Time-dependent Hydrodynamic Model Research Articles

Nanoflare Diagnostics from Magnetohydrodynamic Heating Profiles

Abstract The nanoflare paradigm of coronal heating has proven extremely promising for explaining the presence of hot, multi-million degree loops in the solar corona. In this paradigm, localized heating events supply enough energy to heat the solar atmosphere to its observed temperatures. Rigorously modeling this process, however, has proven difficult because it requires an accurate treatment of both the magnetic field dynamics and reconnection as well as the plasma response to magnetic perturbations. In this paper, we combine fully 3D magnetohydrodynamic (MHD) simulations of coronal active region plasma driven by photospheric motions with spatially averaged, time-dependent hydrodynamic (HD) modeling of coronal loops to obtain physically motivated observables that can be quantitatively compared with observational measurements of active region cores. We take the behavior of reconnected field lines from the MHD simulation and use them to populate the HD model to obtain the thermodynamic evolution of the plasma and subsequently the emission measure distribution. We find that the photospheric driving of the MHD model produces only very low-frequency nanoflare heating that cannot account for the full range of active region core observations as measured by the low-temperature emission measure slope. Additionally, we calculate the spatial and temporal distributions of field lines exhibiting collective behavior, and argue that loops occur due to random energization occurring on clusters of adjacent field lines.

Hydrodynamic simulation of InGaAs terahertz oscillations

Terahertz (THz) oscillations in n[Formula: see text]nn[Formula: see text] In[Formula: see text]Ga[Formula: see text]As diodes have been simulated with the use of a time-dependent hydrodynamic model. Under proper biased voltage and doping concentration, THz self-oscillations show up. The current self-oscillations originate from the formation and propagation of electric field domains in In[Formula: see text]Ga[Formula: see text]As diodes. The In[Formula: see text]Ga[Formula: see text]As device studied here may be presented as an excellent candidate as a solid-state THz source for monolithic integration.

Modeling of interactions between supernovae ejecta and aspherical circumstellar environments

Context. Massive stars are characterized by a significant loss of mass either via (nearly) spherically symmetric stellar winds or pre-explosion pulses, or by aspherical forms of circumstellar matter (CSM) such as bipolar lobes or outflowing circumstellar equatorial disks. Since a significant fraction of most massive stars end their lives by a core collapse, supernovae (SNe) are always located inside large circumstellar envelopes created by their progenitors. Aims. We study the dynamics and thermal effects of collision between expanding ejecta of SNe and CSM that may be formed during, for example, a sgB[e] star phase, a luminous blue variable phase, around PopIII stars, or by various forms of accretion. Methods. For time-dependent hydrodynamic modeling we used our own grid-based Eulerian multidimensional hydrodynamic code built with a finite volumes method. The code is based on a directionally unsplit Roe’s method that is highly efficient for calculations of shocks and physical flows with large discontinuities. Results. We simulate a SNe explosion as a spherically symmetric blast wave. The initial geometry of the disks corresponds to a density structure of a material that orbits in Keplerian trajectories. We examine the behavior of basic hydrodynamic characteristics, i.e., the density, pressure, velocity of expansion, and temperature structure in the interaction zone under various geometrical configurations and various initial densities of CSM. We calculate the evolution of the SN–CSM system and the rate of aspherical deceleration as well as the degree of anisotropy in density, pressure, and temperature distribution. Conclusions. Our simulations reveal significant asphericity of the expanding envelope above all in the case of dense equatorial disks. Our “low density” model however also shows significant asphericity in the case of the disk mass-loss rate Ṁcsd = 10−6 M⊙ yr−1. The models also show the zones of overdensity in the SN–disk contact region and indicate the development of Kelvin-Helmholtz instabilities within the zones of shear between the disk and the more freely expanding material outside the disk.

Hydrodynamic simulations of terahertz oscillation in double-layer graphene * * Project supported by the National Natural Science Foundation of China (No. 11604126).

