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DOE OSTI2019

ICAT: A numerical scheme to minimize numerical diffusion in advection-dispersion modeling and its application in identifying flow channeling

The advection-dispersion equation for scalar transport is essential for the numerical modeling of many fluid dynamics problems. However, solutions from numerical schemes always suffer from numerical diffusion and/or oscillation. In this study, we develop an Intra-Cell Advection Tracking (ICAT) scheme to minimize numerical diffusion and preserve monotonicity for advection-dispersion modeling. The key idea is to introduce “queues” in each discretized cell, and using a sequential transport rule and a flow distribution mechanism to track the scalar transport in these queues temporally and spatially. The capability and limitations of ICAT are first investigated through three test cases. Compared with the results obtained from other numerical schemes, the results from ICAT show substantially reduced numerical diffusion and agree better with analytical solutions. We also employ ICAT to simulate the transport process of a conservative tracer in a fracture with a highly heterogeneous aperture distribution. We report discrete flow channels in the fracture are better discerned by ICAT than by other numerical schemes, indicating the suitability of ICAT for modeling tracer transport in channelized flow fields.

15 GEOTHERMAL ENERGY↗

DOE OSTI2022

Dust-planetary boundary layer interactions amplified by entrainment and advections

Mineral dust contributes to more than half of the global aerosol loading. However, the radiative impacts of dust aerosols on planetary boundary layer (PBL) structure have not been explored sufficiently. During a typical dust storm event over Tarim Basin, dust aerosols exhibit a well-mixed distribution during the daytime in spite of a shallow layer of dust particles accumulated at higher altitudes. By contrast, nocturnal dust plumes are located near the surface due to stable stratification. We demonstrate that these differentiated vertical distributions determine the spatial heterogeneity of dust loading, radiative fluxes and PBL height variations. Dust aerosols cause daytime PBL suppression and nighttime PBL promotion through modulating surface and atmospheric radiative budgets. Specifically, dust-induced cooling effect within PBL directly inhibits the daytime PBL development. PBL suppression effect is then amplified by entrainment processes resulting in excessively low PBL height, especially for dust particles below but near the PBL top. Dust plumes weaken updrafts from PBL and downdrafts of the free atmosphere, which further reduce the entrainment mixing through attenuating horizontal and vertical advection, and eventually amplify PBL suppression. At night, near-surface dust aerosols stimulate a warm and unstable lower atmosphere, generate warm advection heating and promote the PBL development. Our study highlights the importance of specifying entrainment parameters and nighttime advection activities in quantifying the dust-PBL interactions.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2017

Vertical Structure of Radiation-pressure-dominated Thin Disks: Link between Vertical Advection and Convective Stability

In the classic picture of standard thin accretion disks, viscous heating is balanced by radiative cooling through the diffusion process, and the radiation-pressure-dominated inner disk suffers convective instability. However, recent simulations have shown that, owing to the magnetic buoyancy, the vertical advection process can significantly contribute to energy transport. In addition, in comparing the simulation results with the local convective stability criterion, no convective instability has been found. In this work, following on from simulations, we revisit the vertical structure of radiation-pressure-dominated thin disks and include the vertical advection process. Our study indicates a link between the additional energy transport and the convectively stable property. Thus, the vertical advection not only significantly contributes to the energy transport, but it also plays an important role in making the disk convectively stable. Our analyses may help to explain the discrepancy between classic theory and simulations on standard thin disks.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Stability Analysis of Coupled Advection-Diffusion Models with Bulk Interface Condition

Numerical stability is of critical importance in general circulation models because it affects the design of algorithms, time to solution, and computational costs associated with the simulations, which are very expensive in practice. In this paper we extend the stability analysis for ocean-atmosphere coupling proposed in [Zhang et al., J. Sci. Comput. 84, 44(2020)] to a more realistic model that includes horizontal advection. We analyze various time-stepping strategies. We find that advection has a stabilizing effect in scenarios common to climate models when bulk interface condition and explicit flux coupling are used. We also show that our method can be used to study the stability impact of advection for other interface conditions such as Dirichlet-Neumann conditions.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Fast Advective Water Flow through Nanochannels in Clay Interlayers: Implications for Moisture Transport in Soils and Unconventional Oil/Gas Production

