Turbulent Shock Research Articles

A weakly nonlinear framework to study shock–vorticity interaction

Linear interaction analysis (LIA) is routinely used to study the shock–turbulence interaction in supersonic and hypersonic flows. It is based on the inviscid interaction of elementary Kovásznay modes with a shock discontinuity. LIA neglects nonlinear effects, and hence it is limited to small-amplitude disturbances. In this work, we extend the LIA framework to study the fundamental interaction of a two-dimensional vorticity wave with a normal shock. The predictions from a weakly nonlinear framework are compared with high-order accurate numerical simulations over a range of wave amplitudes ( $\epsilon$ ), incidence angles ( $\alpha$ ) and shock-upstream Mach numbers ( $M_1$ ). It is found that the nonlinear generation of vorticity at the shock has a significant contribution from the intermodal interaction between vorticity and acoustic waves. Vorticity generation is also strongly influenced by the curvature of the normal shock wave, especially for high incidence angles. Further, the weakly nonlinear analysis is able to predict the correct scaling of the nonlinear effects observed in the numerical simulations. The analysis also predicts a Mach number dependent limit for the validity of LIA in terms of the maximum possible amplitude of the upstream vorticity wave.

Turbulent Business Cycles

Recessions are associated with sharp increases in turbulence that reshuffles firms' productivity rankings. To study the business cycle implications of turbulence shocks, we use Compustat data to construct a measure of turbulence based on the (inverse of) Spearman correlations of firms' productivity rankings between adjacent years. We document evidence that turbulence rises in recessions, reallocating labor and capital from high-to low-productivity firms and reducing aggregate TFP and the stock market value of firms. A real business cycle model with heterogeneous firms and financial frictions can generate the observed macroeconomic and reallocation effects of turbulence. In the model, increased turbulence makes high-productivity firms less likely to remain productive, reducing their expected equity values and tightening their borrowing constraints relative to low-productivity firms. Thus, labor and capital are reallocated to low-productivity firms, reducing aggregate TFP and generating a recession with synchronized declines in aggregate output, consumption, investment, and labor hours, in line with empirical evidence.

Application of bandwidth-optimized WENO schemes to DNS of shock–turbulence interaction problems

Application of bandwidth-optimized WENO schemes to DNS of shock–turbulence interaction problems

Geometry and dynamics of passive scalar structures in compressible turbulent mixing

We present a structure-based numerical analysis of passive scalar mixing in decaying homogeneous isotropic turbulence (DHIT) and shock-turbulence interaction canonical configurations. The analysis focuses on the temporal evolution of ensembles of passive scalar structures, initialized as spheres of different sizes relative to the Taylor microscale. An algorithm is introduced to track the evolution of each individual structure and the interactions with other structures in the ensemble, relating changes in the surface geometry and the underlying physical processes (turbulent transport, scalar dissipation, and shock compression). The tracking algorithm is applied to datasets from shock-capturing direct numerical simulations of DHIT, with Taylor microscale Reynolds number Reλ=40 and turbulence Mach number Mt=0.2, and STI cases in which the turbulence is processed by a shock wave at Mach numbers M = 1.5 and 3.0. Temporal surface convolution increases for initially larger structures, resulting in a higher probability of locally hyperbolic geometries where breakup into smaller structures occurs. Shock-induced deformation of the structures amplifies breakup processes, enhancing mixing, particularly for larger structures. Mixing enhancement by the shock is manifested as an amplification of the surface-averaged scalar gradient, which increases for initially larger structures. The alignment between the scalar gradient and the most extensional strain-rate eigendirection on the scalar isosurfaces also increases across the shock. Larger magnitudes of the scalar gradient and its alignment with the most compressive strain-rate eigendirection correlate with flatter surface regions. Shock-induced structure compression increases the area coverage of flat regions, where the amplification of scalar gradient is localized.

Turbulent Business Cycles

Recessions are associated with sharp increases in turbulence that reshuffle firms' productivity rankings. To study the business cycle implications of turbulence shocks, we use Compustat data to construct a measure of turbulence based on the (inverse of) Spearman correlations of firms' productivity rankings between adjacent years. We document evidence that turbulence rises in recessions, reallocating labor and capital from high- to low-productivity firms and reducing aggregate TFP and the stock market value of firms. A real business cycle model with heterogeneous firms and financial frictions can generate the observed macroeconomic and reallocation effects of turbulence. In the model, increased turbulence makes high-productivity firms less likely to remain productive, reducing their expected equity values and tightening their borrowing constraints relative to low-productivity firms. This leads to a reallocation that reduces aggregate TFP. Unlike uncertainty, turbulence changes both the conditional mean and the conditional variance of the firm productivity distribution, enabling a turbulence shock to generate a recession with synchronized declines in aggregate activities.

