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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Reaction losses of charged particles in CsI(Tl) crystals

To efficiently detect energetic light charged particles, it is common to use arrays of energy-loss telescopes involving two or more layers of detection media. As the energy of the particles increases, thicker layers are usually needed. However, carrying out measurements with thick-telescopes may require corrections for the losses due to nuclear reactions induced by the incident particles on nuclei within the detector and for the scattering of incident particles out of the detector, without depositing their full energy in the active material. In this paper, we develop a method for measuring such corrections and determine the reaction and out-scattering losses for data measured with the silicon-CsI(Tl) telescopes of the newly developed HiRA10 array. Here, the extracted efficiencies are in good agreement with model predictions using the GEANT4 reaction loss algorithm for Z = 1 and Z = 2 isotopes. After correcting for the HiRA10 geometry, we obtain a general function that describes the loss of efficiency due to reaction losses in CsI(Tl) crystals as a function of range.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2018

Uncertainty quantification in the analyses of operational wind power plant performance

In the present work, we examine the variation introduced in the evaluation of an operating plant's wind power production as a result of the choices analysts make in the processing of the operational data. For this study, an idealized power production for individual turbines over an operational period was predicted by fitting power curves to the turbine production data collected during expected operation (that is, without curtailment or availability losses). A set of 240 possible methods were developed for (a) defining what data represented expected operation and (b) modeling the power curve. The spread in the idealized power production as predicted by the different methods was on average almost 3% for the 100 turbines considered. Such significant variation places a lower bound on the precision with which analysts may employ such data as benchmarks for calibration of their energy estimation processes and limits the potential for identification of refinements to the energy estimation models for improved accuracy.

17 WIND ENERGY↗
DOE OSTI2019

Characterization of Creep-Fatigue Crack Growth in Alloy 709 and Prediction of Service Lives in Nuclear Reactor Components (Final Report)

This final report summarizes the activities and results that were obtained by the research team working on the project “Characterization of Creep-Fatigue Crack Growth in Alloy 709 and Prediction of Service Lives in Nuclear Reactor Components”, DOE-NEUP Project 15-8623. This project was mainly concerned with the creep-fatigue crack growth characterization of austenitic stainless-steel Fe-20Cr-25Ni (Alloy 709). For this purpose, an array of experimental and computational activities was performed. The main goal of these activities was to describe and predict the crack growth behavior in Alloy 709 under different conditions of applied loading and temperature. Alloy 709 specimens were tested to describe both the uniaxial creep behavior and creep-fatigue crack growth rates at temperatures between 550°C and 700°C. Microstructure and fracture surface analysis was performed using several experimental techniques, and the defining features of crack growth propagation were identified and described. Thermodynamic and diffusion simulations were performed to understand the microstructure evolution of Alloy 709 at elevated temperatures, and to establish an aging schedule relevant for in-service conditions over extended periods. Experimental testing was performed on both as-received and aged Alloy 709 specimens. Two computational methods were developed to predict crack growth rates and remaining lives in specimens loaded under either fatigue of creep-fatigue. The first computational technique was the finite element method, while the second was strip-yield modeling. Both methods relied on the prediction of crack growth rates using the concept of plasticity-induced crack closure. Crack-tip opening loads were computed and used to perform crack growth rate predictions. The computational predictions matched well with the experimental results. The strip-yield model was shown to be an excellent predictive tool not only for crack growth in austenitic SS Alloy 709, but also in 316 SS, martensitic Cr-Mo steels, Ni-based alloys and Al-based alloys. The main conclusion of this study is that Alloy 709 exhibits excellent creep crack growth resistance at temperatures between 550°C and 700°C. In fact, the crack growth resistance of this alloy appears to be higher than that of 316 SS in similar testing conditions. Moreover, when creep loading with hold (dwell) times of 60s or 600s were intercalated every fatigue cycle, the crack growth rates did not change significantly. The conclusion is that the tests performed revealed that the crack growth is insignificant during the creep portion of a loading cycle, as compared with the crack growth during the fatigue portion of the cycle. In general, Alloy 709 shows excellent resistance to creep deformations and creep crack growth up to 700°C.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

The 4DEnVar-based weakly coupled land data assimilation system for E3SM version 2

