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At least 685 records · Page 38
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

TEAMER: Water Tunnel Data from Testing the Pterofin Skimmer Concept

Pterofin's Skimmer concept relies on a flapping and pitching hydrofoil to extract hydrokinetic energy from water flows. The concept aims to utilize unsteady fluid dynamics phenomena (added mass, shed vorticity, and unsteady boundary layer development) to achieve higher lift coefficients, enabling increased power density of the hydrokinetic device and a fundamental shift in the rpm/torque scaling of the power take off compared with turbines. The Applied Research Laboratory at Penn State, in collaboration with Pterofin, designed and built a proof-of-concept flapping/pitching mechanism which was subsequently tested in ARL's 12-inch water tunnel facility. The mechanical power supplied to or extracted from the mechanism was measured for a range of hydrofoils provided by Pterofin over operating conditions including reduced frequency, Reynolds number, and the ratio between pitching and flapping amplitudes. The power lost to friction in the mechanism was removed from the net power measurement by means of a bare hub tare, with the resultant hydrodynamic power being used to calculate a mechanism-independent and non-dimensional power coefficient. The product of this effort is a dataset describing the power coefficient of a hydrofoil having simultaneous pitching and flapping motions, both of which are approximately sinusoidal. Power coefficients were collected for a range of primary design variables including: - Reduced frequency: 0.01 to 0.95 - Pitching/flapping peak angle ratio: 1.5 to 3.0 - Chord-based Reynolds number: 60,000 to 560,000 Secondary design variables relating to the hydrofoil geometry were explored including: - Aspect ratio - Planform shape - Section thickness distribution - Hydrofoil position relative to the pitching axis - Hydrofoil sweep angle relative to the pitching axis Measured data are provided in mean and time series formats. MATLAB scripts are provided which can be used to generate figures of time-averaged and phase-averaged hydrodynamic power coefficients calculated from the measured data. A complete description of the experiment and data reduction can be found in the Post Access Report for the Pterofin Skimmer test effort which will be available on the TEAMER website. This work was supported by the Pacific Energy Ocean Trust via a TEAMER award.

16 TIDAL AND WAVE POWER↗
NASA NTRS1973

The starting transient of solid propellant rocket motors with high internal gas velocities

A comprehensive analytical model which considers time and space development of the flow field in solid propellant rocket motors with high volumetric loading density is described. The gas dynamics in the motor chamber is governed by a set of hyperbolic partial differential equations, that are coupled with the ignition and flame spreading events, and with the axial variation of mass addition. The flame spreading rate is calculated by successive heating-to-ignition along the propellant surface. Experimental diagnostic studies have been performed with a rectangular window motor (50 cm grain length, 5 cm burning perimeter and 1 cm hydraulic port diameter), using a controllable head-end gaseous igniter. Tests were conducted with AP composite propellant at port-to-throat area ratios of 2.0, 1.5, 1.2, and 1.06, and head-end pressures from 35 to 70 atm. Calculated pressure transients and flame spreading rates are in very good agreement with those measured in the experimental system.

Peretz, A.↗
NASA NTRSDate not supplied

Investigation into Stimulated Microgravity Techniques used to Study Biofilm Growth

Bacterial growth in liquid media in microgravity conditions is not well understood. Trends such as a shortened lag phase, longer log phase, slower growth rate, and a higher final population concentration have been noted but the underlying cause remains unclear. At the single cell level, it is predicted that bacteria are less gravity-sensitive than larger species. The effects on their immediate environment, including the lack of cell settlement and slower mass transfer of nutrients due to lack of density driven convection, could help explain the trends. Ground-based spaceflight analogs, or simulated microgravity devices, are often employed to achieve different attributes of weightlessness to study effects on bacterial growth. Though these technologies could isolate gravity’s role in various biological processes, they cannot replicate all its effects and underlying mechanisms. Hence, interpretation of results could be misleading, even if similar to spaceflight. In this study two common simulated microgravity devices were investigated to determine whether they could simulate relevant microgravity conditions for bacterial growth. A bioreactor, the high aspect ratio vessel (HARV), was used with dyes of different density mounted on a random positioning machine (RP machine) or a rotating wall vessel (RWV). The RP machine displayed higher mixing rates than the RWV. The RWV was further tested at different rotations per minute (RPM). The range to minimize effects of density driven convection (low speeds) or centrifugal forces (high speeds) was between a range of 15-20 RPM. These results will help inform the selection of simulated microgravity device as well as interpretation of subsequent biofilm growth results.

