Strong Downflows Research Articles

On the disruption of the horseshoe vortex in flow past bed-mounted cylinders

The present study investigates the disruption of the horseshoe vortex (HSV) formed around a bed-mounted circular cylinder using helical strakes. Three cylinders were studied: one plain and two with helical strakes, oriented at 30° and 0° to the vertical mid-plane, respectively. A planar particle image velocimetry technique was employed for the measurement of the velocity field near the upstream cylinder-bed junction. The results revealed that strakes oriented at 0° prevent the formation of the HSV by disrupting the downward flow near the cylinder-bed junction. In contrast, a strong downflow was observed near the bed for the plain and 30° straked cylinder. The 0° helical strakes can be potentially used as scour-countermeasure around the pier due to their ability to disrupt the HSV. Analysis of turbulent stresses further demonstrated that the 0° straked cylinder experienced a reduction in Reynolds shear stress compared to both the plain and 30° straked cylinder.

Intensification of magnetic field in merging magnetic flux tubes driven by supergranular vortical flows

ABSTRACT The spatiotemporal dynamics of vorticity and magnetic field in the region of a photospheric vortex at a supergranular junction of the quiet Sun is studied, using Hinode’s continuum intensity images and longitudinal magnetograms. We show that in a 30-min interval during the vortex lifetime, the magnetic field is intensified at the centres of two merging magnetic flux tubes trapped inside the vortex boundary. Moreover, we show that the electric current density is intensified at the interface boundary layers of merging tubes, resulting from strong vortical downflows in a supergranular vertex. Evidence of Lagrangian chaos and vortex stretching in the photospheric plasma turbulence responsible for driving the intensification of magnetic fields is analysed. In particular, we report the first solar observation of the intensification of electromagnetic energy flux resulting from the merger of magnetic flux tubes.

Length Scale of Photospheric Granules in Solar Active Regions

Investigating the length scales of granules could help understand the dynamics of granules in the photosphere. In this work, we detected and identified granules in an active region near disk center observed at wavelength of TiO (7057 Å) by the 1.6 m Goode Solar Telescope (GST). By a detailed analysis of the size distribution and flatness of granules, we found a critical size that divides the granules in motions into two regimes: convection and turbulence. The length scales of granules with sizes larger than 600 km follow Gauss function and demonstrate “flat” in flatness, which reveal that these granules are dominated by convection. Those with sizes smaller than 600 km follow power-law function and behave power-law tendency in flatness, which indicate that the small granules are dominated by turbulence. Hence, for the granules in active regions, they are originally convective in large length scale, and directly become turbulent once their sizes turn to small, likely below the critical size of 600 km. Comparing with the granules in quiet regions, they evolve with the absence of the mixing motions of convection and turbulence. Such a difference is probably caused by the interaction between fluid motions and strong magnetic fields in active regions. The strong magnetic fields make high magnetic pressure which creates pressure walls and slows down the evolution of convective granules. Such walls cause convective granules extending to smaller sizes on one hand, and cause wide intergranular lanes on the other hand. The small granules isolated in such wide intergranular lanes are continually sheared, rotated by strong downflows in surroundings and hereby become turbulent.

Quantifying Properties of Photospheric Magnetic Cancellations in the Quiet Sun Internetwork

We analyzed spectropolarimetric data from the Swedish 1 m Solar Telescope to investigate the physical properties of small-scale magnetic cancellations in the quiet Sun photosphere. Specifically, we looked at the full Stokes polarization profiles along the Fe i 557.6 nm and of the Fe i 630.1 nm lines measured by the CRisp Imaging SpectroPolarimeter to study the temporal evolution of the line-of-sight magnetic field during 42.5 minutes of quiet Sun evolution. From this magnetogram sequence, we visually identified 38 cancellation events. We then used the Yet Another Feature Tracking Algorithm to characterize the physical properties of these magnetic cancellations. We found on average 1.6 × 1016 Mx of magnetic flux canceled in each event with an average cancellation rate of 3.8 × 1014 Mx s−1. The derived canceled flux is associated with strong downflows, with an average speed of V LOS ≈ 1.1 km s−1. Our results show that the average lifetime of each event is 9.2 minutes with an average of 44.8% of initial magnetic flux being canceled. Our estimates of magnetic fluxes provide a lower limit since studied magnetic cancellation events have magnetic field values that are very close to the instrument noise level. We observed no horizontal magnetic fields at the cancellation sites and therefore cannot conclude whether the events are associated with structures that could cause magnetic reconnection.