Abstract. A new weakly coupled land data assimilation (WCLDA) system based on the four-dimensional ensemble variational (4DEnVar) method is developed and applied to the fully coupled Energy Exascale Earth System Model version 2 (E3SMv2). The dimension-reduced projection four-dimensional variational (DRP-4DVar) method is employed to implement 4DVar using the ensemble technique instead of the adjoint technique. With an interest in providing initial conditions for decadal climate predictions, monthly mean anomalies of soil moisture and temperature from the Global Land Data Assimilation System (GLDAS) reanalysis from 1980 to 2016 are assimilated into the land component of E3SMv2 within the coupled modeling framework with a 1-month assimilation window. The coupled assimilation experiment is evaluated using multiple metrics, including the cost function, assimilation efficiency index, correlation, root-mean-square error (RMSE), and bias, and compared with a control simulation without land data assimilation. The WCLDA system yields improved simulation of soil moisture and temperature compared with the control simulation, with improvements found throughout the soil layers and in many regions of the global land. In terms of both soil moisture and temperature, the assimilation experiment outperforms the control simulation with reduced RMSE and higher temporal correlation in many regions, especially in South America, central Africa, Australia, and large parts of Eurasia. Furthermore, significant improvements are also found in reproducing the time evolution of the 2012 US Midwest drought, highlighting the crucial role of land surface in drought lifecycle. The WCLDA system is intended to be a foundational resource for research to investigate land-derived climate predictability.

58 GEOSCIENCES↗
DOE OSTI2018

β-cyclodextrin-enhanced Spectrofluorometric Methods for the Determination of Substituted Benzamides (Itopride Hydrochloride, Alizapride, and Mosapride Citrate) in Pharmaceutical Preparations

Two spectrofluorometric methods are developed and optimized for the determination of substituted benz amides, namely itopride hydrochloride (ITO), alizapride (ALI), and mosapride citrate (MOS), in drug substances and pharmaceutical formulations. The first method is based on the measurement of the relative fluorescence intensity of the cited drugs in the absence of methyl-β-cyclodextrin at 380 ± 2 nm using an excitation wavelength of 310 nm in an aqueous solution. The linearity ranges were found to be 0.05–10, 0.1–10, and 0.1–10 μg/mL, with mean recoveries of 100.04% ± 0.21, 100.06% ± 0.65, and 100.08% ± 0.26 for ITO, ALI, and MOS, respectively. The second method is based on the significant enhancement of the fluorescence intensities of the drugs produced through complex formation with methyl-β-cyclodextrin in an aqueous solution at pH 6.6 in the case of ITO and pH 7.2 in the case of ALI and MOS. The fluorescence intensities of the formed complexes were measured at 420 ± 2 nm using an excitation wavelength of 310 nm. The linearity ranges were found to be 5–35, 3–15, and 2–30 ng/mL, with mean recoveries of 100.22 ± 30, 100.12 ± 0.24, and 100.30 ± 0.44, and limits of detection of 1.98, 1.32, and 0.66 ng/mL for ITO, ALI, and MOS, respectively. 1:1 stoichiometries for β -CD-drugs complexes were established. Association constants and Gibbs free energy were calculated by applying the Benesi–Hil de brand equation. The results were found to agree statistically with those obtained from the reference methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Development of comprehensive two-dimensional liquid chromatography for investigating aging of plastic bonded explosives

The feasibility of measuring the aging and degradation of PBX 9501 via online two dimensional liquid chromatography (LC × LC) is investigated, and a preliminary instrumental setup and method is developed. Plastic-Bonded eXplosive (PBX) 9501 is nominally composed of 94.9 wt% HMX, 2.5 wt% Estane® 5703 (poly (ester urethane)), 2.5 wt% BDNPA/F (nitroplasticizer), 0.1 wt% Irganox 1010 and PBNA (N-phenyl-naphthylamine) at low concentrations. When exposed to various environmental conditions, PBX 9501 will degrade through different pathways. Because PBX 9501 is composed of both low molecular weight compounds (BDNPA/F, Irganox 1010, PBNA, and potential degradation products) and high molecular weight compounds (Estane® 5703), analysis is normally performed via two independent analyses. Additionally, the low molecular weight species are analyzed via high pressure liquid chromatography (HPLC) and the high molecular weight species via size exclusion chromatography (SEC). While these individual techniques yield information about the aging of PBX 9501, the combination of HPLC and SEC (i.e. HPLC × SEC) can simplify and streamline the analyses while also providing additional chemical information. A simplified sample preparation method is proposed for LC × LC analysis. Various SEC columns and HPLC column selection, flow rate, and gradient ramps were investigated for their application of measuring aged PBX 9501. Lastly, two LC × LC separations of a library standard of PBX 9501 and a sample of aged PBX 9501 are compared.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Optimization strategies for produced water networks with integrated desalination facilities

