SEARCH · Engineering Papers
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
A well-organized, very low energy ocean swell system off the East Coast of the United States was tracked with the Seasat synthetic aperture radar from deep water, across the continental shelf, and into shallow water. The results indicate that spaceborne imaging radar may be used to accurately measure ocean wavelength and direction, even in coastal areas and in the presence of a mixed ocean.
Standard vector calculus formulas of Cartesian three space are projected onto the surface of a sphere. This produces symmetric equations with three nonindependent horizontal velocity components. Each orthogonal axis has a velocity component that rotates around its axis (eastward velocity rotates around the north–south axis) and a specific angular momentum component that is the product of the velocity component multiplied by the cosine of axis’ latitude. Angular momentum components align with the fixed axes and simplify several formulas, whereas the rotating velocity components are not orthogonal and vary with location. Three symmetric coordinates allow vector resolution and calculus operations continuously over the whole spherical surface, which is not possible with only two coordinates. The symmetric equations are applied to one-layer shallow water models on cubed-sphere and icosahedral grids, the latter being computationally simple and applicable to an ocean domain. Model results are presented for three different initial conditions and five different resolutions.
We develop a statistical framework for the dynamical closure of spatiotemporal dynamics governed by partial differential equations. Employing the mathematical framework of quantum mechanics to embed the original classical dynamics into a quantum mechanical representation, we use the space of quantum density operators to model the unresolved degrees of freedom of the original dynamics in a statistical sense, and the framework of quantum measurement to predict their contributions to the resolved dynamics. The embedded dynamics is discretized by a positivity preserving process, leading to a compressed representation that is invariant under the dynamical symmetries of the resolved dynamics. We present a data based formulation of the closure scheme and apply it to a closure problem for the shallow water equations. The numerical results demonstrate that our closure model can accurately predict the main features of the true dynamics, including for out of sample initial conditions.
The Hyperspectral Imager for the Coastal Ocean (HICO) aboard the International Space Station has offered for the first time a dedicated space-borne hyperspectral sensor specifically designed for remote sensing of the coastal environment. However, several processing steps are required to convert calibrated top-of-atmosphere radiances to the desired geophysical parameter(s). These steps add various amounts of uncertainty that can cumulatively render the geophysical parameter imprecise and potentially unusable if the objective is to analyze trends and/or seasonal variability. This research presented here has focused on: (1) atmospheric correction of HICO imagery; (2) retrieval of bathymetry using an improved implementation of a shallowwater inversion algorithm; (3) propagation of uncertainty due to environmental noise through the bathymetry retrieval process; (4) issues relating to consistent geo-location of HICO imagery necessary for time series analysis, and; (5) tide height corrections of the retrieved bathymetric dataset. The underlying question of whether a temporal change in depth is detectable above uncertainty is also addressed. To this end, nine HICO images spanning November 2011 to August 2012, over the Shark Bay World Heritage Area, Western Australia, were examined. The results presented indicate that precision of the bathymetric retrievals is dependent on the shallow water inversion algorithm used.Within this study, an average of 70% of pixels for the entire HICO-derived bathymetry dataset achieved a relative uncertainty of less than +/-20%. A per-pixel t-test analysis between derived bathymetry images at successive timestamps revealed observable changes in depth to as lowas 0.4 m. However, the present geolocation accuracy of HICO is relatively poor and needs further improvements before extensive time series analysis can be performed.
We consider the parallel-in-time solution of both linear and nonlinear hyperbolic partial differential equation (PDE) systems in one spatial dimension. In the nonlinear setting, the discretized equations are solved with a preconditioned residual iteration based on a global linearization. The linear(ized) equation systems are approximately solved parallel-in-time using a block preconditioner applied in the characteristic variables of the underlying linear(ized) hyperbolic PDE. This change of variables is motivated by the observation that intervariable coupling between characteristic variables is weak, at least locally where spatio-temporal variations in the eigenvectors of the associated flux Jacobian are sufficiently small, while that between the original variables is not. For an ℓ-dimensional system of PDEs, applying the preconditioner consists of solving a sequence of ℓ scalar linear(ized)-advection-like problems, each associated with a different characteristic wave-speed in the underlying linear(ized) PDE. Furthermore, we approximately solve these linear advection problems using multigrid reduction-in-time (MGRIT); however, any other suitable parallel-in-time method could be used. Numerical examples are shown for the (linear) acoustics equations in heterogeneous media and for the (nonlinear) shallow water equations and Euler equations of gas dynamics with shocks and rarefactions. For many test problems, the solver converges in just a handful of iterations and with mesh-independent convergence rates.