Magnetic activities on two single-lined RS Canum Venaticorum binaries IM Pegasi and σ Geminorum

ABSTRACT We present the study on continuous high-resolution spectroscopic observations of two long-period single-lined RS Canum Venaticorum (RS CVn) binary stars IM Pegasi (IM Peg) and σ Geminorum (σ Gem), obtained with the Hertzsprung SONG telescope during the 2015–2016 season. Chromospheric activity indicators Hα, $\rm{Na\,\,{\small I}}$ D1, D2 doublet, $\rm{He\,\,{\small I}}$ D3, and Hβ lines have been analysed by using the spectral subtraction technique. The expected chromospheric emission features in the Hα, $\rm{Na\,\,{\small I}}$ D1, D2 doublet, and Hβ lines confirm that both of two stars are very active systems. In the spectra, the $\rm{He\,\,{\small I}}$ D3 line had been always detected in absorption feature. Although the behaviour of chromospheric activity indicators is very similar for both stars, the activity level of IM Peg is much stronger than that of σ Gem. Moreover, the equivalent width variations of the Hα, $\rm{He\,\,{\small I}}$ D3, and Hβ line subtractions correlate well and show different behaviour among different orbital cycles, which indicates the presence and evolution of activity longitudes over the surface of two stars. Furthermore, the subtracted Hα line profile is usually asymmetric. The red-shifted excess absorption features could be interpreted as a strong down-flow of cool absorbing material, while the blue-shifted emission component is probably caused by up-flow of hot materials through microflare events.

Effects of the gap on the local scour around two tandem piles in shallow flows

Local scour around two tandem piles in shallow water is numerically investigated under clear-water conditions. The characteristics of the scour process, depth, and flow fields are shown to be significantly influenced by the pile gap ratio (G/D = 1.0–5.0) and water depth ratio (h/D = 0.5–3.0). Under the same G/D, the dimension of the scour hole and the maximum scour depth around two piles become larger with the increase of h/D. Under the shallowest water depth condition (h/D = 0.5), the scour dimension and maximum scour depth of the rear pile are larger than that of the front pile, due to the weak upflow and strong downflow upstream of the rear pile. However, under the deepest water depth condition (h/D = 3.0), the scour hole becomes smaller than that of the front pile, due to the significant upflow downstream the front pile by less confinement from the high water surface. The vortex shedding patterns and their interaction with the sediment transport in different G/D and h/D cases are also discussed.

CFD modeling for the prediction of molecular weight distribution in the LDPE autoclave reactor: Effects of non-ideal mixing

A commercial Low-density polyethylene (LDPE) reactor was modeled to investigate the effects of highly nonlinear hydrodynamics in an industrial-scale autoclave reactor on the polymer Molecular weight distribution (MWD). To reduce the extremely high computational burden of Computational fluid dynamics (CFD) runs and detailed MWD calculations, a combination of the CFD multicompartment model and probability generating function transformation is proposed. The validity of the proposed model was verified by a comparison with experimental data on industrial equipment. The computation time was shown to be only 37% of the actual operation time. The proposed model showed that strong downflow and weak reverse-flow coexisted to form circulation flow between the disks in the autoclave. Polymerization mainly occurred in the strong downflow region of the tubular regime. The circulation flow increased the accumulation of dead polymers to enhance the chain transfer to polymer, which produces long-branched living polymer chains and termination by recombination for a broad MWD with bimodality. Further analysis based on the simulation without the circulation flow showed a narrow MWD and no bimodality. These results indicate that the flow pattern must be properly controlled to produce polymers with desired properties in large-scale polymerization reactors.

