Horizontal Velocity Field Research Articles

A High-Resolution Modeling Study of the Circulation Patterns at a Coastal Embayment: Ría de Pontevedra (NW Spain) Under Upwelling and Downwelling Conditions

Estuarine exchange flow plays an important role in the biogeochemical properties exchange between the coastal ocean and the estuaries. Circulation patterns inside the Rias Baixas (NW Iberian Peninsula) have been widely studied, while the Ría de Pontevedra has received less attention. A high-resolution ROMS-AGRIF system configuration with three online two-way nesting domains was used and validated to enhance the knowledge about the circulation patterns of this Ría. Two representative estuarine circulation patterns were studied: a coastal upwelling event and a downwelling event associated with a maximum river runoff of 84 m3/s. An analysis using Empirical Orthogonal Functions (EOF) was applied to the horizontal subtidal velocity fields at the surface layer and at 20 m depth and to the subtidal normal velocity across vertical cross-sections. Upwelling events are characterized by a reinforcement of the positive estuarine circulation, in which the surface waters outflow and deep waters inflow at the main sill of the Ría, whilst full water column inflow (outflow) is observed at the northern (southern) openings. Conversely, downwelling events induce an opposite behavior, consisting of a negative estuarine circulation with the surface (deep) inflow (outflow) at the main sill of the Ría and outflow (inflow) at the northern (southern) openings. Evidences of a front splitting two vertical clockwise circulation cells were found. These cells are associated with the ocean water subduction that enters through the surface layer under downwelling favorable winds and this surface inflow opposes to the direction of the inner estuarine circulation. The EOF study confirms that shelf wind forcing has an important contribution to the variability of the velocity field, inducing positive or negative estuarine like circulation. The temporal principal components (PC) of EOF analysis present correlations of 0.92 between the meridional wind component and the first mode, and 0.77 between the zonal wind component and the second mode. Third EOF mode represents the circulation during transitional winds when some vorticity structures are visible. The realistic high-resolution simulation of the physical conditions at the Ría de Pontevedra provides new insights into the ocean-estuarine water exchanges and allow the visualization of recirculation processes and characteristic structures that have consequences in the marine ecosystem and in their productivity.

MODELLING THE HORIZONTAL VELOCITY FIELD OF THE NIZHNE-KANSK MASSIF ACCORDING TO GNSS OBSERVATIONS

Within the boundaries of the Nizhne-Kansk granite-gneiss massif, which directly borders on the Atamanovskiy branch of the Yenisei Ridge, the building of an underground research laboratory for validating the safety of disposal of high-level radioactive waste began in 2019. In 2010, researchers of the Mining and Chemical Combine at Zheleznogorsk and the Geophysical Center, Russian Academy of Sciences, organized a satellite geodetic network within the boundaries of the Nizhne-Kansk massif; this network included 30 GNSS stations intended for observations of modern crustal movements.The purpose of this study is to determine vectors and simulate the field of horizontal modern crustal movements from measurements made in 2010 - 2019. The tasks included: creating a catalogue of displacement data; calculating and estimating horizontal velocities of modern crustal movements, modelling the horizontal velocity field using artificial neural networks, developing a kinematic model of the area and comparing it with geological survey data.As a result, the resulting model was found to be in good agreement with the results of structural-geological and geodynamic studies in the area. The rate of convergence between the Siberian Platform and the West Siberian Plate in the interaction zone of the southern part of the Yenisei Ridge can be estimated as 2-4 mm/year. The movements of the selected area are due to sublatitudinal compression along an azimuth of 100-110 degrees. Within the selected tectonic blocks relatively low rates of modern horizontal movements of the earth's crust were obtained, which confirms the stable geodynamic regime of the structural block hosting the underground research laboratory. Thus, the results of the work demonstrate the possibility of disposal of high-level radioactive waste in the selected structural block.