Angie M. Diaz↗
NASA NTRS1977

The clouds of Venus. II - An investigation of the influence of coagulation on the observed droplet size distribution

An approximate numerical technique is used to investigate the influence of coagulation, sedimentation and turbulent motions on the observed droplet size distribution in the upper layers of the Venus clouds. If the cloud mass mixing ratio is less than 0.000001 at 250 K or the eddy diffusivity throughout the cloud is greater than 1,000,000 sq cm per sec, then coagulation is unimportant. In this case, the observed droplet size distribution is the initial size distribution produced by the condensation of the droplets. It is found that all cloud models with droplet formation near the cloud top (e.g., a photochemical model) must produce the observed droplet size distribution by condensation without subsequent modification by coagulation. However, neither meteoritic or surface dust can supply sufficient nucleating particles to account for the observed droplet number density. If the cloud droplets are formed near the cloud bottom, the observed droplet size distribution can be produced solely by the interaction of coagulation and dynamics; all information about the initial size distribution is lost. If droplet formation occurs near the cloud bottom, the lower atmosphere of Venus is oxidizing rather than reducing.

Rossow, W. B.↗
NASA NTRS1977

Wind enhanced planetary escape - Collisional modifications

Effects of collisions and finite winds characteristic of a highly perturbed atmosphere on the thermal escape of terrestrial hydrogen and helium are investigated using a Monte Carlo approach. The limiting cases of vertical and horizontal winds are considered, and the relaxation layer between the collisionless exosphere and the collision-dominated thermosphere is modeled as a plane-parallel slab of given column density, depth, and atmospheric density. For both gases, the upwardly injected flux at the base of the relaxation layer is compared with the returning downward flux distribution at the same location; the technique is also applied to the atmosphere of Titan. The results show that inclusion of collisions in the escape model for terrestrial hydrogen with winds effectively throttles the escape process, that collisional throttling is negligible for helium when the exobase temperature is at least 5000 K, and that the escape of a planetary-atmosphere constituent depends on the ratio of its gravitational and kinetic energies as well as on the ratio of its mass to that of the background gas.

Curtis, S. A.↗
NASA NTRS2013

ALMA Observations of the Galactic Center: SiO Outflows and High Mass Star Formation Near Sgr A

Using ALMA observations of the Galactic center with a spatial resolution of 2.61" x 0.97 ", we detected 11 SiO (5-4) clumps of molecular gas in the within 0.6pc (15") of Sgr A*, interior of the 2-pc circumnuclear molecular ring. Three SiO (5-4) clumps closest to Sgr A* show the largest central velocities of approximately 150 kilometers per second and broadest asymmetric linewidths with total linewidths FWZI approximately 110-147 kilometers per second. Other clumps are distributed mainly to the NE of the ionized minispiral with narrow linewidths of FWHM approximately 11-27 kilometers per second. Using CARMA data, LVG modeling of the broad velocity clumps, the SiO (5-4) and (2-1) line ratios constrain the column density N(SiO) approximately 10(exp 14) per square centimeter, and the H2 gas density n(sub H2) = (3-9) x 10(exp 5) per cubic centimeter for an assumed kinetic temperature 100-200K. The SiO (5-4) clumps with broad and narrow linewidths are interpreted as highly embedded protostellar outflows, signifying an early stage of massive star formation near Sgr A* in the last 104 years. Additional support for the presence of YSO outflows is that the luminosities and velocity widths lie in the range detected from protostellar outflows in star forming regions in the Galaxy. Furthermore, SED modeling of stellar sources along the N arm show two YSO candidates near SiO clumps supporting in-situ star formation near Sgr A*. We discuss the nature of star formation where the gravitational potential of the black hole dominates. In particular, we suggest that external radiative pressure exerted on self-shielded molecular clouds enhance the gas density, before the gas cloud become gravitationally unstable near Sgr A*.

