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A three-hour sequence of observations at the Pic du Midi observatory has been obtained which shows the evolution of solar mesogranules from appearance to disappearance with unprecedented clarity. It is seen that the supergranules, which are known to advect the granules with their convective motion, also advect the mesogranules to their boundaries. This process controls the evolution and disappearance of mesogranules.
This report describes the construction of an explicit, single time-step, conservative, finite-volume method for multidimensional advective flow, based on a uniformly third-order polynomial interpolation algorithm (UTOPIA). Particular attention is paid to the problem of flow-to-grid angle-dependent, anisotropic distortion typical of one-dimensional schemes used component-wise. The third-order multidimensional scheme automatically includes certain cross-difference terms that guarantee good isotropy (and stability). However, above first-order, polynomial-based advection schemes do not preserve positivity (the multidimensional analogue of monotonicity). For this reason, a multidimensional generalization of the first author's universal flux-limiter is sought. This is a very challenging problem. A simple flux-limiter can be found; but this introduces strong anisotropic distortion. A more sophisticated technique, limiting part of the flux and then restoring the isotropy-maintaining cross-terms afterwards, gives more satisfactory results. Test cases are confined to two dimensions; three-dimensional extensions are briefly discussed.
There is a wide-spread belief that most explicit one-dimensional advection schemes need to satisfy the so-called 'CFL condition' - that the Courant number, c = udelta(t)/delta(x), must be less than or equal to one, for stability in the von Neumann sense. This puts severe limitations on the time-step in high-speed, fine-grid calculations and is an impetus for the development of implicit schemes, which often require less restrictive time-step conditions for stability, but are more expensive per time-step. However, it turns out that, at least in one dimension, if explicit schemes are formulated in a consistent flux-based conservative finite-volume form, von Neumann stability analysis does not place any restriction on the allowable Courant number. Any explicit scheme that is stable for c is less than 1, with a complex amplitude ratio, G(c), can be easily extended to arbitrarily large c. The complex amplitude ratio is then given by exp(- (Iota)(Nu)(Theta)) G(delta(c)), where N is the integer part of c, and delta(c) = c - N (less than 1); this is clearly stable. The CFL condition is, in fact, not a stability condition at all, but, rather, a 'range restriction' on the 'pieces' in a piece-wise polynomial interpolation. When a global view is taken of the interpolation, the need for a CFL condition evaporates. A number of well-known explicit advection schemes are considered and thus extended to large delta(t). The analysis also includes a simple interpretation of (large delta(t)) total-variation-diminishing (TVD) constraints.
The existing 2-D alpha-mu scheme and alpha-epsilon scheme based on the method of space-time conservation element and solution element, which were constructed for solving the linear 2-D unsteady advection-diffusion equation and unsteady advection equation, respectively, are tested. Also, the alpha-epsilon scheme is modified to become the V-E scheme for solving the nonlinear 2-D inviscid Burgers equation. Numerical solutions of six test problems are presented in comparison with their exact solutions or numerical solutions obtained by traditional finite-difference or finite-element methods. It is demonstrated that the 2-D alpha-mu, alpha-epsilon, and nu-epsilon schemes can be used to obtain numerical results which are more accurate than those based on some of the traditional methods but without using any artificial tuning in the computation. Similar to the previous 1-D test problems, the high accuracy and simplicity features of the space-time conservation element and solution element method have been revealed again in the present 2-D test results.
We present a trajectory technique, contour advection with surgery (CAS), for tracing the evolution of material contours in a specified (including observed) evolving flow. CAS uses the algorithms developed by Dritschel for contour dynamics/surgery to trace the evolution of specified contours. The contours are represented by a series of particles, which are advected by a specified, gridded, wind distribution. The resolution of the contours is preserved by continually adjusting the number of particles, and finescale features are produced that are not present in the input data (and cannot easily be generated using standard trajectory techniques). The reliability, and dependence on the spatial and temporal resolution of the wind field, of the CAS procedure is examined by comparisons with high-resolution numerical data (from contour dynamics calculations and from a general circulation model), and with routine stratospheric analyses. These comparisons show that the large-scale motions dominate the deformation field and that CAS can accurately reproduce small scales from low-resolution wind fields. The CAS technique therefore enables examination of atmospheric tracer transport at previously unattainable resolution.
