Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Primitive equations”

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.

At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

The ocean model for E3SM global applications: Omega version 0.1.0 – a new high-performance computing code for exascale architectures

This paper introduces Omega, the Ocean Model for E3SM Global Applications. Omega is a new ocean model designed to run efficiently on high performance computing (HPC) platforms, including exascale heterogeneous architectures with accelerators, such as Graphics Processing Units (GPUs). Omega is written in C and uses the Kokkos performance portability library. These were chosen because they are well-supported and will help future-proof Omega for upcoming HPC architectures. Omega will eventually replace the Model for Prediction Across Scales-Ocean (MPAS-Ocean) in the US Department of Energy's (DOE's) Energy Exascale Earth System Model (E3SM). Omega runs on unstructured horizontal meshes with variable-resolution capability and implements the same horizontal discretization as MPAS-Ocean. This work documents the design and performance of Omega Version 0.1.0 (Omega-V0), which solves the shallow water equations with passive tracers and is the first step towards the full primitive equation ocean model. On Central Processing Units (CPUs), Omega-V0 is 1.4 times faster than MPAS-Ocean with the same configuration. Omega-V0 is more efficient on GPUs than CPUs on a per-watt basis – by a factor of 5.3 on Frontier and 3.6 on Aurora, two of the world's fastest exascale computers.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1977

A balanced diagnostic system compatible with a barotropic prognostic model

A system of diagnostic equations for the velocity field, or wind laws, for a barotropic primitive-equation model of large-scale atmospheric flow is derived. Attention is given to the classical balance equation and its ellipticity condition. Numerical solutions of the diagnostic system are presented, including examples of cases of the mixed elliptic-hyperbolic type and cases with non-zero divergence. Procedures for implementing such a system are outlined, along with a review of factors in using the technique for operational numerical weather prediction.

Ghil, M.↗
NASA NTRS1992

Quasigeostrophic vertical motions diagnosed from along- and cross-isentrope components of the Q vector

In a recent paper on the kinematics of frontogenesis, Keyser et al. (1988) conjectured that partitioning the Q vector into along- and cross-isentrope components yields vertical-motion patterns that are respectively cellular and banded: the former on the scale of the baroclinic disturbance, and the latter on the scale of the embedded frontal zones. This conjecture is examined diagnostically through solution of the quasi-geostrophic omega equation, using the output from a nearly adiabatic and frictionless f-plane primitive equation channel model of the evolution of a baroclinic disturbance to finite amplitude. The results of the present study support the proposed conjecture, suggesting the following interpretation of the characteristic comma structure of the vertical-motion field in midlatitude baroclinic disturbances: the dipole is associated with the along-isentrope component of the Q vector, reflecting the wavelike pattern in the potential temperature field within the baroclinic disturbance; the asymmetries are associated with the cross-isentrope component of the Q vector, reflecting the presence of frontal zones within the baroclinic disturbance.

Keyser, Daniel↗
NASA NTRS1979

Effect of subjectively enhancing the initial vorticity field in a short-range numerical forecast

The paper tests a simple method to incorporate subsynoptic-scale information into the initial conditions of a forecast model. The amplitude, orientation and vertical structure of the vorticity field associated with the subsynoptic-scale disturbance are estimated subjectively; this is done using a combination of climatological and physical models together with all available data. The initial values of geopotential are then obtained in the vicinity of the subsynoptic-scale disturbance, as over the rest of the domain, through the balance equation. Two sets of initial conditions are tested in 12-hr forecasts using a six-layer version of a primitive equation forecast model (Anthes and Warner, 1978). The analysis schemes consisted of (1) a careful subjective analysis of radiosonde data with a high-resolution objective interpolation, and (2) the same preceding analysis but including data derived from the enhanced vorticity fields in the vicinity of the subsynoptic-scale disturbance. The results are discussed in some detail.

Fried, G. D.↗
NASA NTRS1992

Quasigeostrophic diagnosis of three-dimensional ageostrophic circulations in an idealized baroclinic disturbance

Keyser et al.'s (1989) kinematic technique for the representation of 3D vertical circulations in baroclinic disturbances in terms of a vector eigenfunction, the 'psi vector', is presently projected onto the framework of quasi-geostrophic (QG) theory. The projection of the psi-vector equation onto the cross-front vertical plane leads to a generalization of the QG form of the Sawyer-Eliassen equation that is applicable to 3D flows. The diagnostic methodologies for the total ageostrophic flow and for the generalized Sawyer-Eliassen equation are illustrated by applications to upper-level and surface frontal zones that are simulated in an f-plane primitive equation channel model of a finite-amplitude baroclinic wave.