Flow around a scoured bridge pier: a stereoscopic PIV analysis

We performed stereoscopic particle image velocimetry of the turbulent flow inside a scour hole around a cylinder in a sandy bed. At two planes, symmetry plane and 45^circ with respect to the approach flow, the flow and its turbulence structure were investigated. We used two Reynolds numbers (20, 000 and 39, 000) based on the cylinder diameter and the depth-averaged velocity in the symmetry plane. The flow is characterized by a strong down-flow in front of the cylinder, a large horseshoe vortex inside the scour, and an upstream directed wall jet underneath. The values of vorticity in the horseshoe vortex and of the velocity in the wall jet are larger than in a comparable configuration on a flat bed. Enhanced levels of turbulent kinetic energy are found around the horseshoe vortex and in the shear layer detaching from the rim. The orientation of the main axis of the velocity fluctuations changes when the flow enters the scour hole: from about wall-parallel in the detaching shear layer to vertical at the horseshoe vortex. The production of turbulent kinetic energy shows a maximum upstream of the horseshoe vortex centre with considerable production in the shear layer and in the wall jet underneath the horseshoe vortex. Furthermore, strong wall-parallel velocity fluctuations are visible in this region, and bimodal velocity distributions are found, but not anywhere else. The time-averaged wall-shear stresses are largest under the horseshoe vortex and most likely larger than in a corresponding flat-bed configuration.Graphic abstract

Large Eddy Simulation of Wind Flow over A Realistic Urban Area

A high-resolution large eddy simulation (LES) of wind flow over the Oklahoma City downtown area was performed to explain the effect of the building height on wind flow over the city. Wind flow over cities is vital for pedestrian and traffic comfort as well as urban heat effects. The average southerly wind speed of eight meters per second was used in the inflow section. It was found that heights and distribution of the buildings have the greatest impact on the wind flow patterns. The complexity of the flow field mainly depended on the location of buildings relative to each other and their heights. A strong up and downflows in the wake of tall buildings as well as large-scale coherent eddies between the low-rise buildings were observed. It was found out that high-rise buildings had the highest impact on the urban wind patterns. Other characteristics of urban canopy flows, such as wind shadows and channeling effects, are also successfully captured by the LES. The LES solver was shown to be a powerful tool for understanding urban canopy flows; therefore, it can be used in similar studies (e.g., other cities, dispersion studies, etc.) in the future.

High-resolution spectropolarimetric observations of the temporal evolution of magnetic fields in photospheric bright points

Context. Magnetic bright points (MBPs) are dynamic, small-scale magnetic elements often found with field strengths of the order of a kilogauss within intergranular lanes in the photosphere. Aims. Here we study the evolution of various physical properties inferred from inverting high-resolution full Stokes spectropolarimetry data obtained from ground-based observations of the quiet Sun at disc centre. Methods. Using automated feature-tracking algorithms, we studied 300 MBPs and analysed their temporal evolution as they evolved to kilogauss field strengths. These properties were inferred using both the NICOLE and SIR Stokes inversion codes. We employ similar techniques to study radiative magnetohydrodynamical simulations for comparison with our observations. Results. Evidence was found for fast (∼30−100 s) amplification of magnetic field strength (by a factor of 2 on average) in MBPs during their evolution in our observations. Similar evidence for the amplification of fields is seen in our simulated data. Conclusions. Several reasons for the amplifications were established, namely, strong downflows preceding the amplification (convective collapse), compression due to granular expansion and mergers with neighbouring MBPs. Similar amplification of the fields and interpretations were found in our simulations, as well as amplification due to vorticity. Such a fast amplification will have implications for a wide array of topics related to small-scale fields in the lower atmosphere, particularly with regard to propagating wave phenomena in MBPs.

