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At least 397 records · Page 22

Quantifying Contributions of Land Carbon Fluxes Variability and Atmospheric Transport Variability to Atmospheric CO2 Variability

Much of the uncertainty in predicting variations in greenhouse gases originates in the complex dynamics of the land ecosystem and the atmosphere. To reduce the uncertainties, it is useful to decouple the contributions of land carbon fluxes and atmospheric transport to atmospheric carbon variability. Here we isolate these contributions using a version of the NASA GEOS model that couples carbon, energy and water cycles between the land and the atmosphere. Our current study is a follow-on to a preliminary analysis that suggested that an extreme event (e.g., imposed drought) in a free running AGCM simulation affects atmospheric CO2 more through its impact on atmospheric transport than through a modification of land carbon fluxes. In order to more carefully isolate the effects of the land carbon variability and atmospheric transport variability on atmospheric CO2 variability, we conducted two coupled-AGCM simulations in replay mode, a mode that forces the model's evolution of weather to match that of the MERRA-2 reanalysis. In the control simulation, the land carbon fluxes and the atmospheric CO2 concentrations, as well as the meteorology, are simulated over 2001-2015. We compute the climatological seasonal cycles of net land carbon production from this control simulation and then prescribe, in a second simulation, these climatological carbon fluxes to the atmosphere in the same replay mode. By comparing the atmospheric CO2 variability produced in the two simulations, we fully isolate the part of this variability associated with land surface fluxes. Relative contributions of land flux variability and atmospheric transport variability to CO2 variability are quantified both on a regional basis and as a function of height into the atmosphere to support interpretation of both ground-based and satellite observations.

Lee, Eunjee↗

Magnetic Flux Cancelation as the Buildup and Trigger Mechanism for CME-Producing Eruptions in two Small Active Regions

We follow two small, magnetically isolated CME-producing solar active regions (ARs) from the time of their emergence until the time that their core regions erupt to produce the CMEs several days later. In both cases, magnetograms show: (a) following an initial period where the poles of the emerging regions separate from each other, the poles then reverse direction and start to retract inward; (b) during the retraction period, flux cancelation occurs along the main neutral line of the regions, (c) this cancelation builds the sheared core field/flux rope that eventually erupts to make the CME. In the two cases, respectively 30% and 50% of the maximum flux of the region cancels prior to the eruption. Recent studies indicate that solar coronal jets frequently result from small-scale filaments eruptions, with those “minifilament” eruptions also being built up and triggered by cancelation of magnetic flux. Together, the small-AR eruptions here and the coronal jet results suggest that isolated bipolar regions tend to erupt before or when a threshold of roughly 50% of the region’s maximum flux has canceled. Our observed erupting filaments/flux ropes form at sites of flux cancelation, in agreement with previous observations. Thus, the recent finding that minifilaments that erupt to form jets also form via flux cancelation is further evidence that minifilaments are small-scale versions of the long-studied full-sized filaments.

Sterling, Alphonse C.↗

Afterbody Heat Flux Measurements in the NASA Ames HFFAF Ballistic Range

In order to measure afterbody heat fluxes over a model in the ballistic range, the required modifications to a proven technique for measuring forebody heat fluxes are described. This involves the use of an extended helium gas plume to remove the glowing wake and the use of special high conductivity, high temperature capable graphite-filled plastic for the afterbody. The models and test conditions are described. Data in the form of plots of the surface temperature of the models are presented. Finally, experimental and computational fluid dynamic (CFD) heat flux data for forebody and afterbody heat fluxes are presented and compared. Data are presented for a 45 degree sphere-cone (with a projecting rear stud) at 2.70 km/s and for a sphere at 4.76 km/s. Both models were launched into 76 Torr of CO2 gas. The experimental forebody heat fluxes were within 1.5% of the CFD values. The experimental afterbody heat fluxes were within 1% of the CFD values for the sphere, but only 51% of the CFD values for the sphere-cone.