Yusef-Zadeh, F.↗
NASA NTRS2015

The Structure of Pre-Transitional Protoplanetary Disks. II Azimuthal Asymmetries, Different Radial Distributions of Large and Small Dust Grains in PDS 70

The formation scenario of a gapped disk, i.e., transitional disk, and its asymmetry is still under debate. Proposed scenarios such as disk-planet interaction, photoevaporation, grain growth, anticyclonic vortex, eccentricity, and their combinations would result in different radial distributions of the gas and the small (sub-micron size) and large (millimeter size) dust grains as well as asymmetric structures in a disk. Optical/near-infrared (NIR) imaging observations and (sub-)millimeter interferometry can trace small and large dust grains, respectively; therefore multi-wavelength observations could help elucidate the origin of complicated structures of a disk. Here we report Submillimeter Array observations of the dust continuum at 1.3 mm and CO-12 J = 2 yields 1 line emission of the pre-transitional protoplanetary disk around the solar-mass star PDS 70. PDS 70, a weak-lined T Tauri star, exhibits a gap in the scattered light from its disk with a radius of approx. 65 AU at NIR wavelengths. However, we found a larger gap in the disk with a radius of approx. 80 AU at 1.3 mm. Emission from all three disk components (the gas and the small and large dust grains) in images exhibits a deficit in brightness in the central region of the disk, in particular, the dust disk in small and large dust grains has asymmetric brightness. The contrast ratio of the flux density in the dust continuum between the peak position to the opposite side of the disk reaches 1.4. We suggest the asymmetries and different gap radii of the disk around PDS 70 are potentially formed by several (unseen) accreting planets inducing dust filtration.

Submillimeter Array observations↗
DOE OSTI2025

QUOKKA-based understanding of outflows (QED) – III. Outflow loading and phase structure as a function of galactic environment

ABSTRACT We present results from a suite of 3D high-resolution hydrodynamic simulations of supernova-driven outflows from galactic disc regions with a range of gas surface density, metallicity, and supernova scale height. We use this suite to quantify how outflow properties – particularly the loading factors for mass, metallicity, and energy – vary with these parameters. We find that the winds fall into three broad categories: steady and hot, multiphase and moderately bursty, and cool and highly bursty. The first of these is characterized by efficient metal and energy loading but weak mass loading, the second by moderate loading of mass, metals, and energy, and the third by negligible metal and energy loading but substantial mass loading. The most important factor in determining the kind of wind a galaxy will produce is the ratio of supernova to gas scale heights, with the latter set by a combination of supernova rate, metallicity-dependent cooling rate, and the gravitational potential. These often combine in counterintuitive ways – for example increased cooling causes cold clouds to sink into the galactic midplane more rapidly, lowering the volume-filling factor of dense gas and making the environment more favourable for strong winds. Our findings suggest that the nature of galactic winds is likely highly sensitive to phenomena such as runaway stars occurring at a large height and dense gas and are poorly captured in most simulations, and that metal loading factors for type Ia supernovae may be substantially larger than those for type II, with important implications for galactic chemical evolution.

Vijayan, Aditi (ORCID:0000000277142379)↗
DOE OSTI2021

Dark Matter Constraints from a Unified Analysis of Strong Gravitational Lenses and Milky Way Satellite Galaxies

Joint analyses of small-scale cosmological structure probes have been relatively unexplored yet promise to advance measurements of microphysical dark matter properties using heterogeneous data. Here, we present a multidimensional analysis of dark matter substructure using strong gravitational lenses and the Milky Way (MW) satellite galaxy population, accounting for degeneracies in model predictions and using covariances in the constraining power of these individual probes for the first time. We simultaneously infer the projected subhalo number density and the half-mode mass describing the suppression of the subhalo mass function in thermal relic warm dark matter (WDM), $M_{\mathrm{hm}}$, using the semianalytic model \texttt{Galacticus} to connect the subhalo population inferred from MW satellite observations to the strong lensing host halo mass and redshift regime. Combining MW satellite and strong lensing posteriors in this parameter space yields $M_{\mathrm{hm}}<10^{7.0}\ M_{\mathrm{\odot}}$ (WDM particle mass $m_{\mathrm{WDM}}>9.7\ \mathrm{keV}$) at $95\%$ confidence and disfavors $M_{\mathrm{hm}}=10^{7.4}\ M_{\mathrm{\odot}}$ ($m_{\mathrm{WDM}}=7.4\ \mathrm{keV}$) with a 20:1 marginal likelihood ratio, improving limits on $m_{\mathrm{WDM}}$ set by the two methods independently by $\sim 30\%$. These results are marginalized over the line-of-sight contribution to the strong lensing signal, the mass of the MW host halo, and the efficiency of subhalo disruption due to baryons and are robust to differences in the disruption efficiency between the MW and strong lensing regimes at the $\sim 10\%$ level. This work paves the way for unified analyses of next-generation small-scale structure measurements covering a wide range of scales and redshifts.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1979