Diagnosing Subsurface Vertical Velocities from High-Resolution Sea Surface Fields

AbstractUsing the extended “interior + surface quasigeostrophic” method from the 2019 study by Liu et al. (hereafter L19), subsurface density and horizontal velocities can be reconstructed from sea surface buoyancy and surface height. This study explores the potential of L19 for diagnosing the upper-ocean vertical velocity w field from high-resolution surface information, employing the 1/30° horizontal resolution OFES model output. Specifically, we employ the L19-reconstructed density and horizontal velocity fields in a diabatic version of the omega equation that incorporates a simplified parameterization for turbulent vertical mixing. The w diagnosis is evaluated against OFES output in the Kuroshio Extension region of the North Pacific, and the result indicates that the L19 method constitutes an effective framework. Statistically, the OFES-simulated and L19-diagnosed w fields have a 2-yr-averaged spatial correlation of 0.42–0.51 within the mixed layer and 0.51–0.67 throughout the 1000-m upper ocean below the mixed layer. Including the diabatic turbulent mixing effect has improved the w diagnoses inside the mixed layer, particularly for the cold-season days with the largest correlation improvement reaching 0.31. Our encouraging results suggest that the L19 method can be applied to the high-resolution sea surface height data from the forthcoming Surface Water and Ocean Topography (SWOT) satellite mission for reconstructing 3D hydrodynamic conditions of the upper ocean.

A GNSS velocity field for geophysical applications in Fennoscandia

In Fennoscandia, tectonics, Glacial Isostatic Adjustment (GIA), and climatic changes cause ongoing crustal deformation of some millimetres per year, both vertically and horizontally. These displacements of the Earth can be measured to a high degree of precision using a Global Navigation Satellite System (GNSS). Since about three decades, this is the major goal of the Baseline Inferences for Fennoscandian Rebound, Sea-level, and Tectonics (BIFROST) project.We present a new velocity field for an extended BIFROST GNSS network in the ITRF2008 reference frame making use of the GNSS processing package GPS Analysis Software of MIT (GAMIT). Compared to earlier publications, we have almost doubled the number of stations in our analysis and increased the observation time span, thereby avoiding the early years of the network with many instrument changes. We also provide modelled vertical deformation rates from contributing processes, i.e. elastic deformation due to global atmospheric and non-tidal ocean loading, ice mass and hydrological changes as well as GIA. These values for the vertical component can be used for removal of these contributions so that the residual uplift signal can be further analysed, e.g., in the context of local or regional deformation processes or large-scale but low-magnitude geodynamics.The velocity field has an uplift maximum of 10.3 mm/yr in northern Sweden west of the Gulf of Bothnia and subsidence exceeding 1 mm/yr in northern Central Europe. The horizontal velocity field is dominated by plate motion of more than 20.0 mm/yr from south-west to north-east. The elastic uplift signal sums up to 0.7–0.8 mm/yr for most stations in Northern Europe. Hence, the maximum uplift related to the past glaciation is ca. 9.6 mm/yr. The residual uplift signal after removal of the elastic and GIA contribution may point to possible improvements of the GIA model, but may also indicate regional tectonic and erosional processes as well as local deformation effects. We show an example of such residual signal discussing potential areas of interest for further studies.

Strain and Velocity Across the Great Basin Derived From 15‐ka Fault Slip Rates: Implications for Continuous Deformation and Seismic Hazard in the Walker Lane, California‐Nevada, USA

AbstractAverage strain across the Great Basin over the past 15 Kyr derived from slip rates on individual faults shows a concentration of both right‐lateral shear and extension in the western Great Basin (Walker Lane). Straining is modest across the central Great Basin, with a zone of higher strain in the eastern Great Basin including the Wasatch Front. The horizontal velocity field derived from 15‐ka fault slip rates is similar to the pattern of GPS velocities, suggesting that regional strain release patterns have been constant over the past 15 Kyr. The magnitudes of velocities inferred from fault slip rates, relative to North America, are lower than those from GPS in the Walker Lane, suggesting that the geologic record is missing evidence of strike slip on faults, and seismic hazard may be higher than suggested by fault slip rates alone. The observed strain concentration in the western Great Basin is consistent with a Sierra Nevada block that is more rigid than the surrounding lithosphere of nonlinear rheology, which concentrates strain east of and adjacent to the rigid block. Treating the western U.S. as a thin viscous sheet with the Sierra Nevada block as a rigid boundary provides a consistent history of continuous deformation in the Walker Lane over decadal, millennial, and Neogene timescales.