Optimal management and desalination of produced water is a major challenge for U.S. oil and gas development. Integrating rigorous desalination models into multi-period produced water network optimization problems presents several hurdles, which need to be tackled using advanced optimization strategies. Here, in this work, a novel multi-period produced water network formulation with separate solid and liquid flows is introduced to avoid singularities at zero flows. Rigorous steady state desalination models based on mechanical vapor recompression are embedded at the desalination sites in the network model. An integrated optimization formulation is developed to co-optimize the design of desalination units along with the operation of the network. Furthermore, a more robust approach based on the trust region filter method is developed to efficiently integrate complex desalination models into the multi-period planning problem. Both optimization approaches are demonstrated on a produced water network from the PARETO library (Drouven et al., 2022) using thermal desalination units. Our results show that while the TRF and integrated approaches have comparable solve times, the TRF approach has better performance reliability in terms of solver convergence. Furthermore, the optimal solution obtained by embedding rigorous models into the network is significantly different than when desalination costs are approximated using simple cost models, which motivates further research in this field.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

An Evaluation of Actinide Reactivity with CO 2 , O 2 , and O 2 /He Gases using Inductively Coupled Plasma Tandem Mass Spectrometry: Application to Simultaneous Measurement of 241 Am/ 241 Pu Ratios in Unseparated Complex Matrices

Accurate actinide measurements are critical within the field of nuclear science. Traditional methods for actinide quantification require time-consuming sample processing prior to analysis. There is a need for rapid analytical techniques that still maintain a high degree of accuracy. In this work, actinide reactivity was assessed for multiple oxygen-containing reaction gases using quadrupole inductively coupled plasma tandem mass spectrometry (Q-ICP-MS/MS) to evaluate actinide analysis in complex sample matrices without analyte-matrix separation. A novel method was developed to measure 241 Am/ 241 Pu in complex sample matrices using O 2 /He reaction gas with no matrix removal or analyte pre-concentration. This inline method reduces matrix-derived polyatomic interferences that complicate traditional ICP-MS analyses by mass-shifting to 241 Am 16 O + and 241 Pu 16 O 2 + , allowing Am and Pu to be mass separated for simultaneous analysis. While mass shifting is efficient, a small portion of Am + (<1.3%) and Pu + (<1.4%) react to from AmO 2 + and PuO + , respectively. Therefore, a mass balance approach was used, in combination with reactivity determined from 242 Pu and 243 Am standard solutions, to correct for residual 241 PuO + and 241 AmO 2 + . The method was validated by measuring 241 Am/ 241 Pu in Pu isotope standards CRM-136 and CRM-137 (separated in March/April 1970 and February 2022, respectively) in both neat solutions and complex matrices containing diluted soil (NIST SRM 2711a, >1000 µg·g -1 ). Method detection limits of 15.9 and 9.6 fg·g -1 were determined for 241 Am and 241 Pu, respectively, and 241 Am/ 241 Pu ratios were measured with accuracies within <3.5%. In conclusion, this work presents the first direct analysis of 241 Am/ 241 Pu in unseparated complex matrices, advancing capabilities for rapid actinide measurements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

A Novel Data Segmentation Method for Data-driven Phase Identification

This paper presents a smart meter phase identification algorithm for two cases: meter-phase-label-known and meter-phase-label-unknown. To improve the identification accuracy, a data segmentation method is proposed to exclude data segments that are collected when the voltage correlation between smart meters on the same phase is weakened. Then, using the selected data segments, a hierarchical clustering method is used to calculate the correlation distances and cluster the smart meters. If the phase labels are unknown, a Connected-Triple-based Similarity (CTS) method is adapted to further improve the phase identification accuracy of the ensemble clustering method. The methods are developed and tested on both synthetic and real feeder data sets. Here, simulation results show that the proposed phase identification algorithm outperforms the state-of-the-art methods in both accuracy and robustness.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2019