Bogdanoff, David W.↗

Magnetic Flux Cancelation as the Buildup and Trigger Mechanism for CME-Producing Eruptions in Two Small Active Regions

We follow two small, magnetically isolated CME (Coronal Mass Ejection)-producing solar active regions (ARs) from the time of their emergence until several days later, when their core regions erupt to produce the CMEs. In both cases, magnetograms show: (a) following an initial period where the poles of the emerging regions separate from each other, the poles then reverse direction and start to retract inward; (b) during the retraction period, flux cancelation occurs along the main neutral line of the regions, (c) this cancelation builds the sheared core field/flux rope that eventually erupts to make the CME. In the two cases, respectively 30 percent and 50 percent of the maximum flux of the region cancels prior to the eruption. Recent studies indicate that solar coronal jets frequently result from small-scale filaments eruptions (Sterling et al. 2015), with those “minifilament” eruptions also being built up and triggered by cancelation of magnetic flux (Panesar et al. 2016). Together, the small-AR eruptions here and the coronal jet results suggest that isolated bipolar regions tend to erupt when some threshold fraction, perhaps in the range of 50 percent, of the region’s maximum flux has canceled. Our observed erupting filaments/flux ropes form at sites of flux cancelation, in agreement with previous observations. Thus, the recent finding that minifilaments that erupt to form jets also form via flux cancelation is further evidence that minifilaments are small-scale versions of the long-studied full-sized filaments. (Details are in Sterling et al. 2018, ApJ, 864, 68.) Supported by NASA's Heliophysics Guest Investigators (HGI) Program and the MSFC (Marshall Space Flight Center)/Hinode project.

Sterling, Alphonse C.↗

Estimating Total Open Heliospheric Magnetic Flux

Over the solar-activity cycle, there are extended periods where significant discrepancies occur between the spacecraft-observed total (unsigned) open magnetic flux and that determined from coronal models. In this article, the total open heliospheric magnetic flux is computed using two different methods and then compared with results obtained from insitu interplanetary magnetic-field observations. The first method uses two different types of photospheric magnetic-field maps as input to the Wang–Sheeley–Arge (WSA) model: i) traditional Carrington or diachronic maps, and ii) Air Force Data Assimilative Photospheric Flux Transport model synchronic maps. The second method uses observationally derived helium and extreme-ultraviolet coronal-hole maps overlaid on the same magnetic-field maps in order to compute total open magnetic flux. The diachronic and synchronic maps are both constructed using magnetograms from the same source, namely the National Solar Observatory Kitt Peak Vacuum Telescope and Vector Spectromagnetograph. The results of this work show that the total open flux obtained from observationally derived coronal holes agrees remarkably well with that derived from WSA, especially near solar minimum. This suggests that, on average, coronal models capture well the observed large-scale coronal-hole structure over most of the solar cycle. Both methods show considerable deviations from total open flux deduced from spacecraft data, especially near solar maximum, pointing to something other than poorly determined coronal-hole area specification as the source of these discrepancies.

Wallace, S.↗

Results of Use of Heat Flux Sensors on Liquid Hydrogen Tanks

Heat flux sensors were used to characterize the performance of insulation on the Structural Heat Intercept, Insulation, and Vibration Evaluation Rig (SHIIVER), a large-scale test article designed to simulate upper stage cryogenic propellant tank thermal performance in simulated space environments. Usually, the insulation heat loads are derived from calculations removing all other heat sources and attributing the residual heat load to the insulation system. Testing for SHIIVER included the tank being just insulated with spray-on-foam insulation as well as covering the domes with multilayer insulation while leaving the barrel section insulated with spray-on-foam. Heat flux sensors were located at multiple locations on both domes as well as on the barrel section of the tank. Results from the SHIIVER testing using the heat flux sensors are compared to other calculated heat inputs for both liquid nitrogen and liquid hydrogen testing as a function of tank fill level. Further investigation into the transient nature of the SHIIVER testing including the heat flux sensors provided insight into heat flow patterns that may not have been otherwise seen using temperature sensors and calculated insulation heat loads. While the demonstrated uncertainties in the absolute values in the heat flux sensors are high, the values and the trends match well with other calculation methods. The results of SHIIVER allow for the use of heat flux sensors for measurements of insulation performance and dynamic system thermal response for future applications.