OHAM simulation of 3D transverse magnetic field in rotating flow of Maxwell nanofluid over a stretching sheet with chemical reaction and heat source/sink

AbstractIn this article, we investigate the heat transfer characteristics of a Maxwell nanofluid along a stretching sheet with transverse magnetic field, considering the presence of heat source/sink and chemical reaction. We consider appropriate similarity transformation for transforming the governing nonlinear equations into nondimensional highly nonlinear coupled ordinary differential equations. The optimal homotopy analysis method is utilized for solving the resultant‐coupled equations. The impact of all sundry parameters, like, Deborah number, Prandtl number, magnetic parameter, thermophoresis, rotation parameter, chemical reaction, velocity slip, Schmidt number, Brownian motion parameter, heat sources per sink, Biot number, and Eckert number, on the temperature, velocity, and concentration fields is reported, analyzed, and described through graphs and tables. It is noticed that higher values of magnetic parameter and Deborah number reduce the horizontal velocity field. Furthermore, it is observed that the Biot number and heat source/sink parameter enhance the temperature distribution.

Stepwise transitions in spin-up of rotating Rayleigh–Bénard convection

Abstract

Toward a large-scale particle-based parallel simulator of Aeolian sand transport, including a model for mobile sand availability

We develop a numerical tool for particle-based simulations of Aeolian sand transport. Our model combines a Discrete-Element-Method for the sand particles with an efficient hydrodynamic description of the average turbulent horizontal wind velocity field over the granular bed, which has been developed in previous work and accounts for the two-way coupling of the granular and fluid phases. However, here we implement our model within the open source library LAMMPS for granular massively parallel simulations and incorporate a new grid coarsening scheme for the wind model. We show that our model quantitatively reproduces observed values of the steady-state (saturated) sand flux under various flow conditions. Furthermore, we model different conditions of mobile sand availability and find a strong dependence of the sand flux on this availability.

Three dimensional flows beneath a thin layer of 2D turbulence induced by Faraday waves

Faraday waves occur on a fluid being subject to vertical shaking. Although it is well known that form and shape of the wave pattern depend on driving amplitude and frequency, only recent studies discovered the existence of a horizontal velocity field at the surface, called Faraday flow. This flow exhibits attributes of two-dimensional turbulence and is replicated in this study. Despite the increasing attention towards the inverse energy flux in the Faraday flow and other not strictly two-dimensional (2D) systems, little is known about the velocity fields developing beneath the fluid surface. In this study, planar velocity fields are measured by means of particle image velocimetry with high spatio-temporal resolution on the water surface and at different depths below it. A sudden drop in velocity and turbulent kinetic energy is observed at half a Faraday wavelength below the surface revealing that the surface flow is the main source of turbulent fluid motion. The flow structures below the surface comprise much larger spatial scales than those on the surface leading to very long-tailed temporal and spatial velocity (auto-) correlation functions. The three-dimensionality of the flow is estimated by the compressibility, which increases strongly with depth while the divergence changes its appearance from intermittent and single events to a large scale pattern resembling 2D cut-planes of convection rolls. Our findings demonstrate that the overall fluid flow beneath the surface is highly three-dimensional and that an inverse cascade and aspects of a confined 2D turbulence can coexist with a three-dimensional flow.Graphic abstract

Lagrangian chaotic saddles and objective vortices in solar plasmas

We report observational evidence of Lagrangian chaotic saddles in plasmas, given by the intersections of finite-time unstable and stable manifolds, using an ≈22h sequence of spacecraft images of the horizontal velocity field of solar photosphere. A set of 29 persistent objective vortices with lifetimes varying from 28.5 to 298.3min are detected by computing the Lagrangian averaged vorticity deviation. The unstable manifold of the Lagrangian chaotic saddles computed for ≈11h exhibits twisted folding motions indicative of recurring vortices in a magnetic mixed-polarity region. We show that the persistent objective vortices are formed in the gap regions of Lagrangian chaotic saddles at supergranular junctions.