Dynamics and connectivity of an extended arch filament system

Aims.In this study, we analyzed a filament system, which expanded between moving magnetic features (MMFs) of a decaying sunspot and opposite flux outside of the active region from the nearby quiet-Sun network. This configuration deviated from a classical arch filament system (AFS), which typically connects two pores in an emerging flux region. Thus, we called this system an extended AFS. We contrasted classical and extended AFSs with an emphasis on the complex magnetic structure of the latter. Furthermore, we examined the physical properties of the extended AFS and described its dynamics and connectivity.Methods.The extended AFS was observed with two instruments at the Dunn Solar Telescope (DST). The Rapid Oscillations in the Solar Atmosphere (ROSA) imager provided images in three different wavelength regions, which covered the dynamics of the extended AFS at different atmospheric heights. The Interferometric Bidimensional Spectropolarimeter (IBIS) provided spectroscopic Hαdata and spectropolarimetric data that was obtained in the near-infrared (NIR) Ca IIλ8542 Å line. We derived the corresponding line-of-sight (LOS) velocities and used He IIλ304 Å extreme ultraviolet (EUV) images of the Atmospheric Imaging Assembly (AIA) and LOS magnetograms of the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) as context data.Results.The NIR Ca IIStokes-Vmaps are not suitable to definitively define a clear polarity inversion line and to classify this chromospheric structure. Nevertheless, this unusual AFS connects the MMFs of a decaying sunspot with the network field. At the southern footpoint, we measured that the flux decreases over time. We find strong downflow velocities at the footpoints of the extended AFS, which increase in a time period of 30 min. The velocities are asymmetric at both footpoints with higher velocities at the southern footpoint. An EUV brigthening appears in one of the arch filaments, which migrates from the northern footpoint toward the southern one. This activation likely influences the increasing redshift at the southern footpoint.Conclusions.The extended AFS exhibits a similar morphology as classical AFSs, for example, threaded filaments of comparable length and width. Major differences concern the connection from MMFs around the sunspot with the flux of the neighboring quiet-Sun network, converging footpoint motions, and longer lifetimes of individual arch filaments of about one hour, while the extended AFS is still very dynamic.

Flow dynamics in the vicinity of a gravel embedded vertical retaining wall: conditions corresponding to the initial stages of local erosion

The present study examines the turbulent flow characteristics in the vicinity of the leading edge of a vertical retaining wall structure embedded in a gravel bed. Conditions before and during the initial stages of local scour development were considered. To that end, three laboratory experiments were carried out: one with fixed boundaries as a reference case, a second one with an erodible bed, but immobile channel bank, and a third one characterized by an erodible channel bed and bank. Instantaneous and time-averaged flow features, and turbulence statistics associated with the three-component velocity fields, obtained with a stereoscopic particle image velocimetry system, were analyzed. Water surface examination determined that channel bank erosion alters flow behavior upstream of the retaining wall. This change is manifested through more frequent formation of eddies near the top corner of the junction between the upstream face of the protrusion and the channel bank. Time-averaged and instantaneous velocity vector fields demonstrate the presence of two counter-rotating vortices in the experiments with the fixed channel bank, one located near the junction of retaining wall and the channel bed and one away from it generated as a result of a strong downflow. The latter motion represents a section of a horseshoe vortex. During the channel bank erosion, however, these vortices are not as significant and persistent. The results also indicate that the coherency and magnitude of the streamwise vorticity field diminish as a result of scour. However, it was confirmed that local turbulent kinetic energy and shear stresses increase in the presence of scour due to enhanced local flow separation.