Cryogenic Fluid Management↗

Results of Use of Heat Flux Sensors on Liquid Hydrogen Tanks

ABSTRACT: Heat flux sensors were used to characterize the performance of insulation on the Structural Heat Intercept, Insulation, and Vibration Evaluation Rig (SHIIVER), a large-scale test article designed to simulate upper stage cryogenic propellant tank thermal performance in simulated space environments. Usually, the insulation heat loads are derived from calculations removing all other heat sources and attributing the residual heat load to the insulation system. Testing for SHIIVER included the tank being just insulated with spray-on-foam insulation as well as covering the domes with multilayer insulation while leaving the barrel section insulated with spray-on-foam. Heat flux sensors were located at multiple locations on both domes as well as on the barrel section of the tank. Results from the SHIIVER testing using the heat flux sensors are compared to other calculated heat inputs for both liquid nitrogen and liquid hydrogen testing as a function of tank fill level. Further investigation into the transient nature of the SHIIVER testing including the heat flux sensors provided insight into heat flow patterns that may not have been otherwise seen using temperature sensors and calculated insulation heat loads. While the demonstrated uncertainties in the absolute values in the heat flux sensors are high, the values and the trends match well with other calculation methods. The results of SHIIVER allow for the use of heat flux sensors for measurements of insulation performance and dynamic system thermal response for future applications.

Cryogenic Fluid Management↗

Improving the CERES SYN Cloud and Flux Products by Identifying GOES-17 Scan Anomalies Using a Convolutional Neural Network

The NASA Clouds and the Earth’s Radiant Energy System (CERES) project relies on top-of-atmosphere (TOA) broadband fluxes derived from geostationary (GEO) satellite imagery to account for the diurnal flux variations between the CERES observation intervals, and thereby produce a synoptic gridded (SYN1deg) product based on continuous temporal observations. Consistent broadband flux derivation depends on accurate radiative property measurements and cloud retrievals, which largely determine the radiance-to-flux conversion process. Therefore, it is important to ensure a high quality of cloud property input in order to maintain a reliable broadband flux record. In Edition 4 of the CERES SYN1deg product, a robust automated image anomaly detection algorithm based on inter-line and inter-pixel differences, spatial variance, and 2-D Fourier analysis has been successful in identifying imagery with linear artifacts, but the line-by-line inspection and cleaning process must still be performed by a human. Therefore, further automation of this quality assurance process is warranted, especially considering the excessive amount of additional cleaning necessitated by the GOES-17 Advance Baseline Imager (ABI) cooling system anomaly. As such, this article highlights advancement of the CERES GEO image artifact cleaning approach based on a convolutional neural network (CNN) for classification of bad scanlines. Once trained, the CNN approach is a computationally inexpensive means to ensure greater consistency in cloud retrievals, and therefore broadband flux derivation, based on GOES-17 measurements.

Benjamin Scarino↗

Evaluating CERES TOA Fluxes using ARISE aircraft observations

Uncertainty in observations of top-of-atmosphere (TOA) radiation fluxes are larger in the Arctic than in other regions. The magnitude of these uncertainties limit our understanding of the Arctic surface energy budget and its variability. The significant uncertainties are due to the low sun angles and wide range of highly reflecting, anisotropic, and highly heterogeneous surface conditions. Therefore, quantifying, attributing, and reducing Arctic TOA radiative flux uncertainty enables a better understanding of the rapidly changing Arctic. To advance this goal, we compare the Cloud and Earth’s Radiant Energy System (CERES) TOA radiative fluxes with measurements from the Arctic Radiation-IceBridge Sea and Ice Experiment (ARISE) flow in September 2014. A key objective of ARISE was to evaluate and attribute uncertainty in CERES footprint and gridded TOA radiative fluxes. In this study, we first compare the CERES TOA flux with those obtained from the broadband radiometer measurements from the aircraft using instantaneously matched footprint with the flight track and as the hourly gridded fluxes. This comparison indicates an agreement within uncertainty in the longwave (2 Wm-2 ) for all five grid boxes and agreement in the shortwave (10 Wm-2) for four-out-of-five grid boxes. While not a statistically significant results given the small sample size, the hourly, gridded and the instantaneously matched footprint comparison suggest a -10 Wm-2 bias for CERES in the shortwave. To explore whether this is a robust feature or a statistical artifact, we quantify the individual sources of uncertainty in the differences (temporal and spatial sampling differences, scene evolution, accuracy, angular distribution models, and scene id) to see if any of these differences account for the shortwave bias.

