Outer Core Region Research Articles

Validation of MCNPX Calculational Model for Kartini Reactor Outer Core Neutron Flux

Abstract Kartini reactor in Yogyakarta is a nuclear reactor with a low thermal power of 100 kW that is mainly used for education, training, and research. For that purpose, measuring neutron flux and controlling the power are important operational parameters. The Fission Chamber (FC) type of detector is the main component in the reactor operation and safety system that measures the neutron flux in the outer reactor core. As the FC detector is placed in a fixed location, a numerical calculation model is needed to know the neutron flux in all outer core regions. In this study, the MCNPX code is used. The first step is to validate the model with experimental measurement. The objective of the present study is to obtain a validated model by comparing calculations using MCNPX with measurements using gold foil activation (Neutron Activation Analysis technique). The computational model tested showed promising results with an average difference compared to the gold foil activation method of about 23%. Further research can be done using more gold foil samples or foils from other materials to see the consistency of measurements or minimize the measurement difference.

Calculation of toroidal Alfvén eigenmode mode structure in general axisymmetric toroidal geometry

A workflow is developed based on the ideal MHD model to investigate the linear physics of various Alfvén eigenmodes in general axisymmetric toroidal geometry by solving the coupled shear Alfvén wave (SAW) and ion sound wave (ISW) equations in ballooning space. The model equations are solved by the FALCON code in the singular layer, and the corresponding solutions are then taken as the boundary conditions for calculating parallel mode structures in the whole ballooning space. As an application of the code, the frequencies and mode structures of toroidal Alfvén eigenmode (TAE) are calculated in the reference equilibria of the Divertor Tokamak Test facility with positive and negative triangularities, respectively. As typical result for reactor relevant plasma conditions, which are strongly triangular in the outer core region where magnetic shear is of order unity, we show that the triangularity effect on TAE is generally small. Furthermore, by properly handling the boundary conditions, we demonstrate finite TAE damping due to coupling with the local acoustic continuum and find that the damping rate is small for typical plasma parameters.

Gyrokinetic simulations of electrostatic microturbulence in ADITYA-U tokamak with argon impurity

The effect of impurity on the electrostatic microturbulence in ADITYA-U tokamak is assessed using global gyrokinetic simulations. The realistic geometry and experimental profiles of the ADITYA-U are used, before and after argon gas seeding, to perform the simulations. Before the impurity seeding, the simulations show the existence of the trapped electron mode (TEM) instability in three distinct regions on the radial-poloidal plane. The mode is identified by its linear eigenmode structure and its characteristic propagation in the electron diamagnetic direction. The simulations with Ar1+ impurity ions in the outer-core region show a significant reduction in the turbulence and transport due to a reduction in the linear instability drive, with respect to the case without impurity. A decrease in particle and heat transport in the outer-core region modifies the plasma density profile measured after the impurity seeding. It, thus, results in the stabilization of the TEM instability in the core region. Due to the reduced turbulence activity, the electron and ion temperatures in the central region increase by about 10%.

Assessing core ion thermal confinement in critical-gradient-optimized stellarators

We investigate the core confinement properties of two recently devised quasi-helically symmetric stellarator configurations, HSK and QSTK. Both have been optimized for large critical gradients of the ion temperature gradient mode, which is an important driver of turbulent transport in magnetic confinement fusion devices. To predict the resulting core plasma profiles, assuming a fixed edge temperature, we utilize an advanced theoretical framework based on the gyrokinetic codes GENE and GENE-3D, coupled to the transport code TANGO. Compared to the HSX stellarator, both HSK and QSTK achieve significantly higher core-to-edge temperature ratios, partly thanks to their smaller aspect ratios, with the other part due to more detailed shaping of the magnetic geometry achieved during optimization. The computed core confinement time, however, is less sensitive to core temperature than the fixed edge temperature, simply due to the disproportionate influence, the edge has on stored plasma energy. We, therefore, emphasize the possible benefits of further optimizing turbulence in the outer core region, and the need to include accurate modeling of confinement in the edge region in order to assess overall plasma performance of turbulence optimized stellarators.

Identification of further variation at the lipooligosaccharide outer core locus in Acinetobacter baumannii genomes and extension of the OCL reference sequence database for Kaptive.