Mass-radius relationships in icy satellites

Using published laboratory data for H2O ice, a modeling technique was developed by which the bulk density, density and temperature profile, rotational moment of inertia, central pressure, and location of the rock-ice interface can all be obtained as a function of the radius, the heliocentric distance, and the silicate composition. Models of the interiors of Callisto, Ganymede, Europa, Rhea, and Titan are given, consistent with present mass and radius data. The radius and mass of spheres of ice under self-gravitation for two different temperature classes are given (103 and 77 deg K). Measurements of mass, radius and I/MR2 by spacecraft can be interpreted by this model to yield substantial information about the internal structure and the ice/rock ratio of the icy satellites of Jupiter and Saturn.

Lupo, M. J.↗
NASA NTRS1981

Integrated propulsion for near-Earth space missions. Volume 1: Executive summary

Tradeoffs between electric propulsion system mass ratio and transfer time from LEO to GEO were conducted parametrically for various thruster efficiency, specific impulse, and other propulsion parameters. A computer model was developed for performing orbit transfer calculations which included the effects of aerodynamic drag, radiation degradation, and occultation. The tradeoff results showed that thruster technology areas for integrated propulsion should be directed towards improving primary thruster efficiency in the range from 1500 to 2500 seconds, and be continued towards reducing specific mass. Comparison of auxiliary propulsion systems showed large total propellant mass savings with integrated electric auxiliary propulsion. Stationkeeping is the most demanding on orbit propulsion requirement. At area densities above 0.5 sq m/kg, East-West stationkeeping requirements from solar pressure exceed North-South stationkeeping requirements from gravitational forces. A solar array pointing strategy was developed to minimize the effects of atmospheric drag at low altitude, enabling electric propulsion to initiate orbit transfer at Shuttle's maximum cargo carrying altitude. Gravity gradient torques are used during ascent to sustain the spacecraft roll motion required for optimum solar array illumination. A near optimum cover glass thickness of 6 mils was established for LEO to GEO transfer.

Dailey, C. L.↗
NASA NTRS1991

Calculations of particle-laden flows by second-moment closures

A differential second-moment closure is applied to calculate nonswirling turbulent particle-laden jet flow. The closure is effected by extending constant-density single-phase turbulence models to the continuous (carrier) phase of two-phase flow. The dispersed (discrete) phase is treated by stochastic-Lagrangian technique. To reduce the effects of numerical (false) diffusion on the predicted results, a higher order differencing scheme, namely the flux-spline, is employed. In addition, an experimental study is conducted to provide data of good quality, especially near the inlet, for model assessment. The experiment consists of a confined coaxial jet flow of air with glass beads. The beads' diameter is 105 microns and is injected from the inner jet with a mass loading ratio of 0.9. The computed results are in good agreement with experimental data, especially for the carrier phase. However, the predicted turbulence fluctuations associated with the discrete phase are lower than the data at the downstream region of the flow field.