We have theoretically studied current self-oscillations in double-layer graphene n+nn+ diodes driven by dc bias with the help of a time-dependent hydrodynamic model. The current self-oscillation results from resonant tunneling in the double-layer graphene structure. A detailed investigation of the dependence of the current self-oscillations on the applied bias has been carried out. The frequencies of current self-oscillations are in the terahertz (THz) region. The double-layer graphene n+nn+ device studied here may be presented as a THz source at room temperature.

Two-dimensional modeling of density and thermal structure of dense circumstellar outflowing disks

Context. Evolution of massive stars is affected by a significant loss of mass either via (nearly) spherically symmetric stellar winds or by aspherical mass-loss mechanisms, namely the outflowing equatorial disks. However, the scenario that leads to the formation of a disk or rings of gas and dust around massive stars is still under debate. It is also unclear how various forming physical mechanisms of the circumstellar environment affect its shape and density, as well as its kinematic and thermal structure. Aims. We study the hydrodynamic and thermal structure of optically thick, dense parts of outflowing circumstellar disks that may be formed around various types of critically rotating massive stars, for example, Be stars, B[e] supergiant (sgB[e]) stars or Pop III stars. We calculate self-consistent time-dependent models of temperature and density structure in the disk’s inner dense region that is strongly affected by irradiation from a rotationally oblate central star and by viscous heating. Methods. Using the method of short characteristics, we specify the optical depth of the disk along the line-of-sight from stellar poles. Within the optically thick dense region with an optical depth of τ > 2∕3 we calculate the vertical disk thermal structure using the diffusion approximation while for the optically thin outer layers we assume a local thermodynamic equilibrium with the impinging stellar irradiation. For time-dependent hydrodynamic modeling, we use two of our own types of hydrodynamic codes: two-dimensional operator-split numerical code based on an explicit Eulerian finite volume scheme on a staggered grid, and unsplit code based on the Roe’s method, both including full second-order Navier-Stokes shear viscosity. Results. Our models show the geometric distribution and contribution of viscous heating that begins to dominate in the central part of the disk for mass-loss rates higher than Ṁ ≳ 10−10 M⊙ yr−1. In the models of dense viscous disks with Ṁ > 10−8 M⊙ yr−1, the viscosity increases the central temperature up to several tens of thousands of Kelvins, however the temperature rapidly drops with radius and with distance from the disk midplane. The high mass-loss rates and high viscosity lead to instabilities with significant waves or bumps in density and temperature in the very inner disk region. Conclusions. The two-dimensional radial-vertical models of dense outflowing disks including the full Navier-Stokes viscosity terms show very high temperatures that are however limited to only the central disk cores inside the optically thick area, while near the edge of the optically thick region the temperature may be low enough for the existence of neutral hydrogen, for example.

Development of a thermal-hydraulic analysis code TAC-DS for spent fuel dry-storage system for high-temperature pebble bed reactor

ABSTRACT We report the development of a thermal-hydraulic analysis code (called TAC-DS: Thermal-hydraulic Analysis Code for Dry-storage System). The spent fuel dry-storage system of High-Temperature Reactor Pebble-bed Modules in China is simulated using the TAC-DS to confirm the design basis and to analyze the transient behavior following an accident involving blower failure. The TAC-DS includes mathematical models for the air-coolant system, heat conduction within spent fuel canisters, and thermal radiation between heat structures. The time-dependent hydrodynamic model of the TAC-DS is formulated using one-dimensional mass, momentum and energy equations, and solved using semi-implicit finite-difference scheme. The complicated heat transfer models of heat structure are incorporated into the hydrodynamic system implicitly with enclosure correlations. Code is written in Fortran 90. A validation calculation is performed by solving a simplified model. Thermal performance of the buffer storage region in the system under forced ventilation scenario is studied with TAC-DS to validate the design requirement, as well as to provide the initial condition for the transient analysis. Blower failure accident is studied to assess the performance of the safety features during the transient accident. Since the code is modular, TAC-DS can be easily modified and applied to other spent fuel dry-storage system in the future.