Culverts allow roads to safely traverse small streams or drainage ditches, and their proper design is critical to ensure a safe and reliable transportation network. A correct modelization of these hydraulic structures becomes crucial in the assessment of flood footprints or discharge peak estimation in a risk evaluation plan. The question of how to include culverts comes up frequently when assembling a hydraulic model that requires the presence of as many singular elements as possible. In this work, three different culvert integrations with the surface domain are studied and compared in the context of a 2D shallow water (SW) model. All of them are based on the Federal Highway Administration (FHWA) formulation for the culvert discharge estimation but differ in complexity and in the interaction with the numerical model for surface flow, some of them as internal boundary conditions. Several steady and unsteady validation test cases are presented and the numerical results are compared with the predictions from HEC-RAS 1D and HY-8 software. Furthermore, the culvert area, shape and their sensitivity to the 2D computational mesh is also analyzed.
An energy-conserving and an energy-and-enstrophy conserving numerical schemes are derived by approximating the Hamiltonian formulation of the inviscid shallow water flows based on the vorticity-divergence variables. These schemes also conserve the first-order moments such as mass and vorticity, as usual. The conservative properties of the schemes stem from the skew-symmetry and singularities of the Poisson brackets, which are carefully retained in the discrete approximations. Here, the schemes operate on unstructured orthogonal dual meshes, over bounded or unbounded domains, and they are also shown to possess the same optimal dispersive wave relations as those of the Z-grid scheme, which is a consequence of the use of the vorticity and divergence variables.
Two ocean models are considered for geophysical flow simulations: the multilayer shallow water equations and the multilayer primitive equations. For the former, we investigate the parallel performance of exponential time differencing (ETD) methods, including exponential Rosenbrock–Euler, ETD2wave, and B-ETD2wave. For the latter, we take advantage of the splitting of barotropic and baroclinic modes and propose a new two-level method in which an ETD method is applied to solve the fast barotropic mode. Furthermore, these methods could improve the computational efficiency of numerical simulations because ETD methods allow for much larger time step sizes than traditional explicit time-stepping techniques that are commonly used in existing computational ocean models. Several standard benchmark tests for ocean modeling are performed and comparison of the numerical results demonstrates a great potential of applying the parallel ETD methods for simulating real-world geophysical flows.
In this paper we extend the DGiT multirate framework, developed in Connors and Sockwell (2022) for scalar transmission problems, to a solid–solid interaction (SSI) problem involving two coupled elastic solids and a coupled air–sea model with the rotating, thermal shallow water equations. In so doing we aim to demonstrate the broad applicability of the mathematical theory and governing principles established in Connors and Sockwell (2022) to coupled problems characterized by subproblems evolving at different temporal scales. Further, multirate time integration algorithms employing different time steps, optimized for the dynamics of each subproblem, can significantly improve simulation efficiency for such coupled problems. However, development of multirate algorithms is a highly non-trivial task due to the coupling, which can impact accuracy, stability or other desired properties such as preservation of system invariants. DGiT provides a general template for multirate time integration that can achieve these properties. To elucidate the manner in which DGiT accomplishes this task, we fully detail each step in the application of the framework to the SSI and air–sea coupled problems. Numerical examples illustrate key properties of the resulting multirate schemes for both problems.
A new open source multi-GPU 2D flood model called TRITON is presented in this work. The model solves the 2D shallow water equations with source terms using a time-explicit first order upwind scheme based on an Augmented Roe's solver that incorporates a careful estimation of bed strengths and a local implicit formulation of friction terms. Here, the scheme is demonstrated to be first order accurate, robust and able to solve for flows under various conditions. TRITON is implemented such that the model effectively utilizes heterogeneous architectures, from single to multiple CPUs and GPUs. Different test cases are shown to illustrate the capabilities and performance of the model, showing promising runtimes for large spatial and temporal scales when leveraging the computer power of GPUs. Under this hardware configuration, communication and input/output subroutines may impact the scalability. The code is developed under an open source license and can be freely downloaded in https://code.ornl.gov/hydro/triton.