Recent Crustal Deformation Based on Interpolation of GNSS Velocity in Continental China

We used the interpolation method of two-dimensional vector velocity field data based on Green’s function to conduct coupled interpolation with a Poisson’s ratio of 0.5 for 1966 horizontal velocity field data from 1999 to 2017 and obtained the uniform velocity field and strain rate field with a grid of 1°. The main results are as follows: the eastern Himalayan structure as the center, the eastern Lhasa block, the eastern Qiangtang block, the Sichuan-Yunnan block, and the Burma block form a strong deformation rate zone of continuous deformation in the fan-shaped region, which has been a strong deformation rate zone for earthquakes of magnitude 7 or higher in continental China since 1963. Besides, the eastward movement of crustal material in the Tibetan Plateau is blocked by the stable South China block. Therefore, the direction of crustal material movement is deflected, which gradually forms a clockwise rotation motion system centered on the eastern Himalayan structure. Finally, our research shows that the influencing factors of strong earthquakes include velocity change, non-uniform strain distribution, accumulation of larger strain, and the difference of the second strain rate invariant. Strong earthquakes are closely related to the difference in energy accumulation in space.

Numerical Study Of Water Circulation In Shallow Basin Using Lattice Boltzmann Method

In the present work, a code based on the Lattice Boltzmann method (LBM) has been developed to study the hydrodynamic field in a shallow basin with complicated geometry. It is a non-regular border basin with dikes built inside. The LBM method was therefore used to solve the Navier Stokes equations with boundary conditions which express that the components of the horizontal two-dimensional velocity field are zero at closed boundaries (sealing and non-slip conditions), while the flow is imposed at the entrance of the basin, and a zero speed gradient is imposed at the free exit of the basin (condition of continuity of the flow). The validation of the developed code was verified by comparing the results obtained with those of Charafi et al. [5], where the finite difference method with a MacCormack scheme was used. A good agreement of the results was noted. A series of simulations was made for different values of the Reynolds number, and showed good performance of the code. The main advantage of the LBM method seen in this work lies in the simplicity of its implementation. However, the model suffers from some limitations such as its validity for low Reynolds numbers (Re = 400)

Mapping Small-Scale Horizontal Velocity Field in Panzhinan Waterway by Coastal Acoustic Tomography.

Mapping small-scale high-precision velocity fields is of great significance to oceanic environment research. Coastal acoustic tomography (CAT) is a frontier technology used to observe large-scale velocity field in the horizontal slice. Nonetheless, it is difficult to observe the velocity field using the CAT in small-scale areas, specifically where the flow field is complex such as ocean ranch and artificial upwelling areas. This paper conducted a sound transmission experiment using four 50 kHz CAT systems in the Panzhinan waterway. Notably, sound transmission based on the round-robin method was recommended for small-scale CAT observation. The travel time between stations, obtained by correlation of raw data, was applied to reconstruct the horizontal velocity fields using Tapered Least Square inversion. The minimum net volume transport was 8.7 m3/s at 12:32, 1.63% of the total inflow volume transport indicating that the observational errors were acceptable. The relative errors of the range-average velocity calculated by differential travel time were 1.54% (path 2) and 0.92% (path 6), respectively. Moreover, the inversion velocity root-mean-square errors (RMSEs) were 0.5163, 0.1494, 0.2103, 0.2804 and 0.2817 m/s for paths 1, 2, 3, 4 and 6, respectively. The feasibility and acceptable accuracy of the CAT method in the small-scale velocity profiling measurement were validated. Furthermore, a three-dimensional (3-D) velocity field mapping should be performed with combined analysis in horizontal and vertical slices.

