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DOE OSTI2021

Dynamic Mode Decomposition of Random Pressure Fields over Bluff Bodies

Fluctuating surface pressures on a bluff body exposed to a boundary layer flow generally are characterized as a spatiotemporally varying random field. In this paper, a dynamic mode decomposition (DMD) was applied to extract dominant features embedded in these random pressure fields. Utilizing an unsupervised machine learning algorithm, spatial modes and their temporal variations were grouped into different clusters at scales, e.g., macro, meso, and micro. A proper orthogonal decomposition (POD) of the experimental data was carried out to observe commonalities and distinctive perspectives each decomposition offers. Here, a comprehensive examination of the DMD/POD for their convergence criteria, data sufficiency, and modal components analysis was conducted. The physical interpretation of the spatiotemporal pressure field based on these decomposition schemes was discussed. At different scales, the DMD modes can capture the evolution of aerodynamic features, e.g., convection of vortices (or vortex tubes) and other structures. The distribution of energy among these three broad scales also reflects an energy cascade in pressure fluctuations akin to turbulence.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2001

Non-seasonal Gravitational Effects of Interannual Meteorological Oscillations in Atmosphere and Ocean

Via mass transport, the interannual meteorological oscillations (ENSO, NAO, etc.) produce slight variations in the global gravitational field, which can be observed by satellite laser ranging (SLR) and anticipated space missions such as GRACE. The meteorological oscillation modes are identified using empirical orthogonal function and principal component decomposition using de-seasoned surface fields produced from the 40-years of NCEP reanalysis. This decompositional analysis requires an accounting for issues associated with area-weighting and non-zero mean. The atmospheric contributions to gravitational variation, mode by mode and in combinations, are then computed via regional integration. To address the corresponding oceanic contributions, we examine the output of the numerical POCM ocean circulation model (1992-1998) in two ways: ocean bottom pressure field and ocean surface topography minus steric effect. The resulting lowest-degree Stokes coefficients for both NCEP reanalysis and POCM are then compared with space geodetic SLR observations, to identify the importance of each meteorological oscillations in gravitational variation signals.

Chao, Benjamin F.↗

NASA NTRS1980

Handling Qualities of Large Flexible Aircraft

The effects on handling qualities of elastic modes interaction with the rigid body dynamics of a large flexible aircraft are studied by a mathematical computer simulation. An analytical method to predict the pilot ratings when there is a severe modes interactions is developed. This is done by extending the optimal control model of the human pilot response to include the mode decomposition mechanism into the model. The handling qualities are determined for a longitudinal tracking task using a large flexible aircraft with parametric variations in the undamped natural frequencies of the two lowest frequency, symmetric elastic modes made to induce varying amounts of mode interaction.

Poopaka, S.↗

NASA NTRS2023

Numerical Study on the Aerodynamics of an Iced Airfoil With Scale-Resolving Simulations

Scale-resolving simulations of the NACA 23012 airfoil with horn ice accretion on the leading edge are conducted using the hybrid Reynolds-averaged Navier–Stokes/large-eddy simulation (hybrid RANS/LES) and wall-modeled large-eddy simulation (WMLES) approaches implemented in the Launch, Ascent, and Vehicle Aerodynamics (LAVA) framework. Aerodynamic results at the Reynolds number of 1.8 million show good comparison with the experimental measurements at different angles of attack from pre-stall to post-stall regimes. The pressure plateaus caused by the flow separation and the recovery of pressure inside the separation bubble around the iced leading edge are well predicted with the scale-resolving simulations when sufficient grid resolution is used around the accreted ice. The unsteadiness of the turbulent flows around the iced airfoil is also examined through the turbulent kinetic energy with the Reynolds normal stress anisotropy. Kelvin–Helmholtz instability (KHI) arises at the shear layer triggered by the upper ice horn and leads to rapid laminar-to-turbulent transition over a large range of angle of attack. With the increase of the angle of attack, the region with high turbulence intensity induced by the unstable shear layer spreads quickly over the entire upper surface of the airfoil. The coherent KHI modes from the upper and lower ice horns are extracted using the spectral proper orthogonal decomposition (SPOD) technique. The SPOD modes extracted from the upper shear layer have large-scale variations in the spanwise direction and low-rank behavior where the energy of the leading SPOD mode at each Strouhal number of the KHI largely represents the total energy when the mode number in the spanwise direction is small.