Water flow in nanometer or sub-nanometer hydrophilic channels bears special importance in diverse fields of science and engineering. However, the nature of such water flow remains elusive. In this work, we report our molecular-modeling results on water flow in a sub-nanometer clay interlayer between two montmorillonite layers. We show that a fast advective flow can be induced by evaporation at one end of the interlayer channel, that is, a large suction pressure created by evaporation (~818 MPa) is able to drive the fast water flow through the channel (~0.88 m/s for a 46 Å-long channel). Scaled up for the pressure gradient to a 2 μm particle, the velocity of water is estimated to be about 95 μm/s, indicating that water can quickly flow through a μm-sized clay particle within seconds. The prediction seems to be confirmed by our thermogravimetric analysis of bentonite hydration and dehydration processes, which indicates that water transport at the early stage of the dehydration is a fast advective process, followed by a slow diffusion process. The possible occurrence of a fast advective water flow in clay interlayers prompts us to reassess water transport in a broad set of natural and engineered systems such as clay swelling/shrinking, moisture transport in soils, water uptake by plants, water imbibition/release in unconventional hydrocarbon reservoirs, and cap rock integrity of supercritical CO 2 storage.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2018

On the Importance of Advective Versus Diffusive Transport in Controlling the Distribution of Methane Hydrate in Heterogeneous Marine Sediments

The occurrence of methane hydrate in marine reservoirs often correlates with the physical properties of the host sediments. High hydrate saturations (>60% of the pore volume) found in association with coarser-grained strata have been attributed to both enhanced advective transport through more permeable sediment layers and to perturbations in phase equilibrium related to pore space geometry that results in increased diffusive transport. To assess the relative importance of these mechanism in controlling hydrate occurrence, we develop a 1-D model for hydrate growth along dipping, coarse-grained layers embedded in a fine-grained sediment package. We explicitly account for pore size effects on methane solubility and permeability-driven variations in fluid flux. We show how the vertical distribution of hydrate varies in response to changes in grain size and rates of fluid advection, sedimentation, and in situ methane production. We then use our model to simulate centimeter-scale variations in hydrate saturation observed at Walker Ridge Block 313, Hole H in the Gulf of Mexico. We find that the largest concentrations of hydrate are controlled by diffusion, while increased advective methane supply favors more distributed growth throughout high-permeability regions. Our results hold promise for using well log-derived estimates of hydrate saturation to infer sediment properties and the sources and rates of methane supply during reservoir emplacement.

58 GEOSCIENCES↗

DOE OSTI2019

Episodes of Warm-Air Advection Causing Cloud-Surface Decoupling During the MARCUS

It has been understood for decades that advection of a cloud-topped marine boundary layer (CTBL) over warmer sea surface causes the stratification (or decoupling) of the CTBL via the entrainment feedback, a mechanism commonly known as “deepening-warming” decoupling that is typical in subtropics. This study focuses on the opposite direction of advection, that is, low-level warm air advection (LLWAA), and its impacts on the decoupling degree of a CTBL. Our hypothesis is that LLWAA stabilizes a CTBL, causing a decoupling of the CTBL. It is tested for three LLWAA episodes observed during the Measurements of Aerosols, Radiation, and CloUds over the Southern Ocean (MARCUS) field campaign between the Hobart (43°S, 147°E), Australia, and several Antarctic coast stations. By synthesizing the shipborne measurements of CTBL structure, Himawari-8 satellite imagery of cloud fields, and reanalysis of meteorological field, four common characteristics of CTBLs under the LLWAA are found: (1) CTBLs are highly stratified to the extent that penetrations of cumulus into main temperature inversions, which are common for subtropical decoupled CTBLs, do not exist; (2) sea surface temperature is 1–2 K lower than the near-surface air temperature; (3) clouds manifest stratiform with lifetime as long as several tens of hours; and (4) they locate in warm sectors of middle-latitude cyclones. Possible mechanisms for the maintenance of decoupled clouds under LLWAA are discussed in terms of dynamic and thermodynamic factors. Lapse rates of the decoupled CTBLs are markedly lower than those commonly used for passive satellite estimation of cloud top heights.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Evaluation of Atmospheric Boundary Layer Height From Wind Profiling Radar and Slab Models and Its Responses to Seasonality of Land Cover, Subsidence, and Advection