The evolution of pressure gain in turbulent fast flames

This research quantifies the evolution of pressure for fast burning regimes characterized by various degrees of compressibility and involving turbulent flames and shocks. The experimental exploration is conducted in a Turbulent Shock Tube facility, where the level of flame compressibility is controlled by varying the equivalence ratio of the hydrogen-air mixture. High-speed particle image velocimetry, chemiluminescence, schlieren, and pressure measurements are simultaneously acquired to capture the rise in stagnation pressure for various regimes from fast flames to shock-flame complexes. The pressure and velocity measurements are used to analyze combustion regimes on the Rankine-Hugoniot diagram that shows the flame-driven compression for a range of fast flame conditions evolving toward detonation onset. Various levels of compression are dependent on the level of shock-flame coupling and flame velocities. Lower degrees of compressibility show 52% efficiency of an ideal ZND cycle with 40% thermal efficiency, while shock-flame complexes are shown to produce 81% of the work produced by an ideal ZND cycle with 53% thermal efficiency.

Classification of Filament Formation Mechanisms in Magnetized Molecular Clouds

Abstract Recent observations of molecular clouds show that dense filaments are the sites of present-day star formation. Thus, it is necessary to understand the filament formation process because these filaments provide the initial condition for star formation. Theoretical research suggests that shock waves in molecular clouds trigger filament formation. Since several different mechanisms have been proposed for filament formation, the formation mechanism of the observed star-forming filaments requires clarification. In the present study, we perform a series of isothermal magnetohydrodynamics simulations of filament formation. We focus on the influences of shock velocity and turbulence on the formation mechanism and identified three different mechanisms for the filament formation. The results indicate that when the shock is fast, at shock velocity v sh ≃ 7 km s−1, the gas flows driven by the curved shock wave create filaments irrespective of the presence of turbulence and self-gravity. However, at a slow shock velocity v sh ≃ 2.5 km s−1, the compressive flow component involved in the initial turbulence induces filament formation. When both the shock velocities and turbulence are low, the self-gravity in the shock-compressed sheet becomes important for filament formation. Moreover, we analyzed the line-mass distribution of the filaments and showed that strong shock waves can naturally create high-line-mass filaments such as those observed in the massive star-forming regions in a short time. We conclude that the dominant filament formation mode changes with the velocity of the shock wave triggering the filament formation.

Evaluating the deHoffmann‐Teller Cross‐Shock Potential at Real Collisionless Shocks

AbstractShock waves are common in the heliosphere and beyond. The collisionless nature of most astrophysical plasmas allows for the energy processed by shocks to be partitioned amongst particle sub‐populations and electromagnetic fields via physical mechanisms that are not well understood. The electrostatic potential across such shocks is frame dependent. In a frame where the incident bulk velocity is parallel to the magnetic field, the deHoffmann‐Teller frame, the potential is linked directly to the ambipolar electric field established by the electron pressure gradient. Thus measuring and understanding this potential solves the electron partition problem, and gives insight into other competing shock processes. Integrating measured electric fields in space is problematic since the measurements can have offsets that change with plasma conditions. The offsets, once integrated, can be as large or larger than the shock potential. Here we exploit the high‐quality field and plasma measurements from NASA's Magnetospheric Multiscale mission to attempt this calculation. We investigate recent adaptations of the deHoffmann‐Teller frame transformation to include time variability, and conclude that in practice these face difficulties inherent in the 3D time‐dependent nature of real shocks by comparison to 1D simulations. Potential estimates based on electron fluid and kinetic analyses provide the most robust measures of the deHoffmann‐Teller potential, but with some care direct integration of the electric fields can be made to agree. These results suggest that it will be difficult to independently assess the role of other processes, such as scattering by shock turbulence, in accounting for the electron heating.