Temporal evolution of arch filaments as seen in He I 10 830 Å

Aims. We study the evolution of an arch filament system (AFS) and of its individual arch filaments to learn about the processes occurring in them. Methods. We observed the AFS at the GREGOR solar telescope on Tenerife at high cadence with the very fast spectroscopic mode of the GREGOR Infrared Spectrograph (GRIS) in the He I 10 830 Å spectral range. The He I triplet profiles were fitted with analytic functions to infer line-of-sight (LOS) velocities to follow plasma motions within the AFS. Results. We tracked the temporal evolution of an individual arch filament over its entire lifetime, as seen in the He I 10 830 Å triplet. The arch filament expanded in height and extended in length from 13″ to 21″. The lifetime of this arch filament is about 30 min. About 11 min after the arch filament is seen in He I, the loop top starts to rise with an average Doppler velocity of 6 km s−1. Only two minutes later, plasma drains down with supersonic velocities towards the footpoints reaching a peak velocity of up to 40 km s−1 in the chromosphere. The temporal evolution of He I 10 830 Å profiles near the leading pore showed almost ubiquitous dual red components of the He I triplet, indicating strong downflows, along with material nearly at rest within the same resolution element during the whole observing time. Conclusions. We followed the arch filament as it carried plasma during its rise from the photosphere to the corona. The material then drained toward the photosphere, reaching supersonic velocities, along the legs of the arch filament. Our observational results support theoretical AFS models and aids in improving future models.

Inversions of synthetic umbral flashes: Effects of scanning time on the inferred atmospheres

Context. The use of instruments that record narrowband images at selected wavelengths is a common approach in solar observations. They allow scanning of a spectral line by sampling the Stokes profiles with two-dimensional images at each line position, but require a compromise between spectral resolution and temporal cadence. The interpretation and inversion of spectropolarimetric data generally neglect changes in the solar atmosphere during the scanning of line profiles. Aims. We evaluate the impact of the time-dependent acquisition of various wavelengths on the inversion of spectropolarimetric profiles from chromospheric lines during umbral flashes. Methods. Numerical simulations of nonlinear wave propagation in a sunspot model were performed with the code MANCHA. Synthetic Stokes parameters in the Ca II 8542 Å line in NLTE were computed for an umbral flash event using the code NICOLE. Artificial profiles with the same wavelength coverage and temporal cadence from reported observations were constructed and inverted. The inferred atmospheric stratifications were compared with the original simulated models. Results. The inferred atmospheres provide a reasonable characterization of the thermodynamic properties of the atmosphere during most of the phases of the umbral flash. The Stokes profiles present apparent wavelength shifts and other spurious deformations at the early stages of the flash, when the shock wave reaches the formation height of the Ca II 8542 Å line. These features are misinterpreted by the inversion code, which can return unrealistic atmospheric models from a good fit of the Stokes profiles. The misguided results include flashed atmospheres with strong downflows, even though the simulation exhibits upflows during the umbral flash, and large variations in the magnetic field strength. Conclusions. Our analyses validate the inversion of Stokes profiles acquired by sequentially scanning certain selected wavelengths of a line profile, even in the case of rapidly changing chromospheric events such as umbral flashes. However, the inversion results are unreliable during a short period at the development phase of the flash.

Statistical Investigation of Supersonic Downflows in the Transition Region above Sunspots

Abstract Downflows at supersonic speeds have been observed in the transition region (TR) above sunspots for more than three decades. These downflows are often seen in different TR spectral lines above sunspots. We have performed a statistical investigation of these downflows using a large sample that was missing previously. The Interface Region Imaging Spectrograph (IRIS) has provided a wealth of observational data of sunspots at high spatial and spectral resolutions in the past few years. We have identified 60 data sets obtained with IRIS raster scans. Using an automated code, we identified the locations of strong downflows within these sunspots. We found that around 80% of our sample shows supersonic downflows in the Si iv 1403 Å line. These downflows mostly appear in the penumbral regions, though some of them are found in the umbrae. We also found that almost half of these downflows show signatures in chromospheric lines. Furthermore, a detailed spectral analysis was performed by selecting a small spectral window containing the O iv 1400/1401 Å and Si iv 1403 Å lines. Six Gaussian functions were simultaneously fitted to these three spectral lines and their satellite lines associated with the supersonic downflows. We calculated the intensity, Doppler velocity, and line width for these lines. Using the O iv 1400/1401 Å line ratio, we find that the downflow components are around one order of magnitude less dense than the regular components. Results from our statistical analysis suggest that these downflows may originate from the corona and that they are independent of the background TR plasma.