Ultrasonic Determination of the Jahn–Teller Effect Parameters in Impurity-Containing Crystals

A method is developed to determine the symmetry properties of strains and the type of Jahn–Teller effect in crystals with impurity ions in a triply degenerate electronic T state. This method is based on a calculation of the isothermal contribution of the impurity subsystem to the elastic moduli of a crystal and the absorption and velocity of normal modes for all three possible problems, namely, T ⊗ e, T ⊗ t{sub 2}, and T ⊗ (e + t{sub 2}). The calculation results are compared with experimental data. The efficiency of the method is demonstrated for a CdSe:Cr{sup 2+} crystal. The CrSe{sub 4} center is found to be described in terms of the problem T ⊗ e. The parameters of the ground-state adiabatic potential are determined.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Conservative Multimoment Transport along Characteristics for Discontinuous Galerkin Methods

A set of algorithms based on characteristic discontinuous Galerkin methods is presented for tracer transport on the sphere. The algorithms are designed to reduce message passing interface communication volume per unit of simulated time relative to current methods generally, and to the spectral element scheme employed by the U.S. Department of Energy's Exascale Earth System Model (E3SM) specifically. Two methods are developed to enforce discrete mass conservation when the transport schemes are coupled to a separate dynamics solver; constrained transport and Jacobian-combined transport. A communication-efficient method is introduced to enforce tracer consistency between the transport scheme and dynamics solver; this method also provides the transport scheme's shape preservation capability. A subset of the algorithms derived here is implemented in E3SM and shown to improve transport performance by a factor of 2.2 for the model's standard configuration with 40 tracers at the strong scaling limit of one element per core. Read More: https://epubs.siam.org/doi/10.1137/18M1165943

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Deciphering controls on metal migration within floodplains: The critical role of redox environments on metal-organic complexes (Final Technical Report)

Our project elucidates the effect of differing hydrologic regimes on nutrient and contaminant dynamics within floodplains, and we explore the impact of varying sources of hydrologic extremes on nutrient-contaminant fate and transport. We use a combination of field measurements and laboratory experiments to examine the relationships between redox conditions, functionality of dissolved organic matter, metal speciation (specifically examining metal-ligand complexes), and nutrient-contaminant fate, particularly during hydrologic extremes. Floodplain biogeochemical variation through climatic extremes and beaver-induced hydrologic variation provide a unique look at controls on nutrient-contaminant fate and transport. Through our work, we have developed a novel approach that provides an unprecedented ability to resolve aqueous metal-organic complexes that reveals metal binding preferences for natural organic matter based on metal-ligand chemistry. We have developed novel methods to separate, quantify, and characterize organic-metal complexes in natural DOM that pair with field experiments comprising floodplains having systematic variation in biogeochemical conditions. We also developed a comprehensive computational approach for molecular characterization of metal-organic species that merges LC-coupled high resolution (HR) mass spectrometry and ICP-MS analysis. Importantly, we show that beaver dams have an outsized influence on hydrologic extremes, dwarfing the impact of climatic variation, that ultimate control biogeochemical conditions and water quality. Additionally, beaver dams impose a hydrologic driver that leads to improved, river water quality by divert water through soils and the hyporheic zone. We further show that iron(III) minerals have a dominant control on carbon mineralization across floodplains independent of hydrologic conditions, and that iron and aluminum associations with organic matter are a controlling factor in carbon mineralization. Ultimately, our work is helping to advancing a robust predictive understanding of how hydrologic changes in watersheds affect water quality and carbon and metal cycling in riparian zones.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Compaction of crushed salt for safe containment – overview of the KOMPASS project