Hydrodynamic Modeling of the St. Lawrence Fluvial Estuary. I: Model Setup, Calibration, and Validation

In this study, a high-resolution, two-dimensional (2D), time-dependent hydrodynamic model of the St. Lawrence fluvial estuary was developed with the objective of documenting the tidal hydrodynamics of this complex yet poorly understood region. The hydrodynamic model solves the shallow-water equations over a finite-element–discretized domain, with an average spatial resolution of 50 m, and includes a drying–wetting component for the treatment of shallow intertidal areas. The numerical terrain model is composed of high-density topographic data and detailed friction fields associated with bottom substrate and macrophytes. Calibration and validation were carried out using recently acquired data for water level and velocity. Results show very good accuracy in water levels, with prediction skills higher than 0.99 at all stations (where a skill of 1 means perfect agreement between model and observations in terms of their relative average error) and root-mean-square errors (RMSEs) less than 5% of local tidal ranges downstream; at upstream stations where tidal ranges are significantly reduced, RMSEs were lower than 6 cm. Discharges were reproduced with similarly good accuracy, with errors lower than 6% of the maximum observed discharges at 11 of the 13 surveyed transects; the two remaining sections are subject to larger interpolation and bathymetric uncertainties. In this paper, critical aspects of model development are discussed, including the 2D approximation, temporal and spatial resolution, bathymetric uncertainty, error in the boundary conditions, and calibration under nonstationary conditions. This work is the first part of a two-part investigation serving as a methodological framework for model setup, calibration, and validation in large tidal rivers.

Hydrodynamic Modeling of the St. Lawrence Fluvial Estuary. II: Reproduction of Spatial and Temporal Patterns

This is the second part of an investigation aimed at documenting the tidal hydrodynamics of the St. Lawrence fluvial estuary (SLFE). In Part I, the calibration and validation of a high-resolution, two-dimensional (2D), time-dependent hydrodynamic model of the SLFE was presented. Herein, the process-based (structural) validation procedure used to quantitatively assess the ability of the model to reproduce spatial and temporal patterns observed in the field data is presented. Tidal and flow features were found to be reproduced satisfactorily in terms of their lateral and longitudinal variability at both the intratidal and fortnightly scales. These properties can be used to describe the real system dynamics, including flooding–drying processes, tidal propagation and modulation, and transient momentum balance, providing insights into the general physical processes of the SLFE and of large tidal rivers globally.

Time-dependent modeling of extended thin decretion disks of critically rotating stars

During their evolution massive stars can reach the phase of critical rotation when a further increase in rotational speed is no longer possible. Direct centrifugal ejection from a critically or near-critically rotating surface forms a gaseous equatorial decretion disk. Anomalous viscosity provides the efficient mechanism for transporting the angular momentum outwards. The outer part of the disk can extend up to a very large distance from the parent star. We study the evolution of density, radial and azimuthal velocity, and angular momentum loss rate of equatorial decretion disks out to very distant regions. We investigate how the physical characteristics of the disk depend on the distribution of temperature and viscosity. We calculated stationary models using the Newton-Raphson method. For time-dependent hydrodynamic modeling we developed the numerical code based on an explicit finite difference scheme on an Eulerian grid including full Navier-Stokes shear viscosity. The sonic point distance and the maximum angular momentum loss rate strongly depend on the temperature profile and are almost independent of viscosity. The rotational velocity at large radii rapidly drops accordingly to temperature and viscosity distribution. The total amount of disk mass and the disk angular momentum increase with decreasing temperature and viscosity. The time-dependent one-dimensional models basically confirm the results obtained in the stationary models as well as the assumptions of the analytical approximations. Including full Navier-Stokes viscosity we systematically avoid the rotational velocity sign change at large radii. The unphysical drop of the rotational velocity and angular momentum loss at large radii (present in some models) can be avoided in the models with decreasing temperature and viscosity.