Small-Scale Activity Above the Penumbra of a Fast-Rotating Sunspot

High-resolution observations of small-scale activity above the filamentary structure of a fast-rotating sunspot of NOAA Active Region 10930 are presented. The penumbral filament that intrudes into the umbra shows a central dark core and substructures. It almost approached another end of the umbra, like a light bridge. The chromospheric Ca ii H images show many jet-like structures with a bright leading edge above it. These bright jets move across the filament tips and show coordinated up and down motions. Transition region images also show brightening at the same location above the intrusion. Coronal 195 A images suggest that one end of the bright coronal loop footpoints resides in this structure. The intrusion has opposite polarity with respect to the umbra. Strong downflows are observed at the edges along the length of the intrusion where the opposite-polarity field is enhanced. We also observe a counter-Evershed flow in the filamentary structure that also displays brightening and energy dissipation in the upper atmosphere. This scenario suggests that the jets and brightenings are caused by low-altitude reconnection driven by opposite-polarity fields and convective downflows above such structures.

The structure and budget of turbulent kinetic energy in front of a wall-mounted cylinder

We investigate the flow and turbulence structure in front of a cylinder mounted on a flat plate by a combined study using highly resolved large-eddy simulation and particle image velocimetry. The Reynolds number based on the bulk velocity and cylinder diameter is $Re_{D}=39\,000$. As the cylinder is placed in an open channel, we take special care to simulate open-channel flow as the inflow condition, including secondary flows that match the inflow in the experiment. Due to the high numerical resolution, subgrid contributions to the Reynolds stresses are negligible and the modelled dissipation plays a minor role in major parts of the flow field. The accordance of the experimental and numerical results is good. The shear in the approach flow creates a vertical pressure gradient, inducing a downflow in the cylinder front. This downflow, when deflected in the upstream direction at the bottom plate, gives rise to a so-called horseshoe vortex system. The most upstream point of flow reversal at the wall is found to be a stagnation point which appears as a sink instead of a separation point in the symmetry plane in front of the cylinder. The wall shear stress is largest between the main (horseshoe) vortex and the cylinder, and seems to be mainly governed by the strong downflow in front of the cylinder as turbulent stresses are small in this region. Due to a strong acceleration along the streamlines, a region of relatively small turbulent kinetic energy is found between the horseshoe vortex and the cylinder. When passing under the horseshoe vortex, the upstream-directed jet formed by the deflected downflow undergoes a deceleration which gives rise to a strong production of turbulent kinetic energy. We find that pressure transport of turbulent kinetic energy is important for the initiation of the large production rates by increasing the turbulence level in the upstream jet near the wall. The distribution of the dissipation of turbulent kinetic energy is similar to that of the turbulent kinetic energy. Large values of dissipation occur around the centre of the horseshoe vortex and near the wall in the region where the jet decelerates. While the small scales are nearly isotropic in the horseshoe vortex centre, they are anistotropic near the wall. This can be explained by a vertical flapping of the upstream-directed jet. The distribution and level of dissipation, turbulent and pressure transport of turbulent kinetic energy are of crucial interest to turbulence modelling in the Reynolds-averaged context. To the best of our knowledge, this is the first time that these terms have been documented in this kind of flow.

