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Results for “Enstrophy conservation”

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.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1979

An energy and potential enstrophy conserving scheme for the shallow water equations

A three-dimensional finite difference scheme for the solution of the shallow water momentum equations which accounts for the conservation of potential enstrophy in the flow of a homogeneous incompressible shallow atmosphere over steep topography as well as for total energy conservation is presented. The scheme is derived to be consistent with a reasonable scheme for potential vorticity advection in a long-term integration for a general flow with divergent mass flux. Numerical comparisons of the characteristics of the present potential enstrophy-conserving scheme with those of a scheme that conserves potential enstrophy only for purely horizontal nondivergent flow are presented which demonstrate the reduction of computational noise in the wind field with the enstrophy-conserving scheme and its convergence even in relatively coarse grids.

Arakawa, A.↗
NASA NTRS1988

Generalized energy and potential enstrophy conserving finite difference schemes for the shallow water equations

The conditions under which finite difference schemes for the shallow water equations can conserve both total energy and potential enstrophy are considered. A method of deriving such schemes using operator formalism is developed. Several such schemes are derived for the A-, B- and C-grids. The derived schemes include second-order schemes and pseudo-fourth-order schemes. The simplest B-grid pseudo-fourth-order schemes are presented.

Abramopoulos, Frank↗
NASA NTRS1979

Description and preliminary results of the 9-level UCLA general circulation model

The 9-level general circulation model, with the upper boundary of 50 mb, is a modification of the earlier 6- and 12-level versions used at UCLA. Two major design changes have been made in an effort to improve the model: (1) a potential enstrophy conserving scheme in the equation of motion has replaced the previous scheme which only conserved enstrophy for nondivergent flow, and (2) the treatment of the planetary boundary layer has been modified by making the predicted planetary boundary layer top a coordinate surface. Experiments with idealized steep mountains have been made to test each of the major modifications, and the model is now ready for general circulation simulation experiments.

Suarez, M. J.↗
DOE OSTI2021

Conservative numerical schemes with optimal dispersive wave relations: Part I. Derivation and analysis

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.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Conservative Numerical Schemes with Optimal Dispersive Wave Relations: Part II. Numerical Evaluations

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.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1981

A potential enstrophy and energy conserving scheme for the shallow water equations

To improve the simulation of nonlinear aspects of the flow over steep topography, a potential enstrophy and energy conserving scheme for the shallow water equations is derived. It is pointed out that a family of schemes can conserve total energy for general flow and potential enstrophy for flow with no mass flux divergence. The newly derived scheme is a unique member of this family, that conserves both potential enstrophy and energy for general flow. Comparison by means of numerical experiment with a scheme that conserves (potential) enstrophy for purely horizontal nondivergent flow demonstrated the considerable superiority of the newly derived potential enstrophy and energy conserving scheme, not only in suppressing a spurious energy cascade but also in determining the overall flow regime. The potential enstrophy and energy conserving scheme for a spherical grid is also presented.

Arakawa, A.↗
NASA NTRS1977

The 4th order GISS model of the global atmosphere

The new GISS 4th order model of the global atmosphere is described. It is based on 4th order quadratically conservative differences with the periodic application of a 16th order filter on the sea level pressure and potential temperature equations, a combination which is approximately enstrophy conserving. Several short range forecasts indicate a significant improvement over 2nd order forecasts with the same resolution (approximately 400 km). However the 4th order forecasts are somewhat inferior to 2nd order forecasts with double resolution. This is probably due to the presence of short waves in the range between 1000 km and 2000 km, which are computed more accurately by the 2nd order high resolution model. An operation count of the schemes indicates that with similar code optimization, the 4th order model will require approximately the same amount of computer time as the 2nd order model with the same resolution. It is estimated that the 4th order model with a grid size of 200 km provides enough accuracy to make horizontal truncation errors negligible over a period of a week for all synoptic scales (waves longer than 1000 km).

Kalnay-Rivas, E.↗
NASA NTRS1977

Computational design of the basic dynamical processes of the UCLA general circulation model

The 12-layer UCLA general circulation model encompassing troposphere and stratosphere (and superjacent 'sponge layer') is described. Prognostic variables are: surface pressure, horizontal velocity, temperature, water vapor and ozone in each layer, planetary boundary layer (PBL) depth, temperature, moisture and momentum discontinuities at PBL top, ground temperature and water storage, and mass of snow on ground. Selection of space finite-difference schemes for homogeneous incompressible flow, with/without a free surface, nonlinear two-dimensional nondivergent flow, enstrophy conserving schemes, momentum advection schemes, vertical and horizontal difference schemes, and time differencing schemes are discussed.

Arakawa, A.↗
NASA NTRS1982

Numerical study of terrain-induced mesoscale motions in a mixed layer

Numerical integrations using a potential enstrophy-conserving scheme are presented for the flow within a mixed layer over hilly terrain using the hydrostatic shallow-water equations with a quadratic drag law. The mesoscale area treated is 150 km on a side; cyclic lateral boundary conditions are used. It is found that for the idealized conditions treated (no surface heating, no entrainment and no pressure adjustments aloft), the topography quickly induces a steady state flow pattern by means of surface friction. Unsteadiness does not occur unless a surface-friction Reynolds number is greater than approximately 100. Effects of varying the Rossby number, Froude number and terrain-height parameter are examined.