The outer core locus (OCL) that includes genes for the synthesis of the variable outer core region of the lipooligosaccharide (LOS) is one of the key epidemiological markers used for tracing the spread of Acinetobacter baumannii, a bacterial pathogen of global concern. In this study, we screened 12 476 publicly available A. baumannii genome assemblies for novel OCL sequences, detecting six new OCL types that were designated OCL17-OCL22. These were compiled with previously characterized OCL sequences to create an updated version of the A. baumannii OCL reference database, providing a total of 22 OCL reference sequences for use with the bioinformatics tool Kaptive. Use of this database against the 12 476 downloaded assemblies found OCL1 to be the most common locus, present in 73.6 % of sequenced genomes assigned by Kaptive with a match confidence score of good or above. OCL1 was most common amongst isolates belonging to sequence types (STs) ST1, ST2, ST3 and ST78, all of which are over-represented clonal lineages. The highest level of diversity in OCL types was found in ST2, with eight different OCLs identified. The updated OCL reference database is available for download from GitHub (https://github.com/klebgenomics/Kaptive; under version v. 2.0.5), and has been integrated for use on Kaptive-Web (https://kaptive-web.erc.monash.edu/) and PathogenWatch (https://pathogen.watch/), enhancing current methods for A. baumannii strain identification, classification and surveillance.

Extension of Global Gyrokinetic Code for Tokamak Edge Turbulence Simulation

A field-aligned coordinate system using a shifted metric technique has been implemented to a global gyrokinetic code GKNET. This coordinate system allows for simulations with lower resolution in the direction along the magnetic field line, which is especially effective in the outer core regions with higher q values. Realistic tokamak geometries, including up-down asymmetric equilibria, have also been implemented by using a newly developed interface code that connects GKNET and a free-boundary 2D Grad-Shafranov equation solver. This is essential for tokamak edge simulations, which will be developed in the future. As an application, the nonlinear simulation of the ion temperature gradient (ITG) mode with the JT-60SA ITER-like plasma [M. Nakata et al., Plasma Fusion Res. 9, 1403029 (2014)] has been performed. The result shows that the linear ITG instability with high poloidal modes and resultant zonal flow generation are properly traced. In this case, it is estimated that the number of computational grids can be reduced to 1/94 compared to that of the flux surface coordinate system.

MGGC2.0: A preprocessing code for the multi-group cross section of the fast reactor with ultrafine group library

How to generate the precise broad group cross section is important for the fast reactor design. In this study, a fast reactor multi-group cross-section generation code MGGC2.0 are developed in-house for processing ultrafine group MATXS format library. Validation and verification are performed for MGGC2.0 code by applying the benchmarks of ICSBEP handbook, and the results of MGGC2.0 agree well with that of MCNP. The consistent PN method with critical buckling search is in good agreement that condensed with TWODANT flux and flux moment for the inner core and outer core region. For the radial blanket and reflector, two region approximation method has been applied in MGGC2.0 by using collision Probability Method neutron flux solver. The RBEC-M benchmark was used to verify the power distribution calculation, and the relative error of power distribution comparison with the reference are less than 0.8% in the fuel region and the maximum relative error is 5.58% in the reflector region. Therefore, the precise broad cross section can be generated by MGGC2.0 for fast reactor.

Implementation and validation of swept density reflectometry for integrated data analysis at ASDEX Upgrade

In the tokamak ASDEX Upgrade, Integrated Data Analysis (IDA) is used to infer plasma quantities, such as electron density, using heterogeneous data sources. Essential is forward modeling from the parameter space into the data space with physically reasonable models for probabilistic evaluation. This paper presents a new forward model for O-mode profile reflectometry, a necessary prerequisite for Bayesian inference and inclusion in IDA. An efficient forward model based on the analytic solution for a piece-wise linear density description allows IDA to overcome problems associated with the established determination of cut-off locations via Abel inversion and Bottollier-Curtet’s method. Instead of using a hard-coded initialization for densities below the first measured cut-off density, other diagnostics, such as the lithium beam, are used to analyze the shape of the initial part of the profile. Error propagation from the measured data, and other uncertain sources, to the uncertainties in the density profile and also its gradient is an intrinsic property of the probabilistic approach, which benefits from the joint analysis. Missing or ambiguous data do not prevent the profile evaluation, but only increase the uncertainty for densities in the affected range. Density profiles together with their uncertainties are determined by the joint analysis of complementary diagnostics, with the newly added reflectometry closing a gap in the outer core region. A stand-alone inversion based on the new forward model, including uncertainty quantification, is introduced, optionally providing an n(R) profile with uncertainties and a gradient. This method is a candidate for real-time analysis, providing error bars.