A Hot Downflowing Model Atmosphere for Umbral Flashes and the Physical Properties of Their Dark Fibrils

Abstract We perform non-LTE inversions in a large set of umbral flashes, including the dark fibrils visible within them, and in the quiescent umbra by using the inversion code NICOLE on a set of full Stokes high-resolution Ca ii λ8542 observations of a sunspot at disk center. We find that the dark structures have Stokes profiles that are distinct from those of the quiescent and flashed regions. They are best reproduced by atmospheres that are more similar to the flashed atmosphere in terms of velocities, even if with reduced amplitudes. We also find two sets of solutions that finely fit the flashed profiles: a set that is upflowing, featuring a transition region that is deeper than in the quiescent case and preceded by a slight dip in temperature, and a second solution with a hotter atmosphere in the chromosphere but featuring downflows close to the speed of sound at such heights. Such downflows may be related, or even dependent, on the presence of coronal loops, rooted in the umbra of sunspots, as is the case in the region analyzed. Similar loops have been recently observed to have supersonic downflows in the transition region and are consistent with the earlier “sunspot plumes,” which were invariably found to display strong downflows in sunspots. Finally, we find, on average, a magnetic field reduction in the flashed areas, suggesting that the shock pressure is moving field lines in the upper layers.

Plasma flows and magnetic field interplay during the formation of a pore

We studied the formation of a pore in AR NOAA 11462. We analysed data obtained with the IBIS at the DST on April 17, 2012, consisting of full Stokes measurements of the Fe I 617.3 nm lines. Furthermore, we analysed SDO/HMI observations in the continuum and vector magnetograms derived from the Fe I 617.3 nm line data taken from April 15 to 19, 2012. We estimated the magnetic field strength and vector components and the LOS and horizontal motions in the photospheric region hosting the pore formation. We discuss our results in light of other observational studies and recent advances of numerical simulations. The pore formation occurs in less than 1 hour in the leading region of the AR. The evolution of the flux patch in the leading part of the AR is faster (< 12 hour) than the evolution (20-30 hour) of the more diffuse and smaller scale flux patches in the trailing region. During the pore formation, the ratio between magnetic and dark area decreases from 5 to 2. We observe strong downflows at the forming pore boundary and diverging proper motions of plasma in the vicinity of the evolving feature that are directed towards the forming pore. The average values and trends of the various quantities estimated in the AR are in agreement with results of former observational studies of steady pores and with their modelled counterparts, as seen in recent numerical simulations of a rising-tube process. The agreement with the outcomes of the numerical studies holds for both the signatures of the flux emergence process (e.g. appearance of small-scale mixed polarity patterns and elongated granules) and the evolution of the region. The processes driving the formation of the pore are identified with the emergence of a magnetic flux concentration and the subsequent reorganization of the emerged flux, by the combined effect of velocity and magnetic field, in and around the evolving structure.

An efficient multi-layer model for pier scour computations

Pier scour has caused bridge failures with catastrophic consequences. The aim of this study was to develop and verify a mathematical model for pier scour predictions. A new approach is taken that combines shallow-water equations with non-hydrostatic pressure corrections and a non-uniform mesh in the horizontal with terrain-following layers in the vertical. This approach significantly improves computational efficiency from the conventional computational fluid dynamics approach. It is concluded that, emerging from the lateral sides of a pier (cylinder), scour deepens while the patterns migrate upstream towards the pier's upstream nose. On the upstream side, scour continues to grow until the bed slope reaches the angle of repose of sediments. On the downstream side, scour grows until equilibrium is reached. The scour hole is shallower downstream than upstream of the pier. The presence of the pier causes a strong downflow near its upstream nose, a strong vortex at its foot on the upstream side and a weak vortex on the downstream side. The predicted flow velocity and scour depth agree well with measurements. The terrain-following layer feature is particularly useful for scour computations; the high efficiency makes the model practical for field-scale applications, which are highly relevant to improved design of pier foundations and pier scour control.