Han, Y.-J.↗
NASA NTRS1984

On the effect of using the Shapiro filter to smooth winds on a sphere

Spatial differencing schemes which are not enstrophy conserving nor implicitly damping require global filtering of short waves to eliminate the build-up of energy in the shortest wavelengths due to aliasing. Takacs and Balgovind (1983) have shown that filtering on a sphere with a latitude dependent damping function will cause spurious vorticity and divergence source terms to occur if care is not taken to ensure the irrotationality of the gradients of the stream function and velocity potential. Using a shallow water model with fourth-order energy-conserving spatial differencing, it is found that using a 16th-order Shapiro (1979) filter on the winds and heights to control nonlinear instability also creates spurious source terms when the winds are filtered in the meridional direction.

Takacs, L. L.↗
NASA NTRS1987

Comparison of horizontal difference schemes for the shallow water equations on a sphere

The accuracy of horizontal difference schemes used in the hydrodynamics parts of General Circulation Models are compared by means of numerical experiments for the shallow water equations on a sphere. As expected, the phase lag of moving waves decreases as the order of accuracy of a scheme increases or as the grid resolution increases. Overall, Takano and Wurtele's partial fourth order energy and potential enstrophy conserving scheme on the C grid is most accurate. It is clearly superior to the other schemes for the Rossby-Haurwitz wave number 6 initial conditions for coarse grid resolution.

Russell, Gary L.↗
NASA NTRS1990

Energy conserving and potential-enstrophy dissipating schemes for the shallow water equations

To incorporate potential enstrophy dissipation into discrete shallow water equations with no or arbitrarily small energy dissipation, a family of finite-difference schemes have been derived with which potential enstrophy is guaranteed to decrease while energy is conserved (when the mass flux is nondivergent and time is continuous). Among this family of schemes, there is a member that minimizes the spurious impact of infinite potential vorticities associated with infinitesimal fluid depth. The scheme is, therefore, useful for problems in which the free surface may intersect with the lower boundary.

Arakawa, Akio↗
NASA NTRS1983

Conservation laws of wave action and potential enstrophy for Rossby waves in a stratified atmosphere

The evolution of wave energy, enstrophy, and wave motion for atmospheric Rossby waves in a variable mean flow are discussed from a theoretical and pedagogic standpoint. In the absence of mean flow gradients, the wave energy density satisfies a local conservation law, with the appropriate flow velocity being the group velocity. In the presence of mean flow variations, wave energy is not conserved, but wave action is, provided the mean flow is independent of longitude. Wave enstrophy is conserved for arbitrary variations of the mean flow. Connections with Eliassen-Palm flux are also discussed.

Straus, D. M.↗
NASA NTRS1983

Conservation laws of wave action and potential enstrophy for Rossby waves in a stratified atmosphere

The evolution of wave energy, enstrophy, and wave motion for atmospheric Rossby waves in a variable mean flow are discussed from a theoretical and pedagogic standpoint. In the absence of mean flow gradients, the wave energy density satisfies a local conservation law, with the appropriate flow velocity being the group velocity. In the presence of mean flow variations, wave energy is not conserved, but wave action is, provided the mean flow is independent of longitude. Wave enstrophy is conserved for arbitrary variations of the mean flow. Connections with Eiiassen-Palm flux are also discussed.

Straus, D. M.↗
DOE OSTI2022

An unconditionally stable, time-implicit algorithm for solving the one-dimensional Vlasov–Poisson system

The development of an implicit, unconditionally stable, numerical method for solving the Vlasov–Poisson system in one dimension using a phase-space grid is presented. The algorithm uses the Crank–Nicolson discretization scheme and operator splitting allowing for direct solution of the finite difference equations. This method exactly conserves particle number, enstrophy and momentum. A variant of the algorithm which does not use splitting also exactly conserves energy but requires the use of iterative solvers. This algorithm has no dissipation and thus fine-scale variations can lead to oscillations and the production of negative values of the distribution function. We find that overall, the effects of negative values of the distribution function are relatively benign. We consider a variety of test cases that have been used extensively in the literature where numerical results can be compared with analytical solutions or growth rates. We examine higher-order differencing and construct higher-order temporal updates using standard composition methods.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1988

Effects of using a posteriori methods for the conservation of integral invariants

The nature and effect of using a posteriori adjustments to nonconservative finite-difference schemes to enforce integral invariants of the corresponding analytic system are examined. The method of a posteriori integral constraint restoration is analyzed for the case of linear advection, and the harmonic response associated with the a posteriori adjustments is examined in detail. The conservative properties of the shallow water system are reviewed, and the constraint restoration algorithm applied to the shallow water equations are described. A comparison is made between forecasts obtained using implicit and a posteriori methods for the conservation of mass, energy, and potential enstrophy in the complete nonlinear shallow-water system.

Takacs, Lawrence L.↗