TEMPORAL EVOLUTION OF THE SCATTERING POLARIZATION OF THE Ca II IR TRIPLET IN HYDRODYNAMICAL MODELS OF THE SOLAR CHROMOSPHERE

Velocity gradients in a stellar atmospheric plasma have an impact on the anisotropy of the radiation field that illuminates each point within the medium, and this may in principle influence the scattering line polarization that results from the induced atomic level polarization. Here we analyze the emergent linear polarization profiles of the Ca II infrared triplet after solving the radiative transfer problem of scattering polarization in time-dependent hydrodynamical models of the solar chromosphere, taking into account the impact of the plasma macroscopic velocity on the atomic level polarization. We discuss the influence that the velocity and temperature shocks in the considered chromospheric models have on the temporal evolution of the scattering polarization signals of the Ca II infrared lines, as well as on the temporally averaged profiles. Our results indicate that the increase of the linear polarization amplitudes caused by macroscopic velocity gradients may be significant in realistic situations. We also study the effect of the integration time, the microturbulent velocity and the photospheric dynamical conditions, and discuss the feasibility of observing with large-aperture telescopes the temporal variation of the scattering polarization profiles. Finally, we explore the possibility of using the differential Hanle effect in the IR triplet of Ca II with the intention of avoiding the characterization of the zero-field polarization to infer magnetic fields in dynamic situations.

Clumped stellar winds in supergiant high-mass X-ray binaries

AbstractThe clumping of massive star winds is an established paradigm, which is confirmed by multiple lines of evidence and is supported by stellar wind theory. We use the results from time-dependent hydrodynamical models of the instability in the line-driven wind of a massive supergiant star to derive the time-dependent accretion rate on to a compact object in the Bondi-Hoyle-Lyttleton approximation. The strong density and velocity fluctuations in the wind result in strong variability of the synthetic X-ray light curves. Photoionization of inhomogeneous winds is different from the photoinization of smooth winds. The degree of ionization is affected by the wind clumping. The wind clumping must also be taken into account when comparing the observed and model spectra of the photoionized stellar wind.

Numerical modeling of hydrodynamic and hydrothermal characteristics in subtropical alpine lake

A three-dimensional, time-dependent hydrodynamic and hydrothermal model was performed and applied to the subtropical alpine Yuan-Yang Lake (YYL) in northeastern region of Taiwan. The model was driven with discharge inflow, heat, and wind stress to simulate the hydrodynamic and hydrothermal in the lake. The model was validated with measured water surface elevation, current, and temperature in 2008. The overall model simulation results are in quantitative agreement with the available field data. The validated model was then used to investigate wind-driven current, mean circulation, and residence time in the YYL. The modeling results reveal that the velocity field along the wind axis present the variations over depth with return current where the velocity at the surface layer is along the wind direction while it is opposite near 1 m below water surface. The simulated mean current indicates that the surface currents flow towards the southwest direction and form a clock-wise rotation. The calculated residence time is strongly dependent on the inflows and wind effects. Regression analysis of model results reveals that an exponential regression equation can be employed to correlate the residence time to change of discharge input. The residence time without wind stress is higher than that with wind effect, indicating that wind plays an important role in lake mixing. The calculated residence time is approximately 2–2.5 days under low inflow with wind effect.

Different turbulence models for stratified flow and salinity

This paper documents a numerical modelling study to calculate the residual current and salinity distributions in a partially mixed estuary. A three-dimensional, time-dependent hydrodynamic model, ELCRIC, was performed and applied to the Danshuei River estuarine system and the adjacent coastal sea in Taiwan. The model experiments were conducted with different turbulence closure models and background diffusivities. Little difference was found in the results of the model with four turbulence closure schemes (k−kl, k−ε, k−ω, and UB (i.e. Umlauf and Burchard)). However, the predictive results reveal that the stratification and residual circulation are sensitive to changes in background diffusivity when the value of the background diffusivity is greater than 10−4 m2/s. The model was then verified using data for water surface elevation, tidal current and salinity measured in 2002 with different turbulence closure schemes and background diffusivities. Overall, the model simulation results were in reasonable agreement with time-series observations of water surface elevation and tidal currents. Among the schemes explored, the k−kl scheme with a background diffusivity of 10−5 m2/s provides the best simulations of the salinity time-series. Both the model experiments and the model/data comparisons highlight the importance of providing a more realistic parameterisation for turbulence mixing in the Danshuei River estuary. However, more detailed observations of the salinity time-series in different layers and locations are required to improve turbulence closures and for proper parameterisation.