Abstract The development of any atmosphere or ocean model warrants a suite of test cases (TCs) to verify its spatial and temporal discretizations, order of accuracy, stability, reproducibility, portability, scalability, etc. In this paper, we present a suite of shallow water TCs designed to verify the barotropic solver of atmosphere and ocean models. These include the non‐dispersive coastal Kelvin wave; the dispersive inertia‐gravity wave; the dispersive planetary and topographic Rossby waves; the barotropic tide; and a non‐linear manufactured solution. These TCs check the implementation of the linear pressure gradient term; the linear constant or variable‐coefficient Coriolis and bathymetry terms; and the non‐linear advection terms. Simulation results are presented for a variety of time‐stepping methods as well as two spatial discretizations: a mimetic finite volume method based on the TRiSK scheme, and a high‐order discontinuous Galerkin spectral element method. The experimental procedure for conducting these numerical experiments is detailed. It underscores several key considerations that vary depending on the chosen spatial discretization method. Finally, convergence studies of every TC are conducted with refinement in both space and time, only in space, and only in time. The convergence slopes match the expected theoretical predictions.
A new energy and enstrophy conserving scheme (EEC) for the shallow water equations is proposed and evaluated using a suite of test cases over the global spherical or bounded domain. The evaluation is organized around a set of pre-defined properties: accuracy of individual operators, accuracy of the whole scheme, conservation of key quantities, control of the divergence variable, representation of the energy and enstrophy spectra, and simulation of nonlinear dynamics. The results confirm that the scheme is between the first and second order accurate, and conserves the total energy and potential enstrophy up to the time truncation errors. Here, the scheme is capable of producing more physically realistic energy and enstrophy spectra, indicating that it can help prevent the unphysical energy cascade towards the finest resolvable scales. With an optimal representation of the dispersive wave relations, the scheme is able to keep the flow close to being non-divergent, and maintain the geostrophically balanced structures with large-scale geophysical flows over long-term simulations.
The rotation of Earth breaks time-reversal and reflection symmetries in an opposite sense north and south of the equator, leading to a topological origin for certain atmospheric and oceanic equatorial waves. Away from the equator, the rotating shallow-water and stably stratified primitive equations exhibit Poincaré inertia–gravity waves that have nontrivial topology as evidenced by their strict superinertial time scale and a phase singularity in frequency–wavevector space. This nontrivial topology then predicts, via the principle of bulk-interface correspondence, the existence of two equatorial waves along the equatorial interface, the Kelvin and Yanai waves. To directly test the nontrivial topology of Poincaré-gravity waves in observations, we examine ERA5 data and study cross correlations between the wind velocity and geopotential height of the midlatitude stratosphere at the 50 hPa height. We find the predicted vortex and antivortex in the relative phase of the geopotential height and velocity at the high frequencies of the waves. By contrast, lower-frequency planetary waves are found to have trivial topology also as expected from theory. These results demonstrate a new way to understand stratospheric waves and provide a new qualitative tool to investigate waves in other components of the climate system.
Flooding events pose significant risk to human life, property, and infrastructure. Physically-consistent quantification of altered flood risks in global models requires hyper-resolution (~1 km) or fine flood simulations using two-dimensional (2D) physics schemes, both of which are unavailable in the current generation Earth System Models. Here, in this work, we have developed the River Dynamical Core (RDycore), which is an open-source, 2D shallow water equation (SWE) library for the U.S. Department of Energy's Energy Exascale Earth System Model (E3SM). RDycore uses PETSc and libCEED libraries that allows it to run efficiently on CPUs and GPUs, as well as select a time-integration algorithm at runtime without requiring any code modifications. RDycore achieves spatial error convergence rates for problems with analytical and manufactured solutions similar to those reported previously in the literature, or consistent with the implemented first-order spatial discretization scheme. RDycore's accuracy in predicting flooding for a well-studied dam break problem is comparable to existing SWE models. For a problem with 471 million grid cells, RDycore achieves a speedup of 6.6x and 7.6x on GPUs compared to CPUs when using 320 compute nodes on DOE's Perlmutter and Frontier supercomputers, respectively. The one-way coupling of the RDycore library within E3SM is demonstrated by performing multiple 5-day flooding simulations during Hurricane Harvey driven by five precipitation datasets. The E3SM--RDycore simulations at 30 m spatial resolution accurately simulate maximum water height during the hurricane when benchmarked against a previously published study and achieve a speedup of 15x (Perlmutter) and 21x (Frontier) on GPUs relative to CPUs. The work presented here is the foundational step in providing hardware and algorithmic portability framework for simulating kilometer-scale river dynamics within E3SM.