A galaxy cluster in the innermost Zone of Avoidance, close to the radio phoenix VLSS J2217.5+5943

Context.Galaxy clusters grow via mergers with other clusters and groups. Extended regions of diffuse radio emission with a steep radio spectral index are thought to be indicators of such merger events. Extended radio sources with a significantly curved spectrum and a complex morphology have been found in several galaxy clusters. It has been proposed that these so-called radio phoenices are witnesses of cluster mergers and of the presence of active galactic nuclei prior to the merger. Shock fronts or turbulence induced by the mergers are believed to reenergize plasma emitted in the past active phase of a galaxy.Aims.The steep spectrum radio source VLSS J2217.5+5943 shows a complex filamentary morphology and a curved spectrum. Therefore, the source has previously been classified as a radio phoenix. However, no galaxy cluster associated with this radio source had confidently been detected until now because the source is located in the direction of the innermost zone of the Galactic plane atb = +2.4°, the innermost Zone of Avoidance (ZoA). The main aim of this work is to identify galaxies that are part of a cluster at the location of VLSS J2217.5+5943, determine their redshifts, and analyze their connection with the radio source. The confirmation of a cluster would corroborate the classification of the radio source as a radio phoenix and demonstrate that extended, diffuse radio sources are useful indicators of the presence of a galaxy cluster, in particular in the innermost ZoA.Methods.We analyzed archival observations in the near infrared and mid infrared (Spitzer) to select the galaxies in the immediate neighborhood of the radio source. A sample of 23 galaxies were selected as candidate cluster members. Furthermore, we carried out deep integral field spectroscopy covering 6450 to 10 500 Å with the red unit of theHobby-EberlyTelescope second generation low resolution spectrograph (LRS2-R). We also reanalyzed archival GMRT observations at 325 and 610 MHz.Results.We selected 23 galaxies within a radius of 2.5 arcmin, centered on RA = 22h17m​.5, Dec = +59° 43′ (J2000). Spectra were obtained for three of the brightest galaxies. For two galaxies we derived redshifts ofz = 0.165 andz = 0.161, based on NaD absorption and TiO band heads. Their spectra correspond to E-type galaxies. Both galaxies are spatially associated with VLSS J2217.5+5943. The spectrum of the third galaxy, which is slightly farther from the radio source, indicates a LINER spectral type atz = 0.042. It is apparently a foreground galaxy with respect to the cluster we identified.Conclusions.VLSS J2217.5+5943 is associated with a massive galaxy cluster at redshiftz = 0.163 ± .003, supporting its classification as a radio phoenix. The intrinsic properties of the radio source, computed for the cluster redshift, are in good agreement with those of other known radio phoenices. The identification of the galaxy cluster demonstrates that far-red spectroscopy with LRS2-R succeeds in determining the redshift of galaxies in the innermost ZoA. Moreover, it confirms that radio sources can be useful indicators of the presence of galaxy clusters in the ZoA.

Hydrogen fueled scramjet combustor with a wavy-wall double strut fuel injector

The demand for the enhancement of scramjet performance is increasing worldwide due to its tremendous and upcoming applications. The major challenge in scramjet engines is the mixing of fuel and air and succeeding combustion at supersonic speed. In a scramjet combustor flow field, the development of high turbulence (flow disturbance), shear-mixing layer, and oblique shock waves are the key factors to magnify the mixing efficiency of fuel and air at the significantly less resident time of air in the combustion chamber. Based on these techniques, an innovative strut fuel injector with a wavy wall surface and double strut has been investigated for possible mixing enhancement of fuel and air. These results are compared with the basic single wedge strut available in the open literature to identify the performance improvement. The computational geometries are modeled with Reynolds-averaged Navier Stokes equations, SST k-ω model, and global one-step reaction mechanism. All the flow modeling has been solved with finite volume and a second ordered upwind discretization scheme. The evaluation of scramjet internal flow structure and numerical results found that the double strut with a wavy-wall shape improved the mixing efficiency and combustion phenomenon significantly. The mixing and combustion profiles reveal that wavy-wall double strut generates an early complete mixing within a distance of 0.17 m with increased mixing and combustion efficiency of 18% and 20%, respectively.