Evolution of exploding granules from coordinated observations by THEMIS, IRIS, SDO/HMI, and HINODE, and a simulation

Exploding granules constitute the strongest horizontal flows on the quiet Sun and contribute to the structure of the surface horizontal velocity fields which build the large-scale organization of the discrete magnetic field. In this work we explore exploding granule expansion through the observations of the ground-based THEMIS telescope, IRIS, SDO, and the Hinode space-borne instruments, and finally with the magnetohydrodynamics simulation. We evaluate the detection and the expansion of exploding granules at several wavelengths and at various spatial and temporal resolutions. To analyze the different temporal sequences, two methods of image segmentation are applied to select the granules. The first allows us to follow individually the exploding granules observed simultaneously by THEMIS, IRIS, and SDO. The second uses long time independent sequences from THEMIS, IRIS, SDO, Hinode, and a simulation. In the first method (called manual) the segmentation isolates the cell of the granules (bright granules and intergranular parts), while in the second method (called statistical) only the bright part of the granules are isolated. The results obtained with simultaneous or distinct temporal observations using the two methods of segmentation are in good agreement. The granule area evolves linearly with an expansion velocity that decreases with the radius. A rapid decrease in the velocity expansion in the first two minutes is observed. The detection and measurement of the dynamics of the explosive granules can be performed from ground- and space-based instruments. Our work reveals the usefulness of SDO data, with low spatial resolution, to study the dynamics of the exploding granules all over the solar surface.

Spatial distribution of earthquake potential along the Himalayan arc

To determine the spatial distribution of earthquake potential along the active Himalayan arc, we utilize GPS measurements and earthquake data. We derive horizontal velocity field and 2-D strain rates from a new set of 41 regional GPS stations along with 446 published velocities. We convert these strain rate tensors to geodetic moment rate build-up within 24 contiguous segments and compare to the seismic moment rate release derived from a reassessed earthquake catalog of 900 years. The geodetic to seismic moment rate ratio, an indicator of stored strain energy, varies from below unity to more than 50 in different segments. The estimated geodetic moment rate ranges from 1.7 × 1018 Nm/yr to 10.2 × 1018 Nm/yr, whereas the seismic moment rate ranges from 3.7 × 1016 Nm/yr to 5.1 × 1019 Nm/yr. This variation between the geodetic and seismic moment rate corresponds to a moment deficit rate of ~1.15×1017 Nm/yr to 7.97 × 1018 Nm/yr along various segments of the study region. The above moment deficit rate provides an equivalent earthquake potential of magnitude 5.7 − 8.2 in different segments. Specifically, the higher earthquake potential (Mw≥8.0) corresponds to the segments in the central seismic gap and the northeast part of Himalaya, whereas the lower earthquake potential (Mw<7.0) corresponds to the segments encompassing the rupture areas of recent large events. The present findings not only provide input constraints on the contemporary crustal deformation but also contributes to the time-dependent seismic hazard analysis along the Himalaya.

Seismogenic potential of the High Durance Fault constrained by 20 yr of GNSS measurements in the Western European Alps