Response of Extratropical Transitioning Tropical Cyclone Size to Ocean Warming: A Case Study for Typhoon Songda in 2016

This study attempts to investigate how future sea surface temperature increases will affect the size (radius of gale-force [17 m s−1] wind at 10 m height; i.e., R17) evolution of tropical cyclones that undergo extratropical transition (ET) through sensitivity experiments of sea surface temperature (SST) for Typhoon Songda (2016) in the northwestern Pacific. Two numerical experiments were carried out, including a control simulation (control) and a sensitivity experiment (SST4.5) with SST increased by 4.5 degrees in the entire domain. The results showed that Songda tended to be stronger and larger with projected higher SSTs. Moreover, the momentum equation for tangential wind was utilized to study the mechanism of R17 evolution in different SST scenarios, in which the radial absolute vorticity flux term played a dominant role in generating a positive tendency of tangential wind. The results indicate that before ET, higher SSTs in the entire domain led to more active rainbands in both inner-core and outer-core regions. As a result, stronger secondary circulation and low-level inflow extended outward, and the absolute angular momentum (AAM) importing from the outer region increased, which led to a larger R17 in SST4.5. During the ET, the peripheral baroclinically driven frontal convection induced extensive boundary layer inflow, which accelerated the tangential flow in the outer frontal region through strong inward AAM transport. However, due to the lower latitude of the cyclone and the strong frontolysis at the outer side of the cold pool in SST4.5, the peripheral frontal convection reached the location of R17 later; thus, the increase in the cyclone size lagged behind that in the control.

SOLPS-ITER modeling of Ar and N seeded discharges in ASDEX upgrade and ITER

In this paper SOLPS-ITER simulations of Ar and N seeded discharges are presented for H-mode conditions on ASDEX Upgrade and for burning plasmas on ITER. These discharges are additionally compared with Ne seeded cases for both tokamaks. It is demonstrated that Ar and N are retained in the divertor, and that the amount of seeded impurity (measured both by the seeding rate in atoms/s and the averaged separatrix density) necessary to achieve the same divertor conditions is lower for Ar than for N. This is attributed to almost the same values of first ionization potential of Ar and N (if compared to e.g. Ne) and to higher Ar radiation efficiency. If the radiated power fraction within the numerical simulation grid is of the order of 50%, which is sufficient to achieve partial detachment at the outer target in both devices, radiation losses from the confined region remain small for Ar seeded ITER cases (about 6% of power from the outer core region included in the SOLPS-ITER computational domain with total volume 135 m3). The fuel dilution by Ar remains lower than that by N and Ne, which corresponds to an Ar averaged separatrix concentration of 0.4%. From the point of view of target power handling, the boundary simulations thus demonstrate that Ar may be a suitable alternative seed impurity on ITER.

The Mean Kinematic Structure of the Tropical Cyclone Boundary Layer and Its Relationship to Intensity Change

Abstract This study investigates the relationship between the azimuthally averaged kinematic structure of the tropical cyclone boundary layer (TCBL) and storm intensity, intensity change, and vortex structure above the BL. These relationships are explored using composites of airborne Doppler radar vertical profiles, which have a higher vertical resolution than typically used three-dimensional analyses and, therefore, better capture TCBL structure. Results show that the BL height, defined by the depth of the inflow layer, is greater in weak storms than in strong storms. The inflow layer outside the radius of maximum tangential wind speed (RMW) is deeper in intensifying storms than in nonintensifying storms at an early stage. The peak BL convergence inside the RMW is larger in intensifying storms than in nonintensifying storms. Updrafts originating from the TCBL are concentrated near the RMW for intensifying TCs, while updrafts span a large radial range outside the RMW for nonintensifying TCs. In terms of vortex structure above the BL, storms with a quickly decaying radial profile of tangential wind outside the RMW (“narrow” vortices) tend to have a deeper inflow layer outside the RMW, stronger inflow near the RMW, deeper and more concentrated strong updrafts close to the RMW, and weaker inflow in the outer core region than those with a slowly decaying tangential wind profile (“broad” vortices). The narrow TCs also tend to intensify faster than broad TCs, suggesting that a key relationship exists among vortex shape, the BL kinematic structure, and TC intensity change. This relationship is further explored by comparisons of absolute angular momentum budget terms for each vortex shape.