ARMD↗

NASA NTRS2023

Numerical Study on the Aerodynamics of an Iced Airfoil With Scale-Resolving Simulations

ARMD↗

DOE OSTI2023

Variational deep learning of equilibrium transition path ensembles

Here, we present a time-dependent variational method to learn the mechanisms of equilibrium reactive processes and efficiently evaluate their rates within a transition path ensemble. This approach builds off of the variational path sampling methodology by approximating the time-dependent commitment probability within a neural network ansatz. The reaction mechanisms inferred through this approach are elucidated by a novel decomposition of the rate in terms of the components of a stochastic path action conditioned on a transition. This decomposition affords an ability to resolve the typical contribution of each reactive mode and their couplings to the rare event. The associated rate evaluation is variational and systematically improvable through the development of a cumulant expansion. We demonstrate this method in both over- and under-damped stochastic equations of motion, in low-dimensional model systems, and in the isomerization of a solvated alanine dipeptide. In all examples, we find that we can obtain quantitatively accurate estimates of the rates of the reactive events with minimal trajectory statistics and gain unique insights into transitions through the analysis of their commitment probability.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1984

On the identification of normal modes of oscillation from observations of the solar periphery

The decomposition of solar oscillations into their constituent normal modes requires a knowledge of both the spatial and temporal variation of the perturbation to the Sun's surface. The task is especially difficult when only limited spatial information is available. Observations of the limb darkening function, for example, are probably sensitive to too large a number of modes to permit most of the modes to be identified in a power spectrum of measurements at only a few points on the limb, unless the results are combined with other data. A procedure was considered by which the contributions from quite small groups of modes to spatially well resolved data obtained at any instant can be extracted from the remaining modes. Combining these results with frequency information then permits the modes to be identified, at least if their frequencies are low enough to ensure that modes of high degree do not contribute substantially to the signal.

Gough, D. D.↗

NASA NTRS1984

On the identification of normal modes of oscillation from observations of the solar periphery

The decomposition of solar oscillations into their constituent normal modes requires a knowledge of both the spatial and temporal variation of the perturbation to the sun's surface. The task can be especially difficult when only limited spatial information is available. Observations of the limb-darkening function, for example, are probably sensitive to too large a number of modes to permit most of the modes to be identified in a power spectrum of measurements at only a few points on the limb, unless the results are combined with other data. In this paper a procedure is considered by which the contributions from quite small groups of modes to spatially well resolved data obtained at any instant can be extracted from the remaining modes. Combining these results with frequency information then permits the modes to be identified, at least if their frequencies are low enough to ensure that modes of high degree do not contribute substantially to the signal.

Gough, D. O.↗

NASA NTRS2021

Moisture and Temperature Influences on Nonlinear Vegetation Trends in Serengeti National Park

While long-term vegetation greening trends have appeared across large land areas over the late 20th century, uncertainty remains in identifying and attributing finer-scale vegetation changes and trends, particularly across protected areas. Serengeti National Park (SNP) is a critical East African protected area, where seasonal vegetation cycles support vast populations of grazing herbivores and a host of ecosystem dynamics. Previous work has shown how non-climate drivers (e.g. land use) shape the SNP ecosystem, but it is still unclear to what extent changing climate conditions influence SNP vegetation, particularly at finer spatial and temporal scales. We fill this research gap by evaluating long-term (1982–2016) changes in SNP leaf area index (LAI) in relation to both temperature and moisture availability using Ensemble Empirical Mode Decomposition and Principal Component Analysis with regression techniques. We find that SNP LAI trends are nonlinear, display high sub-seasonal variation, and are influenced by lagged changes in both moisture and temperature variables and their interactions. LAI during the long rains (e.g. March) exhibits a greening-to-browning trend reversal starting in the early 2000s, partly due to antecedent precipitation declines. In contrast, LAI during the short rains (e.g. November, December) displays browning-to-greening alongside increasing moisture availability. Rising temperature trends also have important, secondary interactions with moisture variables to shape these SNP vegetation trends. Our findings show complex vegetation-climate interactions occurring at important temporal and spatial scales of the SNP, and our rigorous statistical approaches detect these complex climate-vegetation trends and interactions, while guarding against spurious vegetation signals.