SUMMARYDue to the steady moderate seismicity observed along the Briançon seismic arc, in the south-western French Alps, three temporary GNSS (Global Navigation Satellite System) surveys took place in 1996, 2006 and 2011, across a ∼50 × 60 km² wide area, to investigate the surface deformation field. The horizontal velocity field computed from these three surveys showed an east–west extension in the network. A fourth campaign was led in 2016, creating a 20 yr observation span, resulting in measurements which reach a sufficient accuracy to assess whether extension found within the Briançon network is localized onto any particular tectonic feature. Several faults in this area are known to be active normal faults. Assessing the localization of the deformation may lead to a better understanding of the active tectonics of the Alpine belt. To address this issue, a robust velocity field was computed from the combination of the different campaign and permanent GNSS data. Strain rate tensors were derived for the first time in this area on a 0.1 × 0.1 deg grid to assess the distribution of the deformation. The regional deformation appears localized in the Briançon area and reaches up to 20 ± 5 nanostrain yr−1 in the centre of the network. The observed velocities were projected on a profile across the network and compared with modelled interseismic deformation to characterize the behaviour of the major active faults known in the study zone. While a two-fault model provides the best fit to the data, a single fault model has only marginally higher residuals, with parameters which are more consistent with the seismotectonics of the region. The localization of the single modelled fault is consistent with the location of the High Durance Fault (HDF). Therefore, we used the known geological location of this structure as a priori information in a block model to compute a fault slip rate at the interface between the two blocks. The velocities on the interface indicate 0.4–0.5 mm yr−1 of extension, and therefore strain accumulates along the HDF throughout the seismic cycle. The geodetically derived fault slip rate is converted into an equivalent seismic moment release rate, which is consistent within its uncertainty bounds with the known historical and instrumental seismicity of the Briançon area.

Evolution of a vortex in a strongly stratified shear flow. Part 1. Asymptotic analysis

In this paper, we investigate the dynamics of an initially vertical vortex embedded in a shear flow in a stratified fluid by means of a long-wavelength analysis. The main goal is to determine, whether or not, the Kelvin–Helmholtz instability can develop unconditionally as speculated by Lilly ( J. Atmos. Sci. , vol. 40, 1983, pp. 749–761). The analysis is performed in the case of the Lamb–Oseen vortex profile and a shear flow uniform in the horizontal and varying sinusoidally along the vertical using the assumption $\hat{k}_{z}a_{0}F_{h}\ll 1$ , where $\hat{k}_{z}$ is the vertical wavenumber, $a_{0}$ the vortex radius and $F_{h}$ the horizontal Froude number based on the circulation of the vortex. The results show that the vortex axis is advected not only in the direction of the shear flow but also in the perpendicular direction owing to the self-induced motion of the vortex. In addition, internal waves are transiently excited at the beginning, generating an initial non-hydrostatic regime. Their relative effects on the displacements of the vortex axis are weak except initially. The angular velocity of the vortex decays owing to a dynamic effect and viscous effects related to the vertical shear. The former effect is due to the squeezing of isopycnals in the vortex core, which implies a decrease of the vertical vorticity to satisfy potential vorticity conservation. In addition, a horizontal velocity field with an azimuthal wavenumber $m=2$ is generated, meaning that the shape of the vortex becomes slightly elliptical. We further show that the minimum asymptotic Richardson number is bounded, $\min (Ri)>3.43$ , when $\hat{k}_{z}a_{0}F_{h}\ll 1$ and therefore cannot go below the critical value $1/4$ . This is because the growth of the vertical shear of the horizontal velocity of the vortex saturates owing to the decay of its angular velocity and because the squeezing of isopycnals increases the stratification strength. This suggests that the shear instability cannot always develop in strongly stratified flows, contrary to the conjecture of Lilly (as above). These predictions will be tested against direct numerical simulations in Part 2.

Structural analysis of Azerbaijan territory horizontal velocity movement based on GPS-measurements