ITB formation in gyrokinetic flux-driven ITG/TEM turbulence

The formation mechanism of internal transport barriers (ITBs) in flux-driven turbulence is studied by means of the full-f gyrokinetic code GKNET. In the adiabatic electron case with a weak magnetic shear configuration, toroidal momentum injection can change the radial mean electric field through radial force balance, leading to a kind of driven ITB formation in which the ion thermal diffusivity by ion temperature gradient (ITG) turbulence decreases to the neoclassical transport level. Only cocurrent toroidal rotation in the outer core region can benefit the ITB formation, and this mechanism is identified to originate from a positive feedback loop between the radial shear and resultant momentum flux. On the other hand, in the kinetic electron case with a reversed magnetic shear configuration, robust co-intrinsic rotation is driven near the surface in ITG turbulence and sustains the shear through the radial force balance, leading to the spontaneous reduction of ion turbulent thermal diffusivity, while this is not observed in the adiabatic electron case. In the presence of electron heating, counter-intrinsic rotation by trapped electron mode turbulence is selectively driven in the negative magnetic shear region, which provides steeper shear formation and a resultant larger reduction of ion turbulent thermal diffusivity. This indicates that the co-existence of different modes can trigger the ‘discontinuity’ of mode structure, intrinsic rotation, and resultant mean near , leading to spontaneous ITB formation.

Chemoenzymatic synthesis of an α-1,6-glucan-based conjugate vaccine against Helicobacter pylori.

In this study, we investigated the utility of glycoconjugates based on a linear α-1,6-glucan chain synthesized using a recombinant α-1,6-glucosyltransferase from the 26695 strain of Helicobacter pylori. Capillary electrophoresis-mass spectrometry analysis confirmed the main product to contain 9-10 sequentially added α-1,6-linked glucose residues. This was consistent with a length of α-1,6-glucan structure present in the outer core region of H. pylori lipopolysaccharide (LPS) from strains 26695 and 26695 HP0826::Kan. The synthetic α-1,6-glucan was conjugated to either bovine serum albumin or tetanus toxoid and immunological properties of resultant glycoconjugates investigated. The conjugates were immunogenic in rabbits and mice and induced strong and specific IgG responses against purified LPS from typeable and nontypeable α-1,6-glucan-positive H. pylori strains. Furthermore, the post-immune sera from rabbits that received the conjugates were bactericidal and cross-reacted with selected clarithromycin-resistant and clarithromycin-susceptible clinical isolates of H. pylori. This technology offers a novel approach to the design of a synthetic carbohydrate-based vaccine against H. pylori.

Thermal Entrainment in the Core Regions of Transitional Plane Fountains in Linearly Stratified Ambient Fluids

Thermal entrainment is an integral feature of free-shear flows involving temperature changes, including fountains (negatively buoyant jets). The understanding of thermal entrainment is essential for applications involving thermal stratification such as that in a solar water storage tank. In this study, thermal entrainment in the core regions of transitional plane fountains in linearly-stratified ambient fluids is studied numerically over a range of the Froude number, Reynolds number, and dimensionless thermal stratification parameter. The results show that thermal entrainment has a negligible effect on the inner core region, but is significant in the outer core region, particularly at the interfaces among the upflow, downflow, and ambient fluid, and the thermal entrainment parameter, which quantifies the extent of thermal entrainment, decreases with height or in a stronger stratification, but increases with increasing Froude number or Reynolds number. Several numerical relations are obtained with the numerical results for the thermal entrainment parameter.