CERES↗

NASA/GEWEX SRB Surface Radiation Budget Fluxes Through the Prism of Weather States

The NASA/GEWEX Surface Radiation Budget Version 4 (SRB Rel4) product is now publicly available, covering the period from July 1983 through June 2017. This supersedes the SRB Rel3 (Stackhouse et al., 2011) product which has been used in the community for a wide variety of applications, including climate model validation, agriculture, solar energy, and architecture. SRB Rel4 uses the newly recalibrated and processed ISCCP HXS product as its primary input for cloud and radiance data, replacing ISCCP DX with a ninefold increase in pixel count (10km instead of 30km). This version retains a 1°x1° resolution but benefits from a much larger number of samples per grid box than the SRB Rel3. ISCCP also provides an atmospheric temperature and moisture dataset known as nnHIRS which we use here, along with Seaflux and Landflux surface and near-surface meteorological parameters. Rel4 incorporates several important algorithm improvements. These include recalculated shortwave (SW) atmospheric transmissivities and reflectivities yielding a somewhat less transmissive atmosphere. Both shortwave and longwave (LW) now also include variable aerosol composition and radiative properties, allowing for the use of a detailed aerosol history from the Max Planck Institute Aerosol Climatology (MACv1). LW and SW algorithms now produce pristine sky fluxes, allowing the aerosol flux effects to be quantified. For SW, ocean albedo and snow/ice albedo are improved from Release 3. Total solar irradiance is now variable, and reduced to an average of 1361 Wm-2. The radiative treatment of ice cloud is improved. For the LW, a climatological monthly varying spectral surface emissivity is added. Here we evaluate the SRB Rel4 top of atmosphere (TOA) and surface fluxes in the context of weather states and oceanic regions. Weather states (Tselioudis et al., 2013, Tselioudis et al., 2021) are defined by K-means clustering 2-D histograms of satellite-retrieved cloud optical depths and cloud top pressures. The most recent (Tselioudis et al., 2021) weather states derived from the International Satellite Cloud Climatology Project (ISCCP) H-series data results in eight cloud weather states and one clear sky weather state, for a total of nine weather states. We examine the statistics of SRB Rel4 fluxes for each weather state and a variety of relevant land and ocean regions. We compare to similar analyses performed on CERES EBAF and SYN1Deg flux products, and validate against Baseline Surface Radiometer Network (BSRN) land stations and Pacific Marine Environmental Laboratory (PMEL) ocean buoy data. It is demonstrated that the weather state concept is valuable when examining the comparative strengths and weaknesses of satellite radiative flux algorithms.

Atmospheric Radiation↗

Assessing Uncertainties and Variability 34 Years of Surface Radiative Fluxes Using GEWEX SRB Release4-IP

The NASA/GEWEX Surface Radiation Budget (SRB) project produces 3-hrly shortwave and longwave surface and top of atmosphere radiative fluxes for the 1983-near present time period. The new Release 4 Integrated Product (IP) uses the newly recalibrated and processed ISCCP HXS product as its primary input for cloud and radiance data, replacing ISCCP DX with a ninefold increase in pixel count (10 km instead of 30 km). This first version retains a 1°x1° resolution enabling intercomparison against previous versions and other data sets such as CERES, but spans 34 years from July 1983 through June 2017 and was announced by Kummerow et al. 2019 (GEWEX News). This new IP product also uses an atmospheric temperature and moisture dataset known as nnHIRS and other parameters such as near surface and skin temperatures from SeaFlux and LandFlux data sets. In addition to the input data improvements, several important algorithm improvements have been made since Release 3. These include recalculated SW atmospheric transmissivities and reflectivities, updated ocean and snow/ice albedos, and variable total solar irradiance consistent with SORCE measurements. The LW code has been updated to improve the optical property treatment for clouds and aerosols are included in this version. Radiative treatment of ice clouds is also improved in the LW. The variable aerosol optical properties for the SW and LW are specified using a detailed aerosol history from the Max Planck Institute Aerosol Climatology (MAC). Here we present an assessment of the LW radiative fluxes and the uncertainty of those fluxes relative to the various inputs to surface SW/LW flux measurements from BSRN and PMEL buoys measurements. We review the validation of the SW and LW fluxes and then in terms of time series and then assess the products in terms of their long-term variability of the surface SW and LW net fluxes compared to multiple other data products including atmospheric reanalysis products. The comparisons of radiative estimates to observations are performed at various temporal scales and aimed at investigation of agreement at longer time averages but accessing potential change in diurnal magnitude and daily variability. Utilizing this uncertainty information, to access long-term variability of surface radiation components at selected region and global scales, considering satellite sampling/calibration “artifacts” as necessary. At the longer time scales, the net SW and net LW the TOA and surface have implications toward closure of the energy budgets at the surface, we assess these compared to other studies on energy budget closure for the same selected global and regional scales.