Nikjooy, M.↗
NASA NTRS2011

Host Galaxy Properties of the Swift BAT Ultra Hard X-Ray Selected AGN

We have assembled the largest sample of ultra hard X-ray selected (14-195 keV) AGN with host galaxy optical data to date, with 185 nearby (z<0.05), moderate luminosity AGN from the Swift Burst Alert Telescope (BAT) sample. The BAT AGN host galaxies have intermediate optical colors (u -- r and g -- r) that are bluer than a comparison sample of inactive galaxies and optically selected AGN from the Sloan Digital Sky Survey (SDSS) which are chosen to have the same stellar mass. Based on morphological classifications from the RC3 and the Galaxy Zoo, the bluer colors of BAT AGN are mainly due to a higher fraction of mergers and massive spirals than in the comparison samples. BAT AGN in massive galaxies (log Stellar Mass >10.5) have a 5 to 10 times higher rate of spiral morphologies than in SDSS AGN or inactive galaxies. We also see enhanced far-IR emission in BAT AGN suggestive of higher levels of star formation compared to the comparison samples. BAT AGN are preferentially found in the most massive host galaxies with high concentration indexes indicative of large bulge-to-disk ratios and large supermassive black holes. The narrow-line (NL) BAT AGN have similar intrinsic luminosities as the SDSS NL Seyferts based on measurements of [O III] Lambda 5007. There is also a correlation between the stellar mass and X-ray emission. The BAT AGN in mergers have bluer colors and greater ultra hard X-ray emission compared to the BAT sample as whole. In agreement with the Unified Model of AGN, and the relatively unbiased nature of the BAT sources, the host galaxy colors and morphologies are independent of measures of obscuration such as X-ray column density or Seyfert type. The high fraction of massive spiral galaxies and galaxy mergers in BAT AGN suggest that host galaxy morphology is related to the activation and fueling of local AGN.

Koss, Michael↗
DOE OSTI2025

Bayesian model mixing with multireference energy density functional

Reliably predicting nuclear properties across the entire chart of isotopes is important for applications ranging from nuclear astrophysics to superheavy science to nuclear technology. To this day, however, all the theoretical models that can scale at the level of the chart of isotopes remain semiphenomenological. Because they are fitted locally, their predictive power can vary significantly; different versions of the same theory provide different predictions. Bayesian model mixing takes advantage of such imperfect models to build a local mixture of a set of models to make improved predictions. Earlier attempts to use Bayesian model mixing for mass table calculations relied on models treated at single-reference energy density functional level, which fail to capture some of the correlations caused by configuration mixing or the restoration of broken symmetries. In this study we have applied Bayesian model mixing techniques within a multireference energy density functional (MR-EDF) framework. We considered predictions of two-particle separation energies from particle number projection or angular momentum projection with four different energy density functionals—a total of eight different MR-EDF models. We used a hierarchical Bayesian stacking framework with a Dirichlet prior distribution over weights together with an inverse log-ratio transform to enable positive correlations between different models. We found that Bayesian model mixing provides significantly improved predictions compared to the participating models. Published by the American Physical Society 2025

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1990

Molecular clouds associated with luminous far-infrared sources in the outer Galaxy

The stellar content and physical properties of the molecular clouds associated with 21 bright far-IR sources in the outer Galaxy have been determined through C-12O, C-13O, 6-cm radio continuum, and IRAS observations. The molecular cloud masses range from 200 to about 10,000 solar masses. The far-IR luminosity-to-mass ratio for these clouds has a mean value of 6.8 solar luminosity/solar masses and shows no correlation with the cloud mass, a result similar to that found for more massive clouds in the inner Galaxy. The radio continuum survey of the 21 bright far-IR sources indicates that most of these regions probably have a single, massive star providing most of the ionization. The cloud masses derived from virial and LTE analyses are in agreement, supporting the assumptions commonly made in their calculations, and a tight, near-linear correlation is found between the C-12O luminosity and the cloud mass. The H2 column density and integrated C-12O intensity are also correlated on a point-by-point basis, although the scatter is larger than the C-12O luminosity-cloud mass relation.

Carpenter, John M.↗
NASA NTRS2013

Modeling the Redshift Evolution of the Normal Galaxy X-Ray Luminosity Function

Emission from X-ray binaries (XRBs) is a major component of the total X-ray luminosity of normal galaxies, so X-ray studies of high-redshift galaxies allow us to probe the formation and evolution of XRBs on very long timescales (approximately 10 Gyr). In this paper, we present results from large-scale population synthesis models of binary populations in galaxies from z = 0 to approximately 20. We use as input into our modeling the Millennium II Cosmological Simulation and the updated semi-analytic galaxy catalog by Guo et al. to self-consistently account for the star formation history (SFH) and metallicity evolution of each galaxy. We run a grid of 192 models, varying all the parameters known from previous studies to affect the evolution of XRBs. We use our models and observationally derived prescriptions for hot gas emission to create theoretical galaxy X-ray luminosity functions (XLFs) for several redshift bins. Models with low common envelope efficiencies, a 50% twins mass ratio distribution, a steeper initial mass function exponent, and high stellar wind mass-loss rates best match observational results from Tzanavaris & Georgantopoulos, though they significantly underproduce bright early-type and very bright (L(sub x) greater than 10(exp 41)) late-type galaxies. These discrepancies are likely caused by uncertainties in hot gas emission and SFHs, active galactic nucleus contamination, and a lack of dynamically formed low-mass XRBs. In our highest likelihood models, we find that hot gas emission dominates the emission for most bright galaxies. We also find that the evolution of the normal galaxy X-ray luminosity density out to z = 4 is driven largely by XRBs in galaxies with X-ray luminosities between 10(exp 40) and 10(exp 41) erg s(exp −1).