The Asymmetric Precipitation Evolution in Weak Landfalling Tropical Cyclone Rumbia (2018) Over East China

The rainfall in landfalling TC is not always correlated with the storm intensity. Some weak landfalling TCs could bring extremely heavy rainfall during and after landfall. Such extreme events are very challenging to operational forecasts and often lead to disasters in the affected regions. Tropical storm Rumbia (2018) made its landfall in Shanghai with weak intensity but led to long-lasting and increasing rainfall to East China. The asymmetric rainfall evolution of Rumbia during and after its landfall was diagnosed based on the fifth generation European Centre for Medium-Range Weather Forecasting (ECMWF) reanalysis (ERA5) data, the tropical cyclone (TC) best-track data, and rainfall observations from China Meteorological Administration (CMA). Results showed that Rumbia was embedded in an environment with a deep-layer (300–850 hPa) southwesterly vertical wind shear (VWS). The maximum rainfall mostly occurred downshear-left in its inner-core region and downshear-right in the outer-core region. The translation of Rumbia also contributed to the rainfall distribution to some extent, especially prior to and just after its landfall. The strong southwesterly-southeasterly summer monsoon flow transported water vapor from the tropical ocean and the East China Sea to the TC core region, providing moisture and convective instability conditions in the mid-lower troposphere for the sustained rainfall even after Rumbia moved well inland. The results also showed that the low-level convective instability and the deep-layer environmental VWS played an important role in deepening the inflow boundary layer and the redevelopment of the secondary circulation, thus contributing to the heavy rainfall in the northeast quadrant of Rumbia after its landfall. However, further in-depth studies are recommended in regard of the rainfall evolution in the weak TCs. This study further calls for a continuous understanding of the involved physical processes/mechanisms that are responsible for the extreme rainfall induced by landfalling TCs, which can help improve the rainfall forecast skills and support damage mitigation in the future.

A direct aircraft observation of helical rolls in the tropical cyclone boundary layer

Helical rolls are known to play a significant role in modulating both the mean and turbulence structure of the atmospheric boundary layer in tropical cyclones. However, in-situ measurements of these rolls have been limited due to safety restrictions. This study presents analyses of data collected by an aircraft operated by the Hong Kong Observatory in Typhoon Kalmaegi (1415) and Typhoon Nida (1604). Examination of the flight-level data at ~ 600 m altitude confirmed the existence of sub-kilometer-scale rolls. These rolls were mostly observed in the outer-core region. Turbulent momentum fluxes were computed using the eddy correlation method. The averaged momentum flux of flight legs with rolls was found to be ~ 2.5 times that of legs without rolls at a similar wind speed range. This result suggests that rolls could significantly modulate turbulent transfer in the tropical cyclone boundary layer. This roll effect on turbulent fluxes should be considered in the planetary boundary layer parameterization schemes of numerical models simulating and forecasting tropical cyclones.

The Role of Surface Heat Fluxes on the Size of Typhoon Megi (2016)

AbstractThis study attempts to understand how surface heat fluxes in different storm regions affect tropical cyclone (TC) size. The Advanced Research version of the Weather Research and Forecasting (ARW-WRF) Model (version 3.5.1) is used to simulate Typhoon Megi (2016). A series of numerical experiments are carried out, including a control simulation and several sensitivity experiments with surface heat fluxes suppressed in different TC regions [to mimic the reduction of the wind-induced surface heat exchange (WISHE) feedback in the inner and/or outer core]. The results show that with surface heat fluxes suppressed in the entire domain, the TC tends to be smaller. Meanwhile, the TC size is more sensitive to the surface heat flux change in the outer core than to that in the inner core. Suppressing surface heat fluxes can weaken the rainbands around the suppressed area, which in turn slows down the secondary circulation. When the surface heat flux is suppressed in the inner-core region, the weakening of the secondary circulation associated with the diminished inner rainbands is limited to the inner-core region, and only slightly affects the absolute angular momentum import from the outer region, thus having negligible impact on TC size. However, suppression of surface heat fluxes in the outer-core region leads to less active outer rainbands and a more substantial weakening of secondary circulation. This results in less absolute momentum import from the outer region and in turn a smaller TC.