Moisture↗

DOE OSTI2023

Disruption event characterization and forecasting in tokamaks

Disruption prediction and avoidance is a critical need for next-step tokamaks, such as ITER. Disruption Event Characterization and Forecasting (DECAF) research fully automates analysis of tokamak data to determine chains of events that lead to disruptions and to forecast their evolution allowing sufficient time for mitigation or complete avoidance of the disruption. Disruption event chains related to local rotating or global magnetohydrodynamic (MHD) modes and vertical instability are examined with warnings issued for many off-normal physics events, including density limits, plasma dynamics, confinement transitions, and profile variations. Along with Greenwald density limit evaluation, a local radiative island power balance theory is evaluated and compared to the observation of island growth. Automated decomposition and analysis of rotating tearing modes produce physical event chains leading to disruptions. A total MHD state warning model comprised of 15 separate criteria produces a disruption forecast about 180 ms before a standard locked mode detector warning. Single DECAF event analyses have begun on KSTAR, MAST, and NSTX/-U databases with thousands of shot seconds of device operation using from 0.5 to 1 × 10 6 tested sample times per device. An initial multi-device database comparison illustrates a highly important result that plasma disruptivity does not need to increase as βN increases. Global MHD instabilities, such as resistive wall modes (RWMs), can give the briefest time period of warning before disruption compared to other physics events. In an NSTX database with unstable RWMs, the mode onset, loss of boundary and current control, and disruption event warnings are found in all cases and vertical displacement events are found in 91% of cases. An initial time-dependent reduced physics model of kinetic RWM stabilization created to forecast the disruption chain predicts instability 84% of the time for experimentally unstable cases with a relatively low false positive rate. Instances of the disruption event chain analysis illustrate dynamics including H–L back transitions for rotating MHD and global RWM triggering events. Furthermore, disruption warnings are issued with sufficient time before the disruption (on transport timescales) to potentially allow active profile control for disruption avoidance, active mode control, or mitigation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Estimating Eigenenergies from Quantum Dynamics: A Unified Noise-Resilient Measurement-Driven Approach

Ground state energy estimation in physical, chemical, and materials sciences is one of the most promising applications of quantum computing. In this work, we introduce a new hybrid approach that finds the eigenenergies by collecting real-time measurements and post-processing them using the machinery of dynamic mode decomposition (DMD). From the perspective of quantum dynamics, we establish that our approach can be formally understood as a stable variational method on the function space of observables available from a quantum many-body system. We also provide strong theoretical and numerical evidence that our method converges rapidly even in the presence of a large degree of perturbative noise, and show that the method bears an isomorphism to robust matrix factorization methods developed independently across various scientific communities. Our numerical benchmarks on spin and molecular systems demonstrate an accelerated convergence and a favorable resource reduction over state-of-the-art algorithms. The DMD-centric strategy can systematically mitigate noise and stands out as a leading hybrid quantum-classical eigensolver.

Shen, Yizhi↗

DOE OSTI2024

On detrending stream velocity time series for robust tidal flow turbulence characterization

We investigated the impact of detrending techniques on turbulence quantities from tidal stream flow data, focusing on the autocorrelation function, $ρ_{uu}$, and velocity spectrum, $Φ(f)$. Standard detrending methods, including high-pass frequency-based and polynomial-based techniques, are examined, alongside a proposed alternative method, the empirical mode decomposition (EMD). Our results highlight that intervals of flow acceleration and deceleration, typical in tidal and riverine flows, significantly affect the estimation of turbulence quantities using high-pass frequency filtering and polynomial detrending of varying orders. These methods can strongly influence $ρ_{uu}$ and $Φ(f)$, thereby affecting the accurate estimation of derived quantities. We examine two variations of detrending data using EMD; the first removes only the EMD residue, and the second removes both the residue and the largest scale intrinsic mode function (IMF). By comparing the detrended spectra with the modeled von Kármán spectra, we demonstrate that the second variation (i.e., removing the residue and the largest scale IMF) successfully removed the large-scale trend of the data while retaining the energy of other scales.

Detrend↗

NASA NTRS2001

Gravitational Signal of Mass Redistribution Due to Interannual Meteorological Oscillations in Atmosphere and Ocean