In this study, we evaluated the effect of land cover, atmospheric subsidence, and advection on the annual dynamics of atmospheric boundary layer (ABL) height from two contrasting sites. The first site is the Walker Branch forest, a deciduous forest of temperate climate, complex topography, and cloudy summers. The second site is the Sacramento-San Joaquin River Delta, a site of Mediterranean climate, flat terrain on a local scale, and clear summers. After testing a new algorithm to calculate ABL heights from 915 MHz radar wind profilers, we evaluated a hierarchy of three slab models to recreate the diurnal and annual patterns of ABL growth. We found that the lower ABL heights in the Delta, particularly during late summer, are driven by the combined effects of increased atmospheric subsidence and marine air advection. In both sites, the annual pattern of ABL height was strongly correlated to total daily incoming radiation, and in the Delta, the annual pattern of ABL height closely followed the seasonal patterns of sensible heat flux from a mosaic of different land covers. A land composite of latent and sensible heat fluxes obtained through a meso-network of eddy covariance measurements and the ECOsystem Spaceborne Thermal Radiometer Experiment on Space Station (ECOSTRESS) mission resulted in higher model skill, thus showing that land cover heterogeneity is an important driver of ABL growth. To conclude, model simulations show that in the Delta, restoring agricultural land to wetlands with large open water areas could result in a reduction of ABL height during those months with low subsidence and advection.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Reduced-order modeling of advection-dominated systems with recurrent neural networks and convolutional autoencoders

A common strategy for the dimensionality reduction of nonlinear partial differential equations (PDEs) relies on the use of the proper orthogonal decomposition (POD) to identify a reduced subspace and the Galerkin projection for evolving dynamics in this reduced space. However, advection-dominated PDEs are represented poorly by this methodology since the process of truncation discards important interactions between higher-order modes during time evolution. In this study, we demonstrate that encoding using convolutional autoencoders (CAEs) followed by a reduced-space time evolution by recurrent neural networks overcomes this limitation effectively. We demonstrate that a truncated system of only two latent space dimensions can reproduce a sharp advecting shock profile for the viscous Burgers equation with very low viscosities, and a six-dimensional latent space can recreate the evolution of the inviscid shallow water equations. Additionally, the proposed framework is extended to a parametric reduced-order model by directly embedding parametric information into the latent space to detect trends in system evolution. Furthermore, our results show that these advection-dominated systems are more amenable to low-dimensional encoding and time evolution by a CAE and recurrent neural network combination than the POD-Galerkin technique.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

On the time growth of the error of the DG method for advective problems

Abstract In this paper we derive a priori $L^{\infty }(L^{2})$ and L2(L2) error estimates for a linear advection–reaction equation with inlet and outlet boundary conditions. The goal is to derive error estimates for the discontinuous Galerkin method that do not blow up exponentially with respect to time, unlike the usual case when Gronwall’s inequality is used. While this is possible in special cases, such as divergence-free advection fields, we take a more general approach using exponential scaling of the exact and discrete solutions. Here we use a special scaling function, which corresponds to time taken along individual pathlines of the flow. For advection fields, where the time that massless particles carried by the flow spend inside the spatial domain is uniformly bounded from above by some $\widehat{T}$, we derive $\mathcal{O}$(hp+1/2) error estimates where the constant factor depends only on $\widehat{T}$, but not on the final time T. This can be interpreted as applying Gronwall’s inequality in the error analysis along individual pathlines (Lagrangian setting), instead of physical time (Eulerian setting).