Paul W Stackhouse↗

Magnetic Reconnection in a Sheared Magnetic Flux Tube: Slippage Versus Tearing

The process of magnetic reconnection in a flux tube can occur in a time-stationary fashion as slippage reconnection or in a time-dependent manner based on, for example, the tearing instability. However, it is not well known under which conditions a system can sustain slippage reconnection. Likewise, it is unclear whether systems can exhibit slippage reconnection and time-dependent reconnection simultaneously. In order to investigate these questions, we employ a set of 3D magnetohydrodynamic simulation. Using these simulations, we model a twisted flux tube with a spatially localized resistive region in the center of the simulation box, and an applied driver on one end plane of the simulation box. As a result, the Poynting flux injected at the boundary propagates to the resistive region and dissipates there. If the driver is nearly circular, we find a predominance of slippage reconnection, which decouples the applied driver entirely from one half of the flux tube. Second, a tearing-like instability occurs with slippage reconnection in the resistive region when the resistivity is strong enough and the cross section of the flux tube, as defined by the shape of the applied velocity perturbation, is elliptical enough. In this case we find the surprising feature that magnetic field perturbation generated by the tearing-like instability radiates away from the resistive region to influence the entire flux tube shape.

Hidetaka Kuniyoshi↗

Distorted-Toroidal Flux Rope Model

The 3D characterization of magnetic flux ropes observed in the heliosphere has been a challenging task for decades. This is mainly due to the limitations on inferring the 3D global topology and physical properties from the 1D time series from any spacecraft. To advance our understanding of magnetic flux ropes whose configuration departs from the typical stiff geometries, here we present an analytical solution for a 3D flux rope model with an arbitrary cross section and a toroidal global shape. This constitutes the next level of complexity following the elliptic-cylindrical (EC) geometry. The mathematical framework was established by Nieves-Chinchilla et al. with the EC flux rope model, which describes a magnetic topology with an elliptical cross section as a first approach to changes in the cross section. In the distorted-toroidal flux rope model, the cross section is described by a general function. The model is completely described by a nonorthogonal geometry and the Maxwell equations can be consistently solved to obtain the magnetic field and relevant physical quantities. As a proof of concept, this model is generalized in terms of the radial dependence of current density components. The last part of this paper is dedicated to a specific function, F (φ) = δ (1 - λ cosφ), to illustrate possibilities of the model. This model paves the way toward the investigation of complex distortions of magnetic structures in the solar wind. Future investigations will explore these distortions in depth by analyzing specific events; studying implications for physical quantities, such as magnetic fluxes, helicity, or energy; and evaluating the force balance with the ambient solar wind that allows such distortions.

Solar wind↗

(abstract) Monitoring Seasonal State and Mapping Species in Alaskan Taiga Using Imaging Radar as Input to CO(sub 2) Flux Models

Changes in the seasonal CO(sub 2) flux of the boreal forests may result from increased atmospheric CO(sub 2) concentrations and associated atmospheric warming. To monitor this potential change, a combination of remote sensing information and ecophysiological models are required. In this paper we address the use of synthetic aperture radar (SAR) data to provide some of the input to the ecophysiological models: forest type, freeze/thaw state which limits the growing season for conifers, and leaf on/off state which limits the growing season for deciduous species. AIRSAR data collected in March 1988 during an early thaw event and May 1991 during spring breakup are used to generate species maps and to determine the sensitivity of SAR to canopy freeze/thaw transitions. These data are also used to validate a microwave scattering model which is then used to determine the sensitivity of SAR to leaf on/off and soil freeze/thaw transitions. Finally, a CO(sub 2) flux algorithm which utilizes SAR data and an ecophysiological model to estimate CO(sub 2) flux is presented. CO(sub 2) flux maps are generated from which areal estimates of CO(sub 2) flux are derived.