Shock–multicloud interactions in galactic outflows – II. Radiative fractal clouds and cold gas thermodynamics

ABSTRACT Galactic winds are crucial to the cosmic cycle of matter, transporting material out of the dense regions of galaxies. Observations show the coexistence of different temperature phases in such winds, which is not easy to explain. We present a set of 3D shock–multicloud simulations that account for radiative heating and cooling at temperatures between $10^2$ and $10^7\, \rm K$. The interplay between shock heating, dynamical instabilities, turbulence, and radiative heating and cooling creates a complex multiphase flow with a rain-like morphology. Cloud gas fragments and is continuously eroded, becoming efficiently mixed and mass loaded. The resulting warm mixed gas then cools down and precipitates into new dense cloudlets, which repeat the process. Thus, radiative cooling is able to sustain fast-moving dense gas by aiding condensation of gas from warm clouds and the hot wind. In the ensuing outflow, hot gas with temperatures ${\gtrsim}10^6\, \rm K$ outruns the warm and cold phases, which reach thermal equilibrium near ${\approx}10^4$ and ${\approx}10^2\, \rm K$, respectively. Although the volume filling factor of hot gas is higher in the outflow, most of the mass is concentrated in dense gas cloudlets and filaments with these temperatures. More porous multicloud layers result in more vertically extended outflows, and dense gas is more efficiently produced in more compact layers. The cold phase is not accelerated by ram pressure, but, instead, precipitates from warm and mixed gas out of thermal equilibrium. This cycle can explain the presence of high-velocity H i gas with $N_{\rm H\, \small {I}}=10^{19\!-\!21}\, \rm cm^{-2}$ and $\Delta v_{{\rm FWHM}}\lesssim 37\, \rm km\, s^{-1}$ in the Galactic Centre outflow.

Proton Energy Spectra of Energetic Storm Particle Events and Relation with Shock Parameters and Turbulence

Abstract The proton energy spectra of 23 energetic storm particle (ESP) events of various types, occurring either in association with (16 events) or in the absence of (7 events) solar energetic particles (SEPs), are investigated by using data from particle instruments aboard STEREO A in the energy range from 84.1 keV to 100 MeV. The obtained spectra were fitted with several known functions. Out of the 12 ESP events occurring in association with SEPs and quasi-perpendicular shocks, the Weibull distribution provides good fits to the spectra over the whole energy range in five cases. For the other seven events it fits the high energy tail, with lower energies explained by the power law predicted by the diffusive shock acceleration (DSA). Conversely, for the four SEP-associated ESPs at quasi-parallel shocks, a double power law better reproduces the observed spectra. Moreover, a significant correlation of the downstream turbulence level is found with the background subtracted Weibull parameters for quasi-perpendicular shocks, and with the proton peak value in the intermediate energy range of 4–6 MeV for all 16 considered shocks. Our results suggest that the downstream turbulence is a relevant factor in particle acceleration and that stochastic acceleration (SA) can be a plausible mechanism for reacceleration at interplanetary shocks. In the seven cases not associated with SEPs, an Ellison–Ramaty form fits the observed spectra, consistently with a DSA process, suggesting that a strong shock and/or a high energy particle background should be present for the SA to be at work.

The LOFAR and JVLA view of the distant steep spectrum radio halo in MACS J1149.5+2223

Context.Radio halos and relics are Mpc-scale diffuse radio sources in galaxy clusters, which have a steep spectral indexα > 1 (defined asS ∝ ν−α). It has been proposed that halos and relics arise from particle acceleration induced by turbulence and weak shocks that are injected into the intracluster medium (ICM) during mergers.Aims.MACS J1149.5+2223 is a high-redshift (z = 0.544) galaxy cluster possibly hosting a radio halo and a relic. We analysed LOw Frequency Array (LOFAR), Giant Metrewave Radio Telescope, andKarl G. JanskyVery Large Array (JVLA) radio data at 144, 323, and 1500 MHz, respectively. In addition, we analysed archivalChandraX-ray data to characterise the thermal and non-thermal properties of the cluster.Methods.We obtained radio images at different frequencies to investigate the spectral properties of the radio halo. We usedChandraX-ray images to constrain the thermal properties of the cluster and to search for discontinuities (due to cold fronts or shock fronts) in the surface brightness of the ICM. By combining radio and X-ray images, we carried out a point-to-point analysis to study the connection between the thermal and non-thermal emission.Results.We measured a steep spectrum of the halo, which can be described by a power-law withα = 1.49 ± 0.12 between 144 and 1500 MHz. The radio surface brightness distribution across the halo is found to correlate with the X-ray brightness of the ICM. The derived correlation shows a sub-linear slope in the range 0.4–0.6. We also report two possible cold fronts in north-east and north-west, but deeper X-ray observations are required to firmly constrain the properties of the upstream emission.Conclusions.We show that the combination of high-redshift, steep radio spectrum, and sub-linear radio-X scaling of the halo rules out hadronic models. An old (∼1 Gyr ago) major merger likely induced the formation of the halo through stochastic re-acceleration of relativistic electrons. We suggest that the two possible X-ray discontinuities may be part of the same cold front. In this case, the coolest gas pushed towards the north-west might be associated with the cool core of a sub-cluster involved in the major merger. The peculiar orientation of the south-east relic might indicate a different nature of this source and requires further investigation.