Mathematics↗

DOE OSTI2020

A Hybrid Lagrangian/Eulerian Collocated Velocity Advection and Projection Method for Fluid Simulation

Abstract We present a hybrid particle/grid approach for simulating incompressible fluids on collocated velocity grids. Our approach supports both particle‐based Lagrangian advection in very detailed regions of the flow and efficient Eulerian grid‐based advection in other regions of the flow. A novel Backward Semi‐Lagrangian method is derived to improve accuracy of grid based advection. Our approach utilizes the implicit formula associated with solutions of the inviscid Burgers’ equation. We solve this equation using Newton's method enabled by C 1 continuous grid interpolation. We enforce incompressibility over collocated, rather than staggered grids. Our projection technique is variational and designed for B‐spline interpolation over regular grids where multiquadratic interpolation is used for velocity and multilinear interpolation for pressure. Despite our use of regular grids, we extend the variational technique to allow for cut‐cell definition of irregular flow domains for both Dirichlet and free surface boundary conditions.

Gagniere, S.↗

DOE OSTI2023

Analysis of an Arctic cold air outbreak during autumn and related air mass transformations forced by surface changes and advection in higher altitudes

During marine cold air outbreaks (MCAOs), cold and dry Arctic air masses are transported from the central Arctic southward across the closed sea ice and much warmer open oceans. They experience significant transformations including a rapid heating and moistening, often leading to cloud formation. While intense wintertime MCAOs have been analyzed widely, the air mass transformations during other seasons have been studied sparsely. We address this gap by investigating an MCAO case observed in September 2020. To study the transformation processes, we combine the fifth generation of atmospheric reanalyses of the global climate (ERA5), trajectory calculations, as well as shipborne and airborne measurements. In the central Arctic, observations acquired from aboard the research vessel (RV) Polarstern during the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) expedition characterized the initial state of the air mass over closed sea ice. Trajectories indicated the pathway the air mass took from RV Polarstern southward to the Fram Strait. For the first 24 h of the southbound drift, the air masses remained quasi-stationary. Then, still 15 h ahead of the marginal sea ice zone, differential advection across the boundary layer flow introduced humidity and clouds at higher altitudes between 1.5 and 2.5 km. ERA5-derived temperature and humidity tendencies indicated complex vertical interactions. Radiative cloud-top cooling, entrainment, and turbulence were significantly reduced in the lower and enhanced in the upper advected cloud layer. Eventually, the lower cloud deck dissipated. After this confluence of 2 different air masses, observations gathered by Polar 5 in Fram Strait as part of the MOSAiC Airborne observations in the Central Arctic campaign revealed cloudy, moist layers throughout the lowest 3.5 km and an increasing boundary layer height. Comparing the initial with the final state 48 h later, the largest net heating of +8 K was found close to the surface, yet the largest net moistening of +2.5 g kg -1 at an altitude of 1 km, as the initial profile was exceptionally dry here. We conclude that the observed air mass transformations were driven by the surface changes from sea ice to open ocean but additionally strongly impacted by the differential advection of clouds and moisture across the near-surface MCAO flow.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1971

Application of conservative finite-difference methods to advection problems

The possibility of applying the most recent conservative and widely applied numerical techniques in gas dynamics to problems encountered in meteorological computations is investigated. Solutions of the advection equation are obtained using conservative differencing methods. These results are compared to those obtained by differencing the advection equation directly. The comparison shows that better results are obtained when the conservative form of governing equation is used. In addition, better results are obtained with lower order conservative methods as compared with higher order differencing applied to the advection equation.