Experiments with a surface processes model of large-scale (1-1000 km) long-term (1-100 m.y.) erosional denudation are used to establish the controls on the evolution of a model escarpment that is related to the rifting of a continent. The mdoel describes changes in topographic form as a result of sumultaneous short- and long-range mass transport representing hillslope (diffusive) processes and fluvial transport (advection), repsectively. Fluvial entrainment is modeled as a first-order kinetic reaction which reflects the erodibility of the substrate, and therefore the fluvial system is not necessarily carrying at capacity. One dimensional and planform models demonstrate that the principal controls on the evolution of an initially steep model escarpment are (1) antecedent topography/drainage; (2) the timesale (or equivalently a length scale) in the fluvial entrainment reaction; (3) the flexural response of the lithosphere to denudation; and (4) the relative efficiencies of the short- and long-range transport processes. When rainfall and substrate lithology are uniform, a significant amount of discharge draining over the escarpment top causes it to degrade. Only when the top of the model escarpment coincides with a drainage divide can escarpment retreat occur for these conditions. An additional requirement for retreat of a model escarpment without decline is a long reaction time scale for fluvial entrainment. This corresponds to a substrate that is hard to detach by flucial erosion, and therefore to fluvial erosion that is not transport limited. Coninuous backtilting of an escarpment due ot flexural isostatic uplift in response to denudational unloading helps maintain the scarp top as a divide. It is essntial if the escarpment gradient is to be preserved during retreat in a uniform lithology. Low flexural rigidieties propote steep and slowly retreating escarpments. For given rainfall and substrate conditions, the morphology of a retraeating model escarpment is determined by the ratio of hte short-range diffusive and long range advective transport efficiencies. A low ration (which is interpreted to correspond to a more humid, temperate climate) produces a convex upper slope, and concave lower slope morphology and only major escarpments are predicted to preserve a high scarp gradient. Lithological contrasts in hte model produce more complex morphologies and predict the formation of scarps crowned by an erosionaly resistant caprock. However, resistant caprocks are not an essential requirement for model scarps to retreat. We conclude that the inferred controls and model behavior are both consistent with the present-day morphology of rifted continental margins and with modern conceptual models of landscape evolution.
In winter, large interannual fluctuations in the surface skin temperature are observed over central Europe: we observe a difference of 9.8 K comparing warm February 1990 with cold February 1996 for the region 50-60 degrees N; 5-35 degrees E. Previous studies show that advection from the North Atlantic constitutes the forcing to such fluctuations. The advection is quantified by Index I(sub na), the average of the ocean-surface wind speed over the eastern North Atlantic when the direction is from the southwest (when the wind is from another direction, it counts as a zero speed to the average). Average Ina for February 1990 was 10.6 in s(exp -1), but for February 1996 I(sub na) was only 2.4 m s(exp -1). A large value of I(sub na) means a strong southwesterly flow which brings warm and moist air into Europe at low level, producing a steeper tropospheric lapse rate. Strong ascending motions result, which we observe in February 1990 at 700 mb. The near-surface moisture rises to higher (and cooler) levels, producing clouds and precipitation. Total preciptable water and cloud-cover fraction have larger values in February 1990 than in 1996. The difference in the greenhouse effect between these two scenarios can be translated into a virtual irradiating source of 2.6 W m(exp -2) above the February 1990 atmosphere, which, as an order of magnitude estimate, contributes to the warming of the surface by 2.6 K. If we accept this estimate as numerically pertinent, the direct effect stands as 7.2 K (9.8 K - 2.6 K), and therefore its greenhouse-effect reinforcement is by 36%. This constitutes a substantial positive feedback to the direct effect, which is the inflow of warm air to the low troposphere over Europe.
It is well recognized that advection from the North Atlantic has a profound effect on the climatic conditions in central Europe. A new dataset of the ocean-surface winds, derived from the Special Sensor Microwave Imager, SSM/1, is now available. This satellite instrument measures the wind speed, but not the direction. However, variational analysis developed at the Data Assimilation Office, NASA Goddard Space Flight Center, by combining the SSM/I measurements with wind vectors measured from ships, etc., produced global maps of the ocean surface winds suitable for climate analysis. From this SSM/I dataset, a specific index I(sub na) of the North Atlantic surface winds has been developed, which pertinently quantifies the low-level advection into central Europe. For a selected time-period, the index I(sub na) reports the average of the amplitude of the wind, averaging only the speed when the direction is from the southwest (when the wind is from another direction, the contribution counts to the average as zero speed). Strong correlations were found between February I(sub na) and the surface air temperatures in Europe 50-60 deg N. In the present study, we present the correlations between I(sub na) and temperature I(sub s), and also the sensitivity of T(sub s), to an increase in I(sub na), in various seasons and various regions. We specifically analyze the flow of maritime-air from the North Atlantic that produced two extraordinary warm periods: February 1990, and early-winter 2000/2001. The very cold December 2001 was clearly due to a northerly flow. Our conclusion is that the SSM/I dataset is very useful for providing insight to the forcing of climatic fluctuations in Europe.