The Importance of Strategic Agility to Business Survival During Corona Crisis and Beyond

Strategic Agility is seen by many researchers and analysts as an innovative newly developed management paradigm adopted by contemporary organizations to achieve distinction and outperform competitors under conditions of environmental instability and uncertainty. This article is an attempt to introduce the concept of Strategic Agility and to demonstrate its basic characteristics and the importance of adopting it by various organizations to achieve excellence and sustainability. In a competitive environment, characterized by acute turbulence and continual shocks, as in the current environment of COVID-19, strategic agility offers a viable means to harness non-linear scientific and technological breakthroughs with a view to profiting from both the dislocation in the consumer sentiment and behavior and the breakdown in supply chains. Moreover, the article highlights the interaction between strategic agility and firm performance and emphasizes the need to create agile organizations that will thrive in a volatile and uncertain world.

Efficient generation of turbulent collisionless shocks in laser-ablated counter-streaming plasmas

Laser-ablated high-energy-density (HED) plasmas offer a promising route to study astrophysically relevant processes underlying collisionless shock formation, magnetic field amplification, and particle acceleration in the laboratory. Using large-scale, multi-dimensional particle-in-cell simulations, we explore the interpenetration of laser-ablated counter-streaming plasmas for realistic experimental flow profiles. We find that the shock formation and its structure are substantially different from those of more idealized and commonly considered uniform flows: shock formation can be up to 10 times faster due to the transition from small-angle scattering to magnetic reflection and the shock front develops strong corrugations at the ion gyroradius scale. These findings have important consequences for current experimental programs and open exciting prospects for studying the microphysics of turbulent collisionless shocks with currently available high-energy laser systems.

Hydrodynamic holes and Froude horizons: Circular shallow water profiles for astrophysical analogs

Interesting analogies between shallow water dynamics and astrophysical phenomena have offered valuable insight from both the theoretical and experimental point of view. To help organize these efforts, here we analyze systematically the hydrodynamic properties of backwater profiles of the shallow water equations with 2D radial symmetry. In contrast to the more familiar 1D case typical of hydraulics, %already for {even in} isentropic conditions, a solution with minimum-radius horizon for the flow emerges, similar to the black hole and white hole horizons, where the critical conditions of unitary Froude number provide a unidirectional barrier for surface waves. Beyond these time-reversible solutions, a greater variety of cases arises, when allowing for dissipation by turbulent friction and shock waves (i.e., hydraulic jumps) for both convergent and divergent flows. The resulting taxonomy of the base-flow cases may serve as a starting point for a more systematic analysis of higher-order effects linked, e.g., to wave propagation and instabilities, capillarity, variable bed slope, and rotation.

Psychological First Aid: Experience of International Organizations

The turbulent shocks of recent decades—man-made and natural disasters, political instability, pandemics, and military conflicts—highlight the need for psychosocial support for victims. To plan and train those who can provide it, a number of guidelines have been developed at the global and national levels, within international medical organizations that can minimize the impact of the crisis and start the recovery process. The article presents the definition of the concept of Psychological First Aid (PFA), describes the key aspects, structure, time limits, and principles of activity; a description of three leading models of first psychological assistance in the context of international medical organizations: the World Health Organization (WHO), Doctors Without Borders (Médecins Sans Frontières, MSF), and the Johns Hopkins Center for Public Health Preparedness, USA. The RAPID model of first aid and key competencies for psychosocial workers involved in helping victims are described. The principles and techniques of PFA meet four basic standards: they are based on the results of research of risks and resilience after injury; they are practical and suitable for use in the “field”; they meet the age characteristics of development; they take into account cultural differences. The chronogram of mental reactions to a stressful event and the provision of PFA to victims within international medical organizations is divided into four phases which should be taken into account in the organization of psychosocial support. The RAPID model is based on five aspects designed to alleviate acute stress: Rapport and Reflective listening; Assessment of needs; Prioritization; Intervention; Disposition. If control over bodily reactions, emotions, and thoughts in the victims are restored, the narrative of the event is completed and accompanied by appropriate reactions, emotions are accepted, self-esteem and self-confidence are restored, and a sense of the future appears, we can say that the person has successfully adapted to the traumatic event and is ready to move on.

