleigh–Taylor instability

An investigation of compressible Rayleigh-Taylor instability (RTI) using Direct Numerical Simulations (DNS) requires efficient numerical methods, advanced boundary conditions, and consistent initialization in order to capture the wide range of scales and vortex dynamics present in the system, while reducing the computational impact associated with acoustic wave generation and the subsequent interaction with the flow. An advanced computational framework is presented that handles the challenges introduced by considering the compressive nature of RTI systems, which include sharp interfacial density gradients on strongly stratified background states, acoustic wave generation and removal at computational boundaries, and stratification dependent vorticity production. The foundation of the numerical methodology described here is the wavelet-based grid adaptivity of the Parallel Adaptive Wavelet Collocation Method (PAWCM) that maintains symmetry in single-mode RTI systems to extreme late-times. PAWCM is combined with a consistent initialization, which reduces the generation of acoustic disturbances, and effective boundary treatments, which prevent acoustic reflections. A dynamic time integration scheme that can handle highly nonlinear and potentially stiff systems, such as compressible RTI, completes the computational framework. The numerical methodology is used to simulate two-dimensional single-mode RTI to extreme late-times for a wide range of flow compressibility and variable density effects. The results show that flow compressibility acts to reduce the growth of RTI for low Atwood numbers, as predicted from linear stability analysis.

A numerical study of a weakly stratified turbulent wake

Direct numerical simulation (DNS) of a time-developing turbulent wake evolving in a stably stratified background is presented. A large initial Froude number is chosen to allow the wake to become fully turbulent and axisymmetric before stratification affects the spreading rate of the mean defect. Turbulence statistics are formed by averaging over the homogeneous streamwise direction of a domain that is larger than earlier stratified-wake simulations in order to reduce the statistical uncertainty. The DNS results are used to cast light on the mechanisms that lead to the various states of this flow – namely the three-dimensional (essentially unstratified), non-equilibrium (or ‘wake-collapse’) and quasi-two-dimensional (or ‘two-component’) regimes, previously observed for wakes embedded in both weakly and strongly stratified backgrounds. For this relatively high-initial-Reynolds- and Froude-number simulation, we find that the signature reduction in the rate of decay of the maximum mean defect velocity during the wake-collapse regime is due to buoyancy-induced alterations of the turbulence structure, which weaken and redistribute the Reynolds shear stresses whose gradients appear in the streamwise mean momentum equation. The change in the rate of decay of the turbulence kinetic energy (TKE) observed during the wake-collapse regime (which occurs well after the mean velocity decay reduction begins) is not caused by transfer of turbulent gravitational potential energy to TKE, as has been previously suggested. The results instead reveal that the reduction in TKE decay – which for this flow, with its relatively weak internal waves, eventually leads to TKE growth, heralding the arrival of the two-component regime – is caused by an increase in the rate of TKE production associated with the wake structure becoming increasingly two-dimensional, such that the lateral Reynolds shear stress,$-\overline{u^{\prime }v^{\prime }}$, becomes dominant. The present results are also compared with those of previous simulations at different Froude and Reynolds numbers, and whose initial conditions contain different turbulence structures. This comparison confirms a strong degree of commonality in the late-wake behaviour, which lends support to the hypothesis that all wakes in stably stratified environments achieve a universal state in the final stages of decay.

Mean and Turbulent Flow Downstream of a Low-Intensity Fire: Influence of Canopy and Background Atmospheric Conditions

AbstractThis study examines the sensitivity of mean and turbulent flow in the planetary boundary layer and roughness sublayer to a low-intensity fire and evaluates whether the sensitivity is dependent on canopy and background atmospheric properties. The ARPS-CANOPY model, a modified version of the Advanced Regional Prediction System (ARPS) model with a canopy parameterization, is utilized for this purpose. A series of numerical experiments are conducted to evaluate whether the ability of the fire to alter downstream wind, temperature, turbulent kinetic energy (TKE), and vertical heat flux differs between forested and open areas, sparse and dense forests, weak and strong background flow, and neutral and convective background stability. Analysis of all experiments shows that, in general, mean and turbulent flow both prior to and during a low-intensity fire is damped in the presence of a canopy. Greater sensitivity to the fire is found in cases with strong ambient wind speed than in cases with quiescent or weak wind speed. Furthermore, sensitivity of downstream atmospheric conditions to the fire is shown to be strongest with a neutrally stratified background. An analysis of the TKE budget reveals that both buoyancy and wind shear contribute to TKE production during the period of time in which the fire conditions are applied to the model. On the basis of the results of the ARPS simulations, caution is advised when applying ARPS-simulation results to predictions of smoke transport and dispersion: smoke-model users should consider whether canopy impacts on the atmosphere are accounted for and whether neutral stratification is assumed.