Keyser, Daniel↗
NASA NTRS1991

A Variational Formalism for the Radiative Transfer Equation and a Geostrophic, Hydrostatic Atmosphere: Prelude to Model 3

The second step in development of MODEL III is summarized. It combines the four radiative transfer equations of the first step with the equations for a geostrophic and hydrostatic atmosphere. This step is intended to bring radiance into a three dimensional balance with wind, height, and temperature. The use of the geostrophic approximation in place of the full set of primitive equations allows for an easier evaluation of how the inclusion of the radiative transfer equation increases the complexity of the variational equations. Seven different variational formulations were developed for geostrophic, hydrostatic, and radiative transfer equations. The first derivation was too complex to yield solutions that were physically meaningful. For the remaining six derivations, the variational method gave the same physical interpretation (the observed brightness temperatures could provide no meaningful input to a geostrophic, hydrostatic balance) at least through the problem solving methodology used in these studies. The variational method is presented and the Euler-Lagrange equations rederived for the geostrophic, hydrostatic, and radiative transfer equations.

Achtemeier, Gary L.↗
NASA NTRS1991

Diurnal forcing of planetary atmospheres

The utility of the Mars Planetary Boundary Layer Model (MPBL) for calculations in support of the Mars 94 balloon mission was substantially enhanced by the introduction of a balloon equation of motion into the model. Both vertical and horizontal excursions of the balloon are calculated along with its volume, temperature, and pressure. The simulations reproduce the expected 5-min vertical oscillations of a constant density balloon at altitude on Mars. The results of these calculations are presented for the nominal target location of the balloon. A nonlinear balanced model was developed for the Martian atmosphere. It was used to initialize a primitive equation model for the simulations of the Earth's atmosphere at the time of the El Chichon eruption in 1982. It is also used as an assimilation model to update the temperature and wind fields at frequent intervals.

Houben, Howard C.↗
NASA NTRS1992

Results of a zonally truncated three-dimensional model of the Venus middle atmosphere

Although the equatorial rotational speed of the solid surface of Venus is only 4 m s(exp-1), the atmospheric rotational speed reaches a maximum of approximately 100 m s(exp-1) near the equatorial cloud top level (65 to 70 km). This phenomenon, known as superrotation, is the central dynamical problem of the Venus atmosphere. We report here the results of numerical simulations aimed at clarifying the mechanism for maintaining the equatorial cloud top rotation. Maintenance of an equatorial rotational speed maximum above the surface requires waves or eddies that systematically transport angular momentum against its zonal mean gradient. The zonally symmetric Hadley circulation is driven thermally and acts to reduce the rotational speed at the equatorial cloud top level; thus wave or eddy transport must counter this tendency as well as friction. Planetary waves arising from horizontal shear instability of the zonal flow (barotropic instability) could maintain the equatorial rotation by transporting angular momentum horizontally from midlatitudes toward the equator. Alternatively, vertically propagating waves could provide the required momentum source. The relative motion between the rotating atmosphere and the pattern of solar heating, which as a maximum where solar radiation is absorbed near the cloud tops, drives diurnal and semidiurnal thermal tides that propagate vertically away from the cloud top level. The effect of this wave propagation is to transport momentum toward the cloud top level at low latitudes and accelerate the mean zonal flow there. We employ a semispectral primitive equation model with a zonal mean flow and zonal wavenumbers 1 and 2. These waves correspond to the diurnal and semidiurnal tides, but they can also be excited by barotropic or baroclinic instability. Waves of higher wavenumbers and interactions between the waves are neglected. Symmetry about the equator is assumed, so the model applies to one hemisphere and covers the altitude range 30 to 110 km. Horizontal resolution is 1.5 deg latitude, and vertical resolution is 1.5 km. Solar and thermal infrared heating, based on Venus observations and calculations drive the model flow. Dissipation is accomplished mainly by Rayleigh friction, chosen to produce strong dissipation above 85 km in order to absorb upward propagating waves and limit extreme flow velocities there, yet to give very weak Rayleigh friction below 70 km; results in the cloud layer do not appear to be sensitive to the Rayleigh friction. The model also has weak vertical diffusion, and very weak horizontal diffusion, which has a smoothing effect on the flow only at the two grid points nearest the pole.

Newman, M.↗
NASA NTRS1983

Theoretical study of multiple equilibria in simple axisymmetric tropical circulations

The possibility that the asymmetric part of the atmospheric circulation can possess multiple equilibrium states is examined using a two-layer axisymmetric model involving balance equations on an equatorial beta plane. Mountains are excluded from consideration and a Newtonian cooling formulation represents thermal forcing. A temperature maximum at 25 deg N is selected to simulate summer conditions in the Northern Hemisphere. Steady-state solutions obtained are investigated for stability with regard to first and second y-mode perturbations. A single stable mode is found, together with two other quasi-stable states. Attention is given to numerically modeling multiple equilibria in symmetric circulations, and one steady-state is determined for the two-layer model. A model employing primitive equations with the Boussinesq approximation is also examined, and it also furnishes only one steady state. The reasons for the lack of multiple steady-states as derived by the models are discussed.