Radiative transfer with scattering for domain-decomposed 3D MHD simulations of cool stellar atmospheres

We present the implementation of a radiative transfer solver with coherent scattering in the new BIFROST code for radiative magneto-hydrodynamical (MHD) simulations of stellar surface convection. The code is fully parallelized using MPI domain decomposition, which allows for large grid sizes and improved resolution of hydrodynamical structures. We apply the code to simulate the surface granulation in a solar-type star, ignoring magnetic fields, and investigate the importance of coherent scattering for the atmospheric structure. A scattering term is added to the radiative transfer equation, requiring an iterative computation of the radiation field. We use a short-characteristics-based Gauss-Seidel acceleration scheme to compute radiative flux divergences for the energy equation. The effects of coherent scattering are tested by comparing the temperature stratification of three 3D time-dependent hydrodynamical atmosphere models of a solar-type star: without scattering, with continuum scattering only, and with both continuum and line scattering. We show that continuum scattering does not have a significant impact on the photospheric temperature structure for a star like the Sun. Including scattering in line-blanketing, however, leads to a decrease of temperatures by about 350\,K below log tau < -4. The effect is opposite to that of 1D hydrostatic models in radiative equilibrium, where scattering reduces the cooling effect of strong LTE lines in the higher layers of the photosphere. Coherent line scattering also changes the temperature distribution in the high atmosphere, where we observe stronger fluctuations compared to a treatment of lines as true absorbers.

Numerical Parametric Study of the Capillary Plasma Source for Electrothermal–Chemical Guns

This work expands upon previous research into developing a numerical model of a capillary plasma source for application to electrothermal chemical guns. The capillary model is comprised of a kinetic model simulating polyethylene ablation coupled to a one dimensional time-dependent hydrodynamic model to determine the capillary outflow parameters. As input the simulation requires the capillary internal radius, length, and applied electrical current. Previous work found that best agreement with experimentally measured ablated mass could be achieved with the application of a backflux parameter, representing the percentage of the ablated material that was allowed to return to the polyethylene surface and form a film. Using the model, a parameter study is conducted to determine the effects that varying the peak electrical current, internal capillary radius and backflux parameter have on the plasma temperature, peak outflow pressure, and total ablated mass. A sinusoidal electrical current is assumed in the present work, with the peak current and discharge time taken over a range typically encountered in electrothermal chemical gun application. Analysis of the dependence of total ablated mass and peak capillary pressure on the deposited electrical energy yield insight into non- linearities in the capillary energy equation.

Modeling of salinity intrusion under different hydrological conditions in the Arvand River Estuary

Arvand River Estuary is the most important inland water body of Iran and its discharge has been reduced in the last decades due to construction of several dams. Hence, a two-dimensional laterally averaged time dependent hydrodynamic and water quality model called CE-QUAL-W2 was applied to this estuary to assess the impacts of river discharge reduction. The model was first implemented with three different closure schemes for parameterization of vertical transport of mass and momentum. It was found that the W2N scheme performs better than the other schemes in predicting the vertical salinity structure. The model was then used for prediction of salinity intrusion in different hydrological conditions and a simple equation was obtained for estimation of the intrusion length as a function of upstream freshwater discharge.