Integrated modeling of CFETR hybrid scenario plasmas

Demonstration of DEMO relevant fusion power (P fus) level and tritium self-sufficiency are two important goals of the China fusion engineering testing reactor (CFETR). In this work the integrated modeling including self-consistent core–pedestal coupling are used to design the hybrid scenario plasmas at flat-top phase for these goals. Such plasmas have been taken as the reference plasma for studying the compatibility of the hybrid scenario with CFETR engineering design in the past two years. The physics justification for the selection of plasma density, Z eff, safety factor profile, and in particular the choice of auxiliary heating and current drive is presented. According to a scan of plasma density and Z eff, the target of P fus ≈ 1 GW and finite ohmic flux consumption ∆Φohm (4 h) ⩽ 250 Vs can be met with Z eff = 1.9–2.2 and the density at the pedestal top set at 90% of the Greenwald limit. Turbulent transport analysis using the gyro-Landau-fluid model TGLF shows that the electromagnetic effects can enhance the energy confinement but reduce the particle confinement and thus P fus. A baseline hybrid scenario case matching the target in the concept design is built using a combination of neutral beams (NB) and electron cyclotron (EC) waves to flatten the safety factor profile in the deep core region (with the normalized plasma radius ρ ⩽ 0.4). Such profile can yield better particle and energy confinement than that with either higher magnetic shear in the deep core region or higher q value in outer core region (e.g., due to the addition of lower hybrid current drive). Switching a part of auxiliary heating from electron to ions, e.g., replacing a part of EC waves by waves in the ion cyclotron range of frequencies, reduces the particle confinement and thus P fus. Since high harmonic fast waves (HHFW) can drive current at the same location as ECCD with higher current drive efficiency than ECCD and yield more electron heating than NB, the case using HHFW to replace a part of EC waves and NB can yield higher P fus and lower ∆Φohm than the baseline case. A discussion is given on future simulations to explore the improvement in plasma performance and the broadening of the feasible design space.

Bayesian analysis of turbulent transport coefficients in 2D interchange dominated ExB turbulence involving flow shear

While turbulent transport is known to dominate the radial particle and energy transport in the plasma edge, a self-consistent description of turbulent transport in mean-field transport codes remains lacking. Mean-field closure models based on the turbulent kinetic energy (k ⊥) and turbulent enstrophy (ζ⊥) have recently been proposed to self-consistently model this transport. This contribution analyses the diffusive particle transport relations of these models by means of the Bayesian framework for parameter estimation and model comparison. The reference data includes a set of isothermal simulations that not only include the scrape-off layer (SOL) but also the outer core region (in which a drift wave-like model is activated) and a set of anisothermal SOL simulations, both obtained with the TOKAM2D turbulence code. This analysis shows that the k ⊥(–ζ⊥) model does not appropriately capture the diffusion coefficients for these new data sets, presumably due to the strong flows in the diamagnetic direction that appear in these new cases. While flow shear is expected to quench the turbulence and the turbulent transport, its effect was not explicitly taken into account in the earlier k ⊥(–ζ⊥) transport models. As flow shear provides a new mechanism for the decorrelation of the turbulence, we propose to introduce an additional time scale in the diffusive transport relation as . Inspiration is drawn from shear decorrelation times reported in literature to propose several new candidate models, which are then analysed in a Bayesian setting. This allowed identifying irrelevant terms for certain models and to rank all models according to the Bayesian evidence. While the new models accounting for shear do improve the match to the data, significant errors still remain. Also, no single model could be identified that performs best for all data sets.

Swirling turbulent pipe flows: Inertial region and velocity–vorticity correlations

Swirling pipe flows are studied here with an aim towards understanding the onset of the inertial region — where the turbulent-inertia term in the mean momentum equation is balanced by pressure gradient and viscous term is sub-dominant — as well as the clarifying the velocity–vorticity correlations that make up the turbulent inertia. To this end, we first manipulate the mean momentum equation in both axial and azimuthal directions and find some exact results in the inertial region, and carry out direct numerical simulations of swirling pipe flows at axial friction Reynolds numbers of 170 and 500. The swirl number considered in our simulations is S≈0.3, and we compare our results to non-swirling pipe flows at similar Reynolds numbers. We find that swirling produces a drag increase and an influence on the turbulence statistics similar to increasing the Reynolds number except for the streamwise turbulence intensity. An analysis on the axial and azimuthal mean momentum equations shows that swirling shifts the beginning of the inertial region wall-normal location closer to the wall. The turbulent inertia decomposition reveals that the near-wall region the velocity–vorticity correlations of the axial direction are similar to a 2D channel flow and interpreted as vorticity stretching/reorientation and dispersion, whereas in the new correlations in the azimuthal direction can also be given a similar physical meaning in the near-wall region. In the outer-region, however, the pipe axial correlations are different to the 2D-channel, and so are the azimuthal correlations. We find that the pipe has new a ‘geometric’ contribution in both axial and azimuthal directions that play an important role in contributing towards vorticity dispersion in the outer core region of a swirling pipe flow.