The contemporary kinematics of Azerbaijan is generated by the northward movement of Arabian plate relative to Eurasian one. This continuous «intervention» of Arabian plate into Eurasian one is the reason of the deformation of the Earth’s crust of the Caucasian block causing earthquakes which are registered throughout the territory. For the research of geodynamic processes and intraplate deformations it is applied the methods of global positioning (GPS). GPS-network in Azerbaijan was founded in 1998. For the period between 1998 and 2016, in many GPS-points, the measurements were done 3―6 times. The present paper deals with the research of structure distribution of GPS horizontal velocity field of intraplate zones (domains) for Azerbaijan. The comparative analysis of interrelation of seismic events with distribution of horizontal velocity vectors and deformation obtained from Azerbaijan GPS-network monitoring was done aiming to reveal those zones. Deformation distribution throughout the research area was calculated with the formula and approach of Shen with the use of horizontal components of GPS-velocities. Aiming to conduct the comparative analysis of GPS-velocities with seismicity, a map of distribution of earthquake numbers for Azerbaijan during the period of 2003―2017 with magnitude M ≥ 3 was utilized. As a result, the following domain zones were defined, such as the fold system of the Greater Caucasus, the fold system of the Lesser Caucasus, the Middle Kur, Talysh, Gusar-Shabran depression and Gobustan-Absheron zone. It was determined that the areas of high seismicity were located in the zones of high gradients of GPS-velocities, while the areas of high seismicity coincide predominantly with the areas of high velocity compression. However, Gobustan-Absheron zone with high velocity deformation is not characterized by high seismicity. Probably, the reason of this is due to the elasticity of geological environment.

Co-spatial velocity and magnetic swirls in the simulated solar photosphere

Context.Velocity or intensity swirls have now been shown to be widely present throughout the photosphere and chromosphere. It has been suggested that these events could contribute to the heating of the upper solar atmosphere, via exciting Alfvén pulses, which could carry significant amounts of energy. However, the conjectured necessary physical conditions for their excitation, that the magnetic field rotates co-spatially and co-temporally with the velocity field, has not been verified.Aims.We aim to understand whether photospheric velocity swirls exist co-spatially and co-temporally with photospheric magnetic swirls, in order to demonstrate the link between swirls and pulses.Methods.The automated swirl detection algorithm (ASDA) is applied to the photospheric horizontal velocity and vertical magnetic fields obtained from a series of realistic numerical simulations using the radiative magnetohydrodynamics (RMHD) code Bifrost. The spatial relationship between the detected velocity and magnetic swirls is further investigated via a well-defined correlation index (CI) study.Results.On average, there are ∼63 short-lived photospheric velocity swirls (with lifetimes mostly less than 20 s, and average radius of ∼37 km and rotating speeds of ∼2.5 km s−1) detected in a field of view (FOV) of 6 × 6 Mm−2, implying a total population of velocity swirls of ∼1.06 × 107in the solar photosphere. More than 80% of the detected velocity swirls are found to be accompanied by local magnetic concentrations in intergranular lanes. On average, ∼71% of the detected velocity swirls have been found to co-exist with photospheric magnetic swirls with the same rotating direction.Conclusions.The co-temporal and co-spatial rotation in the photospheric velocity and magnetic fields provide evidence that the conjectured condition for the excitation of Alfvén pulses by photospheric swirls is fulfilled.

Practical Application of a Horizontal Intraplate Velocity Field Model for the Territory of Bulgaria

The Republic of Bulgaria is situated on the edge of the Eurasian tectonic plate. This is defined by active tectonic and seismic activity, which is an issue in the implementation of the official coordinate reference system in the country - the ETRS89, as far as precise solutions are concerned. The reason is that the intraplate, relative to Eurasia, tectonic movements south of Stara Planina are about 5 times larger than those north of it. Over a period of time (about 10 years), the coordinate errors of the points from a static network become bigger than the uncertainties of GNSS measurements and thus limit their potential. Thanks to the presence of networks of continuously operating reference GNSS stations (CORS networks), and advanced methods of processing and analysis of the results, it is possible to monitor the crustal deformations with sufficient precision. A model of horizontal intraplate velocities was developed based on measurements from different epochs of the CORS networks operating on the territory of Bulgaria. Precise coordinates and velocities of the stations were estimated using the Bernese GNSS Software v5.2, and the deformation modeling was performed using a method of determining parameters of local deformation and Euler poles of distinctive tectonic blocks to which the country is divided according to the authors. This paper presents the practical applicability of this model for interpolation the velocities of stations from static networks and verification of the official results for the points of the National GPS Network. The results are encouraging for the practical realization of ETRS89 on the territory of Bulgaria.