Interannual meteorological oscillations (ENSO, QBO, NAO, etc.) have demonstrable influences on Earth's rotation. Here we study their effects on global gravitational field, whose temporal variations are being studied using SLR (satellite laser ranging) data and in anticipation of the new space mission GRACE. The meteorological oscillation modes are identified using the EOF (empirical orthogonal function)/PC (principal component) decomposition of surface fields (in which we take care of issues associated with the area-weighting and non-zero mean). We examine two fields, one for the global surface pressure field for the atmosphere obtained from the NCEP reanalysis (for the past 40 years), one for the surface topography field for the ocean from the Topex/Poseidon (T/P) data (for the past 8 years). We use monthly maps, and remove the mean-monthly ("climatology") values from each grid point, hence focusing only on non-seasonal signals. The T/P data were first subject to a steric correction where the steric contribution to the ocean surface topography was removed according to output of the numerical POCM model. The respective atmospheric and oceanic contributions to the gravitational variation, in terms of harmonic Stokes coefficients, are then combined mode-by-mode. Since the T/P data already contain the oceanic response to overlying atmospheric pressure, no regards to the inverted-barometer behavior for the ocean need be considered. Results for the lowest-degree Stokes coefficients can then be compared with space geodetic observations including the Earth's rotation and the SLR data mentioned above, to identify the importance of each meteorological oscillations in gravitational variation signals.

Chao, B. F.↗

DOE OSTI2020

Eigenmode analysis of the sheared-flow Z-pinch

Experiments have demonstrated that a Z-pinch can persist for thousands of times longer than the growth time of global magnetohydrodynamic (MHD) instabilities such as the m=0 sausage and m=1 kink modes. These modes have growth times on the order of ta=a/vi, where vi is the ion thermal speed and a is the pinch radius. Axial flows with duz/dr ≲ vi/a have been measured during the stable period, and the commonly accepted theory is that this amount of shear is sufficient to stabilize these modes as predicted by numerical studies using the ideal MHD equations. However, these studies only consider specific equilibrium profiles that typically have a modest magnitude for the logarithmic pressure gradient, qP≡d ln P/d ln r, and may not represent experimental conditions. Linear stability of the sheared-flow Z-pinch is studied here via a direct eigen-decomposition of the matrix operator obtained from the linear ideal MHD equations. Several equilibrium profiles with a large variation of qP are examined. Considering a practical range of k, 1/3 ≲ ka ≲ 10, it is shown that the shear required to stabilize m=0 modes can be expressed as duz/dr≥Cγ0/(ka)α. Here, γ0=γ0(ka) is the profile-specific growth rate in the absence of shear, which scales approximately with |qP|. Both C and α are profile-specific constants, but C is order unity and α≈1. It is further demonstrated that even a large value of shear, duz/dr=3vi/a, is not sufficient to provide linear stabilization of the m=1 kink mode for all profiles considered. This result is in contrast to the currently accepted theory predicting stabilization at much lower shear, duz/dr=0.1vi/a, and suggests that the experimentally observed stability cannot be explained within the linear ideal-MHD model.

Angus, J. R. (ORCID:0000000314740002)↗

NASA NTRS1993

Interannual Sea Level Variations in the Tropical Indian Ocean from Geosat and Shallow Water Simulations

Sea level variations of the Indian Ocean north of 20 deg S are analyzed from Geosat satellite altimeter data over April 1985-September 1989. These variations are compared and interpreted with numerical simulations derived from a reduced gravity model forced by FSU observed winds over the same period. After decomposition into complex empirical orthogonal functions, the low-frequency anomalies are described by the first two modes for observations as well as for simulations. The sums of the two modes contain 34% and 40% of the observed and simulated variances, respectively. Averaged over the basin, the observed and simulated sea level changes are correlated by 0.92 over 1985-1988. The strongest change happens during the El Ninio 1986-1987: between winter 1986 and summer 1987 the basin-averaged sea level rises by approx. 1 cm. These low-frequency variations can partly be explained by changes in the Sverdrup circulation. The southern tropical Indian Ocean between 1O deg and 20 deg S is the domain where those changes are strongest: the averaged sea level rises by approx. 4.5 cm between winter 1986 and winter 1987. There, the signal propagates southwestward across the basin at a speed similar to free Rossby waves. Sensitivity of observed anomalies is examined over 1987-1988, with different orbit ephemeris, tropospheric corrections, and error reduction processes. The uncertainty of the basin-averaged sea level estimates is mostly due to the way the orbit error is reduced and reaches approx. 1 cm. Nonetheless, spatial correlation is good between the various observations and better than between observations and simulations. Sensitivity of simulated anomalies to the wind uncertainty, examined with Former Soviet Union (FSU) and European Center for Medium-Range Weather Forecasting (ECMWF) forcings over 1985-1988, shows that the variance of the simulations driven by ECMWF is 52% smaller, as FSU winds are stronger than ECMWF. Results show that the wind strength also affects the dynamic response of the ocean: anomalies propagate westward across the basin more than twice as fast with FSU than with ECMWF. It is found that the discrepancy is larger between ECMWF and FSU simulations than between observations and FSU simulations.