Abstract. In Germany, rock salt formations are possible host rock candidates for a repository for heat-emitting radioactive waste. The safety concept of a repository in salt bases on a multibarrier system consisting mainly of the geological barrier salt and geotechnical seals ensuring safe containment. Crushed salt will be used for backfilling of cavities and sealing measures in drifts and shafts due to its favourable properties and its easy availability (mined-off material). The creep of the rock salt leads to crushed salt compaction with time. Thereby, the crushed salts' porosity is reduced from the initial porosity of 30 %–40 % to a value comparable to the porosity of undisturbed rock salt (≤1 %). In such low porosity ranges, technical impermeability is assumed. The compaction behaviour of crushed salt is rather complex and involves several coupled THM processes (Kröhn et al., 2017; Hansen et al., 2014). It is influenced by internal properties like humidity and grain size distribution, as well as boundary conditions such as temperature, compaction rate or stress state. However, the current process understanding has some important gaps referring to the material behaviour, experimental database and numerical modelling. It needs to be extended and validated, especially in the low porosity range. The objective of the KOMPASS project was development of methods and strategies for the reduction of deficits in the prediction of crushed salt compaction leading to an improvement of the prognosis quality. Key results are as follows (KOMPASS Phase 1, 2020): selection of an easily available and permanently producible synthetic crushed salt mixture, acting as a reference material for generic investigations; development and proof of different techniques for producing pre-compacted samples for further investigations; establishment of a tool of microstructure investigation methods to demonstrate the comparability of grain structures of pre-compacted samples with in-situ compacted material for future investigations; execution of various laboratory experiments using pre-compacted samples, e.g. long-term creep tests which deliver reliable information about time- and stress-dependent compaction behaviour; development of a complex experimental investigation strategy to derive necessary model parameters considering individual functional dependencies. Its technical feasibility was successfully verified; benchmarking with various existing numerical models using datasets from three different triaxial long-term tests. The result was not entirely satisfactory; however, the number of influencing factors is small and further validation work has to be done. Overall, the KOMPASS project has made significant progress in the approaches to solving the outstanding question, building the basis for further investigations.

Friedenberg, Larissa↗
DOE OSTI2021

Adaptive downstream tensorial eddy viscosity for hybrid large‐eddy simulations‐Reynolds‐averaged‐Navier–Stokes simulations

An adaptive method is developed to improve the accuracy of eddy‐viscosity Reynolds‐averaged‐Navier–Stokes (RANS) model in hybrid large‐eddy simulations (LES)‐RANS simulations by using available upstream LES results. The method first gets the tensorial eddy viscosity from the upstream LES solution at the LES‐RANS interface and then uses that information to improve the downstream RANS model by invoking the weak‐equilibrium assumption. The proposed method was evaluated via two test problems—flow in a channel and over a periodic hill. Results obtained show the proposed approach to increase the accuracy and stability of hybrid LES‐RANS simulations. Since the modification of the downstream RANS model is based on the tensorial eddy viscosity from the upstream LES solution, the method is adaptive to the problem being studied.

Zhang, Wanjia↗
DOE OSTI2019

Gold Nanoparticles (AuNPs) as Reactive Matrix for Detection of Trace Levels of HCN in Air by Laser Desorption/Ionization Mass Spectrometry (LDI-MS)

Under direct laser desorption/ionization mass spectrometric conditions, the irradiation of target spots made of gold nanoparticle residues generates a series of peaks at m/z 197, 394, 591… representing Au{sub n}{sup −} ions (n = 1–3). In contrast, spectra recorded from gold nanoparticles directly mixed with an alkali cyanide exhibited an additional peak at m/z 249, indicating an abundant generation of gaseous [Au(CN){sub 2}]{sup −} ions upon irradiation. The relative intensity of the m/z 249 peak surged when the amount of cyanide in the mixture was increased. Most remarkably, a peak at m/z 249 was observed even from neat AuNPs upon irradiation, if a nearby spot, which was not irradiated, happened to bear a cyanide sample. We postulated that traces of HCN emanating from the headspace of aqueous cyanide solution during the sample-plate preparation is sufficient to convert gold to AuCN, which is subsequently detected as [Au(CN){sub 2}]{sup −}. Further experiments demonstrated that the relative intensity of the m/z 249 peak diminishes exponentially as the AuNP spot becomes more distant from the putative HCN source. Eventually, the method was developed as an efficient procedure to detect HCN or alkali cyanides. Using KCN, the detection limits were determined to be below 10 pg of CN{sup −} per spot. The method also demonstrated that, upon crushing, the seeds or roots of certain fruits and vegetables such as apple, peach, radish, and cassava, but not carrot, release HCN in amounts detectable by this method. .