Goswami, B. N.↗
NASA NTRS1987

Finite element techniques for the Navier-Stokes equations in the primitive variable formulation and the vorticity stream-function formulation

Finite element procedures for the Navier-Stokes equations in the primitive variable formulation and the vorticity stream-function formulation have been implemented. For both formulations, streamline-upwind/Petrov-Galerkin techniques are used for the discretization of the transport equations. The main problem associated with the vorticity stream-function formulation is the lack of boundary conditions for vorticity at solid surfaces. Here an implicit treatment of the vorticity at no-slip boundaries is incorporated in a predictor-multicorrector time integration scheme. For the primitive variable formulation, mixed finite-element approximations are used. A nine-node element and a four-node + bubble element have been implemented. The latter is shown to exhibit a checkerboard pressure mode and a numerical treatment for this spurious pressure mode is proposed. The two methods are compared from the points of view of simulating internal and external flows and the possibilities of extensions to three dimensions.

Glaisner, F.↗
DOE OSTI2021

Comparing numerical accuracy and stability for different horizontal discretizations in MPAS-Ocean

This manuscript investigates the effectiveness of two possible horizontal discretizations for the global ocean model MPAS-Ocean, both applied to Spherical Centroidal Voronoi Tessellations (SCVTs). The first discretization is TRiSK, a C-grid, finite-volume method, that possesses many desirable mimetic properties, but has a low order accuracy. The second discretization was introduced for the first time by Peixoto (2016), and consists of modifications to the TRiSK scheme designed to achieve at least first-order accuracy in the L ∞ norm, with the loss of some of the mimetic properties. Tests on shallow-water and primitive-equation models show that the scheme due to Peixoto is indeed more accurate, but presents stability issues with respect to TRiSK. Here, TRiSK is indeed found to be often more stable in time and more robust with respect to errors in the geometric properties of the grid.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Turbulence modeling to aid tidal energy resource characterization in the Western Passage, Maine, USA

Numerical models combined with field measurements are regularly used to characterize tidal energy resources at potential energetic sites. However, most existing works only focus on the tidal hydrodynamic characteristics, and turbulence parameters are often not reported because of the lack of high-quality turbulence measurements and the limitations of numerical models in resolving turbulent eddies. In this study, we used FVCOM - a hydrostatic primitive equation (HPE) model - to characterize the tidal energy resource in the Western Passage, Maine, USA, by taking care of the essential macro-scale turbulence properties. We observed an excellent model performance using the Mellor-Yamada Level 2.5 Turbulence Model; estimating the spatial and vertical distribution of the turbulent kinetic energy and intensity added a new perspective to the site ranking for tidal energy converter (TEC) deployments. In addition, we also examined the role of channel geometry and bathymetry, such as headlands and underwater sills, in enhancing turbulent eddies around potential TEC siting locations. Ultimately, the detailed analysis of the turbulent flow characteristics has changed the site-ranking results and demonstrated that the regional-scale HPE models could be used for the relative understanding of more or less turbulent sites for a refined resource assessment.

16 TIDAL AND WAVE POWER↗
DOE OSTI2021

Persistent meanders and eddies lead to quasi-steady Lagrangian transport patterns in a weak western boundary current

The Brazil Current (BC) is a weak western boundary current flowing along the Southwestern Atlantic Ocean. It is frequently described as a flow with intense mesoscale activity and relatively low volume transport between 5.0 and 10.0 Sv. We use a 13-year eddy-resolving primitive-equation simulation to show that the presence of persistent meanders and eddies leads to characteristic quasi-steady Lagrangian transport patterns, aptly extracted through climatological Lagrangian Coherent Structures (cLCS). The cLCS position the surface expression of the BC core along the 2000-m isobath, in excellent visual agreement with high resolution satellite sea-surface temperature and the model Eulerian mean velocity. The cLCS deformation pattern also responds to zonally persistent cross-shelf SSH transition from positive (high) values near coastline to low (negative) values between 200- and 2000-m and back to positive (high) offshore from the 2000-m isobath. Zonally-paired cyclonic and anticyclonic structures are embedded in this transition, also causing the cLCS to deform into chevrons. An efficient transport barrier is identified close to the 200-m isobath confirmed by limited inshore movement of drogued drifters and accurately indicated by an along slope maxima of climatological strength of attraction. We also show that the persistent cyclonic and anticyclonic structures may induce localized cross-shelf transport. Regions of low climatological strength of attraction coincide with large shelves and with stagnant synthetic trajectories. We also show that cLCS accurately depict trajectories initiated at the location of Chevron’s spill (November 2011) as compared to synthetic and satellite-tracked trajectories, and the outline of the oil from that accident. There is also an agreement between the large-scale oil slicks reaching the Brazilian beaches (from August 2019 to February 2020) and the strength of climatological attraction at the coast. Our work also clarifies the influence of persistent mesoscale structures on the regional circulation. The identification and quantitative description of climatological Lagrangian coherent structures is expected to improve the effectiveness of future emergency response to oil spills, contingency planning, rescue operations, larval and fish connectivity assessment, drifter launch strategies, waste pollutant and marine debris dispersion and destination.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1973