Numerous recent studies calculate horizontal and vertical advection terms for budget studies of net ecosystem exchange of carbon. One potential uncertainty in such studies is the estimate of mean vertical motion. This work addresses the reliability of vertical advection estimates by contrasting the vertical motion obtained from the standard practise of measuring the vertical velocity and applying a tilt correction, to the vertical motion calculated from measurements of the horizontal divergence of the flow using a network of towers. Results are compared for three different tilt correction methods. Estimates of mean vertical motion are sensitive to the choice of tilt correction method. The short-term mean (10 to 60 minutes) vertical motion based on the horizontal divergence is more realistic compared to the estimates derived from the standard practise. The divergence shows long-term mean (days to months) sinking motion at the site, apparently due to the surface roughness change. Because all the tilt correction methods rely on the assumption that the long-term mean vertical motion is zero for a given wind direction, they fail to reproduce the vertical motion based on the divergence.
This paper focuses on the evolution of advection upstream splitting method(AUSM) schemes. The main ingredients that have led to the development of modern computational fluid dynamics (CFD) methods have been reviewed, thus the ideas behind AUSM. First and foremost is the concept of upwinding. Second, the use of Riemann problem in constructing the numerical flux in the finite-volume setting. Third, the necessity of including all physical processes, as characterised by the linear (convection) and nonlinear (acoustic) fields. Fourth, the realisation of separating the flux into convection and pressure fluxes. The rest of this review briefly outlines the technical evolution of AUSM and more details can be found in the cited references. Keywords: Computational fluid dynamics methods, hyperbolic systems, advection upstream splitting method, conservation laws, upwinding, CFD
The 2nd-order upwind inviscid flux scheme implemented in the multi-block, structured grid, cell centered, finite volume, high-speed reacting flow code VULCAN has been modified to reduce numerical dissipation. This modification was motivated by the desire to improve the codes ability to perform large eddy simulations. The reduction in dissipation was accomplished through a hybridization of non-dissipative and dissipative discontinuity-capturing advection schemes that reduces numerical dissipation while maintaining the ability to capture shocks. A methodology for constructing hybrid-advection schemes that blends nondissipative fluxes consisting of linear combinations of divergence and product rule forms discretized using 4th-order symmetric operators, with dissipative, 3rd or 4th-order reconstruction based upwind flux schemes was developed and implemented. A series of benchmark problems with increasing spatial and fluid dynamical complexity were utilized to examine the ability of the candidate schemes to resolve and propagate structures typical of turbulent flow, their discontinuity capturing capability and their robustness. A realistic geometry typical of a high-speed propulsion system flowpath was computed using the most promising of the examined schemes and was compared with available experimental data to demonstrate simulation fidelity.
The anomalously large radii of strongly irradiated exoplanets have remained a major puzzle in astronomy. Based on a two-dimensional steady-state atmospheric circulation model, the validity of which is assessed by comparison to three-dimensional calculations, we reveal a new mechanism, namely the advection of the potential temperature due to mass and longitudinal momentum conservation, a process occurring in the Earth's atmosphere or oceans. In the deep atmosphere, the vanishing heating flux forces the atmospheric structure to converge to a hotter adiabat than the one obtained with 1D calculations, implying a larger radius for the planet. Not only do the calculations reproduce the observed radius of HD 209458b, but also reproduce the observed correlation between radius inflation and irradiation for transiting planets. Vertical advection of potential temperature induced by non-uniform atmospheric heating thus provides a robust mechanism to explain the inflated radii of irradiated hot Jupiters.
This work uses 17 years of upper mesospheric carbon monoxide (CO) and temperature observations by the Microwave Limb Sounder (MLS) on-board the Aura satellite to present and explain the seasonal and interannual variability of the migrating diurnal tide (DW1) component of upper mesospheric CO. This work then compares these observations to simulations by the Specified Dynamics – Whole Atmosphere Community Climate Model with Ionosphere/Thermosphere eXtension (SD-WACCM-X). Results show that, for all seasons, MLS CO local-time perturbations peaks above 85 km and has a latitude structure resembling the (1,1) mode in temperature. On the other hand, SD-WACCM-X DW1 also peaks above 85 km and has a latitude structure resembling the (1,1) mode but it simulates 2 local maximum of the (1,1) mode between 85 km and 92 km. Despite the differences in altitude structure, a tendency analysis and the adiabatic displacement method revealed that, on seasonal and interannual timescales, observed and modelled CO’s (1,1) component can be reproduced solely using vertical advection. It was also found that both observed and modelled CO’s (1,1) component contains interannual oscillations with periodicities close to that of the Quasi-biennial Oscillation and the El Niño–Southern Oscillation. From these results, this work concludes that on seasonal and interannual timescales, the observed and modelled (1,1) mode affects the global structure of upper mesospheric CO primarily through vertical advection.