Fattahi, B.↗

NASA NTRS1975

Variational optimization analysis of temperature and moisture advection in a severe storm environment

Horizontal wind components, potential temperature, and mixing ratio fields associated with a severe storm environment in the south central U.S. were analyzed from synoptic upper air observations with a nonhomogeneous, anisotropic weighting function. Each data field was filtered with variational optimization analysis techniques. Variational optimization analysis was also performed on the vertical motion field and was used to produce advective forecasts of the potential temperature and mixing ratio fields. Results show that the dry intrusion is characterized by warm air, the advection of which produces a well-defined upward motion pattern. A corresponding downward motion pattern comprising a deep vertical circulation in the warm air sector of the low pressure system was detected. The axes alignment of maximum dry and warm advection with the axis of the tornado-producing squall line also resulted.

Mcfarland, M. J.↗

NASA NTRS1976

The prediction of sea-surface temperature variations by means of an advective mixed-layer ocean model

An advective mixed layer ocean model was developed by eliminating the assumption of horizontal homogeneity in an already existing mixed layer model, and then superimposing a mean and anomalous wind driven current field. This model is based on the principle of conservation of heat and mechanical energy and utilizes a box grid for the advective part of the calculation. Three phases of experiments were conducted: evaluation of the model's ability to account for climatological sea surface temperature (SST) variations in the cooling and heating seasons, sensitivity tests in which the effect of hypothetical anomalous winds was evaluated, and a thirty-day synoptic calculation using the model. For the case studied, the accuracy of the predictions was improved by the inclusion of advection, although nonadvective effects appear to have dominated.

Atlas, R. M.↗

NASA NTRS1981

Advection fog formation in a polluted atmosphere

Large quantities of atmospheric aerosols with compositions SO4(2-), NO3(-) and NH4(+) have been detected in highly industrialized areas. The major portions of aerosol products are the results of energy-related fuel combustion. Both microphysical and macrophysical processes are considered in investigating the time-dependent evolution of the saturation spectra of condensation nuclei associated with both polluted and clean atmospheres during the time periods of advection fog formation. The results show that the condensation nuclei associated with a polluted atmosphere provide more favorable conditions than condensation nuclei associated with a clean atmosphere to produce dense advection fog, and that attaining a certain degree of supersaturation is not necessarily required for the formation of advection fog with condensation nuclei associated with a polluted atmosphere for monodisperse distribution.

Hung, R. J.↗

NASA NTRS1984

Kelvin-wave-induced anomalous advection and the onset of surface warming in El Nino events

A simple advective model for tropical ocean surface warming can produce anomalous sea surface temperature (SST) fields similar to those of the first several months of the 1982 El Nino. The physics invoked assumes that the existing SST field is advected by anomalous currents to produce the anomalous warming, and that the anomalous currents are those induced subsequent to the passage of downwelling Kelvin wave fronts. Numerical experiments with a fully nonlinear and thermally active ocean model support the physical relevance of the more idealized study. The anomalous horizontal advection model also accounts for the initial SST evolution during the more common type of El Nino event.

Harrison, D. E.↗

NASA NTRS1986

Numerical advection by conservation of second-order moments

A new, accurate, and nondiffusive method for three-dimensional advection of trace species is presented. The method preserves tracer structures by conserving the second-order moments of the spatial distribution of tracer during advection. Upstream transport and second-order tracer distribution are described, and the moments of the tracer distribution about the center of a grid box are formally defined and related to the polynomial distribution. Formulas are presented which describe how the moments of a grid box are decomposed into a unique set of moments centered about each subbox and how they are reassembled into new grid boxes. A one-dimensional example if tracer transport is given, and limits necessary to maintain positive tracer concentrations are derived. The accuracy and stability of this method are analytically examined, and numerical experiments testing the effective resolution are presented. The method is compared with other methods for numerical advection of tracers.

Prather, M. J.↗