Impacts of grid turbulence on the side projection of planar shock waves

In this study, the characteristics of side-projected planar shock waves propagating through grid turbulence were investigated using a counter-driver shock tube. At the location of visualization of the shock–turbulence interactions, the range of the shock Mach numbers was $$M_{\mathrm {s}} = 1.01{-}1.15$$ and the representative values of the turbulent Mach numbers $$\widetilde{M_{\mathrm {t}}}$$ were $$ 0.005{-}0.014$$ . The interaction length between the shock wave and grid turbulence was in the range approximately from $$-50$$ to $$300$$ times the integral length scale of the turbulence. For the interaction involving the strongest turbulence with $$\widetilde{M_{\mathrm {t}}} = 0.014$$ , the weakest planar shock wave with $$M_{\mathrm {s}} = 1.01$$ was largely deformed and could not be detected on the projected shadowgraph and schlieren images. The density changes on the grayscale in the projected images of the shock waves weakened and expanded multidimensionally. This undetectable profile of the shock wave could indicate that the shock wave locally lost discontinuous property change profile. The shock waves with $$M_{\mathrm {s}} \ge 1.05$$ did not show the undetectable profile in the projected image. In these cases, the projected thickness of the shock wave increased with an increase in the interaction length. The increase in the projected thickness became larger as the turbulent Mach number increased, and the shock Mach number decreased.

Velocity and temperature fluctuations in a high-speed shock–turbulence interaction

Abstract

ЦИФРОВІ ГРАДІЄНТИ ЯК КЛЮЧОВІ АТРИБУТИ СТАНОВЛЕННЯ ОСВІТИ 5.0 ТА ІНДУСТРІЇ Х.0

The article substantiates digital competencies produced by Education 5.0 in order to form Industry X.0 in all sectors of the economy. Among digital competencies are the ability to work with digital content, communications, quality interaction, digital information literacy and the ability to work with data, digital security, the ability to solve technical problems independently. The peculiarities of the institutionalization of the Institute of Education 5.0, which takes place during the study of digital entrepreneurship, are indicated. A number of obstacles that slow down the implementation of quality training in digital entrepreneurship within the existing institute of education are considered, including the low level of inter-country cooperation of mentors-innovators, digital researchers and teachers involved in the implementation of training in digital entrepreneurship education with R&D departments of large corporations. 4.0 and Industry X.0. Author’s definite content of the categories “Industry X.0”, “attributes of Education 5.0”, “digital educational technologies”, “digital gradients”, “Institute of Education 5.0” is proposed. Authors consider Industry X.0 as a new approach to the organization of production, in conditions of institutional turbulence and economic shocks, based on highly intelligent integrated new products and digital ecosystems that form a fully innovative digital value chain, add new competencies and implement deep cultural changes in the direction of becoming a new virtual reality. The Institute of Education 5.0 recognizes, on the one hand, a system of ideas, rules, norms, standards of behavior of participants in educational activities in terms of teaching digital entrepreneurship, and on the other – a set of certain institutions, individuals provided with certain materials and attributes and perform relevant social functions during the implementation of teaching digital entrepreneurship. Attributes of Education 5.0 are considered as an integral property necessary to ensure the integrity of the object (subject) or subject (person), its part, application, ie we mean various digital educational technologies, tools, digital applications in terms of implementation educational process in digital entrepreneurship. Digital educational technologies/solutions at the Institute of Education 5.0 are proposed to be considered as various digital educational programs, applications, content (including video lectures, e-books), which are designed to achieve ambitious educational goals in terms of digital entrepreneurship or those that can used for these purposes.