Perigaud, Claire↗

NASA NTRS2004

Trend and Variability of China Precipitation in Spring and Summer: Linkage to Sea Surface Temperatures

Observational records in the past 50 years show an upward trend of boreal-summer precipitation over central eastern China and a downward trend over northern China. During boreal spring, the trend is upward over southeastern China and downward over central eastern China. This study explores the forcing mechanism of these trends in association with the global sea-surface temperature (SST) variations on the interannual and inter-decadal timescales. Results based on Singular Value Decomposition analyses (SVD) show that the interannual variability of China precipitation in boreal spring and summer can be well defined by two centers of actions for each season, which are co-varying with two interannual modes of SSTs. The first SVD modes of precipitation in spring and summer, which are centered in southeastern China and northern China, respectively, are linked to an ENSO-like mode of SSTs. The second SVD modes of precipitation in both seasons are confined to central eastern China, and are primarily linked to SST variations over the warm pool and Indian Ocean. Features of the anomalous 850-hPa winds and 700-Wa geopotential height corresponding to these modes support a physical mechanism that explains the causal links between the modal variations of precipitation and SSTs. On the decadal and longer timescale, similar causal links are found between the same modes of precipitation and SSTs, except for the case of springtime precipitation over central eastern China. For this case, while the interannual mode of precipitation is positively correlated with the interannual variations of SSTs over the warm pool and Indian Ocean; the inter-decadal mode is negatively correlated with a different SST mode, the North Pacific mode. The later is responsible for the observed downward trend of springtime precipitation over central eastern China. For all other cases, both the interannual and inter-decadal variations of precipitation can be explained by the same mode of SSTs. The upward trend of springtime precipitation over southeastern China and downward trend of summertime precipitation over northern China are attributable to the warming trend of the ENSO-like mode. The recent frequent summertime floods over central eastern China are linked to the warming trend of SSTs over the warm pool and Indian Ocean.

Yang, Fanglin↗

DOE OSTI2022

Diagnosis of the imploding shell asymmetry in polar-direct-drive deuterium–tritium cryogenic target implosions on OMEGA

We discuss the analyses of gated, x-ray imaging data from polar-direct-drive experiments with cryogenically layered deuterium–tritium targets on the OMEGA laser. The in-flight shell asymmetries were diagnosed at various times during the implosion, which was caused by the beam pointing geometry and preimposed variations in the energy partition between the different groups of laser beams. The shape of the ablation surface during the acceleration phase of the implosion was measured along two different lines of sight, and a Legendre mode (ℓ-mode) decomposition was applied for modes of up to ten to investigate shell asymmetries. A clear causal relationship between the imposed beam imbalance and the shape of the in-flight shell asymmetries was observed. The imploded shell with a balanced energy ratio shows smaller values of the amplitudes of ℓ-mode 2 compared to that from implosions with an imbalanced ring energy ratio. The amplitudes of ℓ-modes 4 and 6 are the same within the measurement uncertainty with respect to the change in beam energy ratio.

47 OTHER INSTRUMENTATION↗

NASA NTRS1999

East Asian Summer Monsoon Rainfall: A Historical Perspective of the 1998 Flood over Yangtze River

One of the main factors that might have caused the disastrous flood in China during 1998 summer is long-term variations that include a trend indicating increasing monsoon rainfall over the Yangtze River Valley. China's 160-station monthly rainfall anomaly for the summers of 1955-98 is analyzed for exploring such long-term variations. Singular value decomposition (SVD) between the summer rainfall and the global sea surface temperature (SST) anomalies reveals that the rainfall over Yangtze River Valley is closely related to global and regional SST variabilities at both interannual and interdecadal timescales. SVD1 mode links the above normal rainfall condition in central China to an El Nino-like SSTA distribution, varying on interannual timescale modified by a trend during the period. SVD3 mode links positive rainfall anomaly in Yangtze River Valley to the warm SST anomaly in the subtropical western Pacific, varying on interannual timescales modified by interdecadal timescales. This link tends to be stronger when the Nino3 area becomes colder and the western subtropical Pacific becomes warmer. The 1998 summer is a transition season when the 1997/98 El Nino event was in its decaying phase, and the SST in the Nino3 area emerged below normal anomaly while the subtropical western Pacific SST above normal. Thus, the first and third SVD modes become dominant in 1998 summer, favoring more Asian summer monsoon rainfall over the Yangtze River Valley.

Weng, H.-Y.↗