Tremmel, M.↗
DOE OSTI2025

The Three Hundred Project: Modeling baryon and hot-gas fraction evolution in simulated clusters

The baryon fraction of galaxy clusters, expressed as the ratio between the mass in baryons (including both stars and cold or hot gas) and the total mass, is a powerful tool to provide information on the cosmological parameters, while the hot-gas fraction provides indications on the physics of the intracluster plasma and its interplay with the processes that drive galaxy formation. Using cosmological hydrodynamical simulations of about 300 simulated massive galaxy clusters with a median mass M 500 ≈ 7 × 10 14 M ⊙ at z = 0, we model the relations between total mass and either baryon fraction or the hot gas fractions at overdensities Δ = 2500, 500, and 200 with respect to the cosmic critical density, and their evolution from z ∼ 0 to z ∼ 1.3. We utilized the simulated galaxy clusters from the Three Hundred project, which include star formation and feedback from both supernovae and active galactic nuclei. We fit the simulation results for such scaling relations against three analytic forms (linear, quadratic, and logarithmic in a logarithmic plane) and three forms for the redshift dependence, and we considered as a variable both the inverse of the cosmic scale factor, (1 + z), and the Hubble expansion rate, E(z). We show that power-law dependencies on cluster mass poorly describe the investigated relations. A power law fails to simultaneously capture the flattening of the total baryon and gas fractions at high masses, their drop at low masses, and the transition between these two regimes. The other two functional forms provide a more accurate description of the curvature in mass scaling. The fractions measured within smaller radii exhibit a stronger evolution than those measured within larger radii. From the analysis of these simulations, we evince that as long as we include systems in the mass range herein investigated, the baryon or gas fraction can be accurately related to the total mass through either a parabola or a logarithm in the logarithmic plane. The trends are common to all modern hydro simulations, although the amplitude of the drop at low masses might differ. Being able to observationally determine the gas fraction in groups will thus provide constraints on the baryonic physics.

galaxy clusters↗
DOE OSTI2021

Simultaneous velocity and density measurements of fully developed Rayleigh-Taylor mixing

Here, the dynamics of molecular mixing and the energy transfer process in the Rayleigh-Taylor instability (RTI) are studied through the collection of simultaneous density-velocity measurements. These experiments provide simultaneous density-velocity field measurements, in contrast to previous point measurements. Statistically stationary experiments are performed in a “convective-type” gas tunnel facility, with density contrast achieved through the injection of helium into the bottom stream. Three experiments at Atwood number ≈ 0.1 are captured at three outer scale Reynolds numbers Re = 520, 2260, and 4050. Particle image velocimetry and laser induced fluorescence are employed simultaneously. Statistics of the density and velocity show self-similar collapse of RTI profiles at large Reynolds number Re >2000. Flat velocity profiles indicate homogeneous turbulence characteristics in the core of the mixing region. Significant anisotropy develops in the flow, with horizontal velocity fluctuations being only 60% of the vertical velocity fluctuations. The turbulent mass flux is found to be asymmetric about the centerline, with increased peak towards the spike. Measurements of the molecular mixing show that mixing is maximized at the core of the flow and increases with increased Reynolds number. The transport equation of density-specific-volume correlation b shows that it is mostly produced in the core of the mixing region, and that the spatial evolution of its profile is the result of transport by bulk motion of the bubble and spike. Energy transfer from gravitational potential energy to turbulent kinetic energy and viscous dissipation is observed to occur in the experiment with a ratio of dissipated energy to potential energy released of 38%. The analysis of the turbulent kinetic energy transport equation budget reveals that production is the primary mechanism towards the growth of turbulent kinetic energy in the core of the flow, and is asymmetrically slightly skewed towards the spike. However, it is through the transport that the strong advection at the edges of the mixing region is maintained.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