Three near-neutral boundary layer data sets were investigated with the aim of finding a dependence of wind stress on both wind speed and significant wave height. The data set most representative of open-ocean wave height, wind speed, and momentum flux conditions, was selected and analyzed by means of the least-squares method to produce a new parameterization for the wind stress as a function of both wind speed and significant wave height. This study shows that the wind stress, and consequently the drag coefficient, decreases with increasing wave height for a fixed wind speed. The study also shows that the curvature of the wind profile decreases with increasing wave height and that the C(DN) = A + BU-bar(10) form for the drag coefficient parameterization is inadequate. A drag coefficient that applies to both smooth and rough flows is proposed. These results are more applicable for open-ocean deep-water conditions and less applicable for sheltered, closed, shallow water sites.
Abstract The effect of climate warming in response to rising atmospheric CO 2 on the ventilation of the ocean remains uncertain. Here we make theoretical advances in elucidating the relationship between ideal age and transit time distribution (TTD) in a time-dependent flow. Subsequently, we develop an offline tracer-transport model to characterize the ventilation patterns and time scales in the time-evolving circulation for the 1850–2300 period as simulated with the Community Earth System Model version 1 (CESMv1) under a business-as-usual warming scenario. We found that by 2300 2.1% less water originates from the high-latitude deep water formation regions (both hemispheres) compared to 1850. In compensation, there is an increase in the water originating from the subantarctic. We also found that slowing meridional overturning circulation causes a gradual increase in mean age during the 1850–2300 period, with a globally averaged mean-age increase of ∼110 years in 2300. Where and when the water will be re-exposed to the atmosphere depends on the post-2300 circulation. For example, if we assume that the circulation persists in its year-2300 state (scenario 1), the mean interior-to-surface transit time in year 1850 is ∼1140 years. In contrast, if we assume that the circulation abruptly recovers to its year-1850 state (scenario 2), the mean interior-to-surface transit time in 1850 is only ∼740 years. By 2300, these differences become even larger; in scenario 1, the mean interior-to-surface transit time increases by ∼200 years, whereas scenario 2 decreases by ∼80 years. The dependence of interior-to-surface transit time on the future ocean circulation produces an additional unavoidable uncertainty in the long-term durability of marine carbon dioxide removal strategies. Significance Statement The ocean’s circulation, when altered by climate warming, can affect its capacity to absorb heat and CO 2 , which are crucial for the global climate. In our study, we investigated how global warming, caused by rising CO 2 levels, might impact the ocean circulation—the way water moves from deep ocean to the surface and vice versa. We discovered that by 2300, if we continue on our current warming trajectory, the origins of water within the ocean will shift, with less coming from deep, cold zones near the poles and more from subantarctic regions. As a result, deep water will take longer time before it resurfaces than shallow water. How quickly this water travels from deep regions to the surface could change, depending on the state of future ocean circulation. If the circulation remains as predicted in 2300, this journey will take longer. Conversely, if it reverts to the pattern in 1850, the process will be quicker. This variability introduces added uncertainty to strategies aimed at mitigating climate change by storing CO 2 in the ocean. Our work highlights the intricate ways in which climate change can influence our oceans, potentially affecting our plans to mitigate global warming.
The author has identified the following significant results. Bands 6 and 7 have fine structure as obtained by proper selection of digital levels in processing the CCT's. This is contrary to the imagery density received. This means that the small lakes can be classified in IR for different types of water masses. At least four distinct water masses have been determined for test lakes. They are shoreline, shallow water, and two deep waters. One deep water is patchy and presents difficulty in training set selection. The excellent weather and a completely successful field test form a significant happening. It required 12 orbits over the test area before perfect weather occurred.
The author has identified the following significant results. Evidence of a heat sink produced by perched water tables was detected with HCMM night thermal data. The region of shallow water was not visible on HCMM visible or day IR imagery. The results are consistant with previous aircraft investigations.