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2023

Computational fluid dynamics investigations of flow, heat transfer, and oxidation in heat recovery steam generator

Modern heat recovery steam generators (HRSGs) operate at elevated temperatures, leading to the formation of oxides inside the tubes of heat exchangers (HXs). This oxide growth reduces the heat recovery efficiency. Moreover, after reaching a certain critical thickness, some oxide scales detach from the tube surface (exfoliation), causing erosion damage to the components downstream. Predicting the metal temperature distribution and associated oxide thickness in the HXs of an HRSG can aid in mitigating these problems. Here, a computational fluid dynamics (CFD) model was developed within the commercial code STAR-CCM+ for the prediction of fluid flow, conjugate heat transfer, and associated oxidation in HRSGs. Moreover, a new Porous Media Model (PMM) method was developed to model the fin effect on the heat transfer in HX, which can substantially reduce the prohibitive computational costs of fin meshes. The developed CFD model was used to conduct a high-fidelity simulation of a real-scale HRSG to investigate flow, heat transfer, and oxide growth. The calculated oxide thickness on different tubes can be used to identify HX regions that require oxide-resistant coatings to prevent exfoliation and ensuing damages. Furthermore, this CFD framework can serve as a reference for future studies that intend to model and investigate high-temperature oxidation in HXs used for any applications.

42 ENGINEERING↗
DOE OSTI2020

Electron transfer calculations between edge sharing octahedra in hematite, goethite, and annite

A key reaction underlying the charge transport in iron containing oxides, clays, micas is the Fe$^{2+}$-Fe$^{3+}$ exchange reaction between edge-sharing iron octahedra. These reactions facilitate conduction in these minerals by the thermally-activated hopping of small polarons across the lattice. Depending on the mineral and local charge state the small polaron can either encase an electron or hole. The probability for conduction of small polarons depends strongly on the height and adiabicity of the reaction barrier, with larger and more diabatic barriers yielding slow conduction associated with either weak coupling or a large prerequisite rearrangement of the lattice during charge transport. To model these reactions, a first principle electron transfer (ET) method was developed to model the small polaron hopping between the edge-sharing octahedra sites in hematite ($e^{-}$ polaron), goethite ($e^{-}$ polaron), and annite ($h^{+}$ polaron) bulk structures. The ET method is based on electronic structure methods (i.e., plane-wave Density Functional Theory) capable of performing calculations with periodic cells and large size systems efficiently while at the same time being accurate enough to be used in the estimation of the electron-transfer coupling matrix element, $V_{AB}$, and the electron transfer transmission factor, $\kappa_{el}$. Additionally, the calculations confirmed the existence of small polarons in all three minerals, and the reactions were predicted to be strongly adiabatic. It was found that transfer of a hole in the octahedral layer of annite had an adiabatic barrier of $0.311$ eV, and the transfer of an extra electron in hematite and goethite had adiabatic barriers of $0.242$ eV and $0.232$ eV respectively. The electronic coupling parameters,$V_{AB}$, were found to be $0.188$ eV, $0.196$ eV, and $0.102$ eV respectively for hematite, goethite, and annite. While similar bonding topologies pertain, the underlying basis for the differences is the subtle differences in local structures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Internal wave energy flux from density perturbations in nonlinear stratifications

Internal gravity wave energy contributes significantly to the energy budget of the oceans, affecting mixing and the thermohaline circulation. Hence it is important to determine the internal wave energy flux $\boldsymbol{J}=p\,\boldsymbol{v}$ , where $p$ is the pressure perturbation field and $\boldsymbol{v}$ is the velocity perturbation field. However, the pressure perturbation field is not directly accessible in laboratory or field observations. Previously, a Green’s function based method was developed to calculate the instantaneous energy flux field from a measured density perturbation field $\unicode[STIX]{x1D70C}(x,z,t)$ , given a constant buoyancy frequency $N$ . Here we present methods for computing the instantaneous energy flux $\boldsymbol{J}(x,z,t)$ for an internal wave field with vertically varying background $N(z)$ , as in the oceans where $N(z)$ typically decreases by two orders of magnitude from the pycnocline to the deep ocean. Analytic methods are presented for computing $\boldsymbol{J}(x,z,t)$ from a density perturbation field for $N(z)$ varying linearly with $z$ and for $N^{2}(z)$ varying as $\tanh (z)$ . To generalize this approach to arbitrary $N(z)$ , we present a computational method for obtaining $\boldsymbol{J}(x,z,t)$ . The results for $\boldsymbol{J}(x,z,t)$ for the different cases agree well with results from direct numerical simulations of the Navier–Stokes equations. Our computational method can be applied to any density perturbation data using the MATLAB graphical user interface ‘EnergyFlux’.

Mechanics↗