leaf cover boreal forests radar backscatter↗

Impacts of Soil-aquifer Heat and Water Fluxes on Simulated Global Climate

Climate models have traditionally only represented heat and water fluxes within relatively shallow soil layers, but there is increasing interest in the possible role of heat and water exchanges with the deeper subsurface. Here, we integrate an idealized 50m deep aquifer into the land surface module of the GISS ModelE general circulation model to test the influence of aquifer-soil moisture and heat exchanges on climate variables. We evaluate the impact on the modeled climate of aquifer-soil heat and water fluxes separately, as well as in combination. The addition of the aquifer to ModelE has limited impact on annual-mean climate, with little change in global mean land temperature, precipitation, or evaporation. The seasonal amplitude of deep soil temperature is strongly damped by the soil-aquifer heat flux. This not only improves the model representation of permafrost area but propagates to the surface, resulting in an increase in the seasonal amplitude of surface air temperature of >1K in the Arctic. The soil-aquifer water and heat fluxes both slightly decrease interannual variability in soil moisture and in landsurface temperature, and decrease the soil moisture memory of the land surface on seasonal to annual timescales. The results of this experiment suggest that deepening the modeled land surface, compared to modeling only a shallower soil column with a no-flux bottom boundary condition, has limited impact on mean climate but does affect seasonality and interannual persistence.

soil↗

The Impact of Trends in the Large Scale Atmospheric Circulation on Mediterranean Surface Turbulent Heat Fluxes

Interannual variations of latent heat fluxes (LHF) and sensible heat fluxes (SHF) over the Mediterranean for the boreal winter season (DJF) show positive trends during 1958-2011. Comparison of correlations between the heat fluxes and the intensity and location of the Azores High (AH), and the NAO and East Atlantic-West Russia (EAWR) teleconnections, along with analysis of composites of surface temperature, humidity and wind fields for different teleconnection states, demonstrates that variations of the AH are found to explain the heat flux changes more successfully than the NAO and the EAWR. Trends in sea level pressure and longitude of the Azores High during DJF show a strengthening, and an eastward shift. DJF Azores High pressure and longitude are shown to co-vary such that variability of the Azores High occurs along an axis defined by lower pressure and westward location at one extreme, and higher pressure and eastward location at the other extreme. The shift of the Azores High from predominance of the low/west state to the high/east state induces trends in Mediterranean Sea surface winds, temperature and moisture. These, combined with sea surface warming trends, produce trends in wintertime Mediterranean Sea sensible and latent heat fluxes.

heat flux↗

Stair-Step Particle Flux Spectra on the Lunar Surface: Evidence for Nonmonotonic Potentials?

We present examples of unusual "stair‐step" differential flux spectra observed by the Apollo 14 Suprathermal Ion Detector Experiment on the lunar dayside surface in Earth's magnetotail. These spectra exhibit a relatively constant differential flux below some cutoff energy and then drop off precipitously, by about an order of magnitude or more, at higher energies. We propose that these spectra result from photoions accelerated on the lunar dayside by nonmonotonic potentials (i.e.,potentials that do not decay to zero monotonically) and present a model for the expected differential flux. The energy of the cutoff and the magnitude of the differential flux are related to the properties of the local space environment and are consistent with the observed flux spectra. If this interpretation is correct, these surface‐based ion observations provide a unique perspective that both complements and enhances the conclusions obtained by remote‐sensing orbiter observations on the Moon's exospheric and electrostatic properties.

Stair-step↗

Application of Flux Conserved Modeling to an Unsteady Combustion Driven Pseudo-Shock

Quasi-steady correlation-based and flux conserved models of the pseudo-shock pressure profile are experimentally assessed in the Air Force Research Lab RC-18 Sub-Scale DirectConnect Isolator Combustion Facility. A bifurcated normal pseudo-shock is established in the 2.67 aspect ratio isolator test section by a downstream cavity-stabilized combustor. The Waltrup-Billig correlation, Smart flux conserved model, and Fiévet data driven flux conserved models are compared against measured pressure profiles. The literature models are found to perform poorly in a high-amplitude forced environment of RC-18, where shock speeds upwards of 20% the isolator Mach number occur. Two modifications to the quasi-steady Fiévet data driven flux conserved model are proposed including incorporating an estimate of pseudo-shock static pressure recovery and exercising the model in a shock stationary reference frame. It is shown that these modifications allow the quasi-steady flux conserved modeling approach to accurately predict pseudo-shock pressure profiles over the discrete phases of high-amplitude forced dynamics.

Shock Train↗