Modeling diagnosis of suspended sediment transport in tidal estuarine system

A three-dimensional, time-dependent hydrodynamic and suspended sediment transport model was performed and applied to the Danshuei River estuarine system and adjacent coastal sea in northern Taiwan. The model was validated with observed time-series salinity in 2001, and with salinity and suspended sediment distributions in 2002. The predicted results quantitatively agreed with the measured data. A local turbidity maximum was found in the bottom water of the Kuan-Du station. The validated model then was conducted with no salinity gradient, no sediment supply from the sediment bed, wind stress, and different freshwater discharges from upstream boundaries to comprehend the influences on suspended sediment dynamics in the Danshuei River estuarine system. The results reveal that concentrations of the turbidity maximum simulated without salinity gradient are higher than those of the turbidity maximum simulated with salinity gradient at the Kuan-Du station. Without bottom resuspension process, the estuarine turbidity maximum zone at the Kuan-Du station vanishes. This suggests that bottom sediment resuspension is a very important sediment source to the formation of estuarine turbidity maximum. The wind stress with northeast and southwest directions may contribute to decrease the suspended sediment concentration. When the freshwater discharges increase at the upstream boundaries, the limits of salt intrusion pushes downriver toward river mouth. Suspended sediment concentrations increase at the upriver reaches in the Danshuei River to Tahan Stream, while decrease at Kuan-Du station.

Numerical determination of residence time and age in a partially mixed estuary using three-dimensional hydrodynamic model

This paper documents a numerical modeling study to calculate the residence time and age of dissolved substances in a partially mixed estuary. A three-dimensional, time-dependent hydrodynamic model was established and applied to the Danshuei River estuarine system and adjacent coastal sea in Taiwan. The model showed good agreement with observations of surface elevation, tidal currents and salinity made in 2002. The model was then applied to calculate the residence time and age distribution response to different freshwater discharges with and without density-induced circulations in the Danshuei River estuarine system. Regression analysis of model results reveals that an exponential equation can be used to correlate the residence time to change of freshwater input. The simulated results show it takes approximately 10, 4.5, and 3 days, respectively, for a water parcel that has entered the headwaters of the estuary to be transported out of the estuary under low, mean, and high flow conditions with density-induced circulation. The calculated age with density-induced circulation is less than that without density-induced circulation. The age of the surface layer is less than that at the bottom layer. Overall the study shows that freshwater discharges are the important factors in controlling the transport of dissolved substances in the Danshuei River estuarine system.

Modeling residence time response to freshwater discharge in a mesotidal estuary, Taiwan

A three-dimensional, time-dependent hydrodynamic model, SELFE, was performed and applied to the Danshuei River estuarine system and adjacent coastal sea in Taiwan. The model forcing functions consist of tidal elevations along the open boundary and freshwater flows from the main stem and tributaries in the Danshuei River system. The model was calibrated and verified with measured water surface elevation, tidal current, residual current, and salinity in 2000 and 2001, respectively. The overall model simulation results are in qualitative agreement with the available field data. The validated model was then used to probe the salinity response to the pulse of high freshwater discharge and residence time in the Danshuei River estuary. The modeling results show that salinity recovers to normal conditions in about 14 days at the Kuan-Du Bridge, 22 days at the Taipei Bridge, and 30 days at both Hwa-Jian Bridge and Pa-Ling Bridge. Regression analysis of model results reveals that an exponential regression equation can be used to correlate the estuarine residence time to change of freshwater input. A short residence time exhibits in the Danshuei River estuary. The simulated results provide useful information for understanding the transport processes and can be employed to estimate dissimilative capacity in the estuary.

Calculation of the energetic neutral atom flux from a 3D time-dependent model heliosphere

With the Interstellar Boundary Explorer (IBEX) the measurement of energetic neutral atoms (ENAs) will enable a remote sensing of the heliospheric boundary region where the solar wind plasma flow meets the interstellar medium. Together with Voyager 1 (& 2) in (and at least near) the healiosheath there will be a very fortunate instrument configuration in space that will allow us to obtain valuable information about the large-scale structure and dynamics of the heliosphere. Following ongoing theoretical discussions we have computed all-sky maps of the differential flux of ENAs produced from charge exchange with solar wind protons in a three-dimensionally structured and time-varying heliosheath. We employ a three-dimensional, time-dependent hydrodynamic model heliosphere to compute the production of ENAs by a generalisation of previous two-dimensional approaches. We find three-dimensionally structured all-sky ENA flux maps that are time-varying due to the solar activity cycle. While the study adds to the complexity of the task to correctly interpret the forthcoming measurements to be made with IBEX, it underlines the potential of this mission to significantly increase our understanding of the structure and dynamics of the heliosphere.