This work uses 17 years of upper mesospheric carbon monoxide (CO) and temperature observations by the Microwave Limb Sounder (MLS) on-board the Aura satellite to present and explain the seasonal and interannual variability of the migrating diurnal tide (DW1) component of upper mesospheric CO. This work then compares these observations to simulations by the Specified Dynamics – Whole Atmosphere Community Climate Model with Ionosphere/Thermosphere eXtension (SD-WACCM-X). Results show that, for all seasons, MLS CO local-time perturbations peaks above 85 km and has a latitude structure resembling the (1,1) mode in temperature. On the other hand, SD-WACCM-X DW1 also peaks above 85 km and has a latitude structure resembling the (1,1) mode but it simulates 2 local maximum of the (1,1) mode between 85 km and 92 km. Despite the differences in altitude structure, a tendency analysis and the adiabatic displacement method revealed that, on seasonal and interannual timescales, observed and modelled CO’s (1,1) component can be reproduced solely using vertical advection. It was also found that both observed and modelled CO’s (1,1) component contains interannual oscillations with periodicities close to that of the Quasi-biennial Oscillation and the El Nino Southern Oscillation. From these results, this work concludes that on seasonal and interannual timescales, the observed and modelled (1,1) mode affects the global structure of upper mesospheric CO primarily through vertical advection.
There are multiple algorithms for parallelizing particle advection for scientific visualization workloads. While many previous studies have contributed to the understanding of individual algorithms, our study aims to provide a holistic understanding of how algorithms perform relative to each other on various workloads. To accomplish this, we consider four popular parallelization algorithms and run a “bake-off” study (i.e., an empirical study) to identify the best matches for each. The study includes 216 tests, going to a concurrency of up to 8192 cores and considering data sets as large as 34 billion cells with 300 million particles. Overall, our study informs three important research questions: (1) which parallelization algorithms perform best for a given workload?, (2) why?, and (3) what are the unsolved problems in parallel particle advection? In terms of findings, we find that the seeding box is the most important factor in choosing the best algorithm, and also that there is a significant opportunity for improvement in execution time, scalability, and efficiency.
Fusion devices are anticipated to produce and consume several kilograms of tritium per year. This rare fuel resource is both highly mobile and radioactive, making tracking inventories a priority for operation and safety. The fusion safety program at the Idaho National Laboratory has been developing the Tritium Migration and Analysis Program (TMAP), of which the latest version is a MOOSE-based application. TMAP8 is verified against its predecessors and possesses additional multi-dimensional tritium migration modeling capabilities. As we extend its capabilities towards both whole device (in multiple dimensions) and whole plant (with multiple components) simulations, the syntax of inputs must become compact, descriptive, compatible with quality assurance processes, and as error-proof as achievable. The new Physics system developed MOOSE can set up equations and instantiating them on plant components. The system permits the automatic definition of complex discretization with a consistency between object parameters achieved programmatically. The Physics system can currently instantiate the equations for heat conduction and Navier Stokes weakly compressible flow. In MOOSE-terms, it automates the definition of kernels, boundary conditions, and several core and helper materials and fields. As part of this effort, Physics classes were developed for tritium migration, trapping and advection within either a multi-dimensional Navier Stokes fluid dynamics simulation, or a 1D thermal hydraulics piping system. In this presentation, we will showcase the new syntax, its application to several verification and validation cases which were already studied using the classical TMAP8 syntax, and a demonstration of the new coupling capabilities for the migration of tritium into blanket coolant channels and the subsequent advection into the coolant loop.
Here, we consider the adaptive-rank integration of multi-dimensional time-dependent advection-diffusion partial differential equations (PDEs) with variable coefficients. We employ a standard finite-difference method for spatial discretization coupled with high-order diagonally implicit Runge-Kutta temporal schemes. The discrete equation is a generalized Sylvester equation (GSE), which we solve with a projection-based adaptive-rank algorithm structured around two key strategies: (i) constructing dimension-wise subspaces using a novel atypical extended Krylov strategy, and (ii) efficiently solving the basis coefficient matrix with a preconditioned GMRES solver. The low-rank decomposition is performed in 2D using SVD and with high-order SVD (HOSVD) in 3D to represent the tensor in a compressed Tucker format. For d-dimensional problems (here, d = 2 or 3), the computational complexity and memory storage of the approach are found numerically to scale as and $\mathscr{O}(Nr^2) + \mathscr{O} (r^{d+1})$ and $\mathscr{O}(Nr) + \mathscr{O} (r^{d})$, respectively, with the one-dimensional resolution and the maximal rank during the Krylov iteration (which we find to be largely independent of on our numerical examples). We present numerical examples that illustrate the advertised properties of the algorithm.
Here we present the analysis of approximation rates of operator learning in Chen and Chen (1995) and Lu et al. (2021), where continuous operators are approximated by a sum of products of branch and trunk networks. In this work, we consider the rates of learning solution operators from both linear and nonlinear advection–diffusion equations with or without reaction. We find that the approximation rates depend on the architecture of branch networks as well as the smoothness of inputs and outputs of solution operators.