Numerical simulation of the world ocean circulation

A multi-level model, based on the primitive equations, is developed for simulating the temperature and velocity fields produced in the world ocean by differential heating and surface wind stress. The model ocean has constant depth, free slip at the lower boundary, and neglects momentum advection; so that there is no energy exchange between the barotropic and baroclinic components of the motion, although the former influences the latter through temperature advection. The ocean model was designed to be coupled to the UCLA atmospheric general circulation model, for the study of the dynamics of climate and climate changes. But here, the model is tested by prescribing the observed seasonally varying surface wind stress and the incident solar radiation, the surface air temperature and humidity, cloudiness and the surface wind speed, which, together with the predicted ocean surface temperature, determine the surface flux of radiant energy, sensible heat and latent heat.

Takano, K.↗
NASA NTRS1974

The GISS model of the global atmosphere

A description and numerical results are presented for a global atmospheric circulation model developed at the Goddard Institute for Space Studies (GISS). The model version described is a 9-level primitive-equation model in sigma coordinates. It includes a realistic distribution of continents, oceans and topography. Detailed calculations of energy transfer by solar and terrestrial radiation make use of cloud and water vapor fields calculated by the model. The model hydrologic cycle includes two precipitation mechanisms: large-scale supersaturation and a parameterization of subgrid-scale cumulus convection. Results are presented both from a comparison of the 13th to the 43rd days (January) of one integration with climatological statistics, and from five short-range forecasting experiments. In the extended integration, the near-equilibrium January-mean model atmosphere exhibits an energy cycle in good agreement with observational estimates, together with generally realistic zonal mean fields of winds, temperature, humidity, transports, diabatic heating, evaporation, precipitation, and cloud cover.

Somerville, R. C. J.↗
NASA NTRS1974

Short-range forecasts with the GISS model of the global atmosphere

A nine-layer, primitive equation (PE) model of the global atmosphere developed at the Goddard Institute for Space Studies (GISS) has been used to generate six 48-hr forecasts during December 1972 and January 1973. Operational analyses north of 18 N and experimental global analyses made available by the National Meteorological Center (NMC), NOAA, were used as the initial conditions; the operational analyses were used to verify the forecasts at 12-hr intervals over the Northern Hemisphere north of 22 N. The combined analyses were used to verify the forecasts in the global domain. RMS errors of the sea-level pressure, 1000-mb heights, and vector geostrophic winds, and 500-mb heights and vector geostrophic winds indicate that the GISS forecasts have skill comparable to those made by operational PE models.

Druyan, L. M.↗
NASA NTRS1975

Three-dimensional time dependent computation of turbulent flow

The three-dimensional, primitive equations of motion are solved numerically for the case of isotropic box turbulence and the distortion of homogeneous turbulence by irrotational plane strain at large Reynolds numbers. A Gaussian filter is applied to governing equations to define the large scale field. This gives rise to additional second order computed scale stresses (Leonard stresses). The residual stresses are simulated through an eddy viscosity. Uniform grids are used, with a fourth order differencing scheme in space and a second order Adams-Bashforth predictor for explicit time stepping. The results are compared to the experiments and statistical information extracted from the computer generated data.

Kwak, D.↗
NASA NTRS1974

Short-range forecasts with the GISS model of the global atmosphere

Results of tests carried out during the period from December 1972 through January 1973 to determine the short-term forecasting accuracy of a multilevel numerical primitive-equation (PE) model of the global atmosphere developed at the Goddard Institute for Space Studies (GISS). Six 48-hr forecasts were carried out with the aid of this model, using nine vertical levels and a horizontal grid spacing of 4 deg in latitude and 5 deg in longitude for an effective grid point separation averaging slightly more than 400 km. Verification of forecast sea-level pressures, 1000-mb heights, and 500-mb heights, as well as 1000-mb and 500-mb vector geostrophic winds, shows that the model has forecast skill comparable to that of operational PE models. Based on the 36-hr evolution of 18 extratropical cyclones, the model forecasts exhibit a tendency toward underestimating their propagation speeds and overestimating their central pressures. Both deficiencies are attributed to inadequate horizontal grid resolution. Quantitative verification of forecast surface temperatures over the eastern United States shows a forecast skill equal to that achieved by combined dynamical-statistical procedures.

Druyan, L. M.↗