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NASA NTRS2010

New Gravity Wave Treatments for GISS Climate Models

Previous versions of GISS climate models have either used formulations of Rayleigh drag to represent unresolved gravity wave interactions with the model resolved flow or have included a rather complicated treatment of unresolved gravity waves that, while being climate interactive, involved the specification of a relatively large number of parameters that were not well constrained by observations and also was computationally very expensive. Here, we introduce a relatively simple and computationally efficient specification of unresolved orographic and non-orographic gravity waves and their interaction with the resolved flow. We show comparisons of the GISS model winds and temperatures with no gravity wave parametrization; with only orographic gravity wave parameterization; and with both orographic and non-orographic gravity wave parameterizations to illustrate how the zonal mean winds and temperatures converge toward observations. We also show that the specifications of orographic and nonorographic gravity waves must be different in the Northern and Southern Hemispheres. We then show results where the non-orographic gravity wave sources are specified to represent sources from convection in the Intertropical Convergence Zone and spontaneous emission from jet imbalances. Finally, we suggest a strategy to include these effects in a climate dependent manner.

Geller, Marvin A.↗

NASA NTRS1984

An overview of wave-mean flow interactions during the winter of 1978-79 derived from LIMS observations

Gradient winds, Eliassen-Palm (EP) fluxes and flux divergences, and the squared refractive index for planetary waves have been calculated from mapped data from the Limb Infrared Monitor of the Stratosphere (LIMS) experiment on Nimbus 7. The changes in the zonal mean atmospheric state, from early winter through 3 disturbances, is described. Convergence or divergence of the EP fluxes clearly produces changes in the zonal mean wind. The steering of the waves by the refractive index structure is not as clear on a daily basis.

Gille, J. C.↗

NASA NTRS1981

A further study of the annual cycle of the zonal mean circulation in the middle atmosphere

The influence on the stratospheric mean circulation of planetary wavenumber 2 disturbances excited by steady forcing at the 100 mb level is investigated using a global semi-spectral primitive equation model. There exists a critical forcing amplitude below which the waves have little effect on the mean flow, while above which the waves produce subseasonal time scale vacillations in the winter hemisphere, including both major and minor warmings. Wave transience induced by the evolving mean flow distribution is responsible for generating the vacillations, while thermal damping serves to reduce the wave-driven changes in the mean flow.

Holton, J. R.↗

NASA NTRS1985

A fully implicit scheme for global numerical weather prediction

A fast-slow factored scheme is presented for use with shallow-water primitive equation numerical weather prediction models. The technique was developed to reduce the rotational mode errors which arise when the fast and slow terms of the governing differential equations are treated simultaneously. The method factors out the fast and slow terms along the coordinate directions by means of a modified Crank-Nicolson scheme. A finite-difference spatial discretization is carried out in the zonal and meridional directions to reduce the factorization error to near-zero, and that time steps of 60-90 min can be used to obtain acceptably accurate results, even in the presence of fine spatial structures in the flow.

Augenbaum, J. M.↗

NASA NTRS1988

A conservative approach for flow field calculations on multiple grids

In the computation of flow fields about complex configurations, it is very difficult to construct body-fitted coordinate systems. An alternative approach is to use several grids at once, each of which is generated independently. This procedure is called the 'multiple grids' or 'zonal grids' approach and its applications are investigated in this study. The method follows the conservative approach and provides conservation of fluxes at grid interfaces. The Euler equations are solved numerically on such grids for various configurations. The numerical scheme used is the finite-volume technique with a three-stage Runge-Kutta time integration. The code is vectorized and programmed to run on the CDC VPS-32 computer. Some steady state solutions of the Euler equations are presented and discussed.

Kathong, M.↗

NASA NTRS1987

A simplified model of the modified Hadley circulation

In this paper, a simplified model of modified Hadley circulation that is amenable to analysis is developed to find the low-latitude upper-tropospheric circulation which would exist in the absence of transient eddies. The model is developed as a perturbation of the ideal Hadley circulation solution due to zonally assymmetric thermal forcing and is solved semianalytically. The modified Hadley circulation, found using forcing derived from observed outgoing long-wave radiation, exhibits some similarities to observed features of the tropical and subtropical time-mean upper-tropospheric flow, particularly with regard to the velocity potential.

Schneider, Edwin K.↗

NASA NTRS1988

A conservative approach for flow field calculations on multiple grids

In the computation of flow fields about complex configurations, it is very difficult to construct body-fitted coordinate systems. An alternative approach is to use several grids at once, each of which is generated independently. This procedure is called the multiple grids or zonal grids approach and its applications are investigated in this study. The method follows the conservative approach and provides conservation of fluxes at grid interfaces. The Euler equations are solved numerically on such grids for various configurations. The numerical scheme used is the finite-volume technique with a three-state Runge-Kutta time integration. The code is vectorized and programmed to run on the CDC VPS-32 computer. Some steady state solutions of the Euler equations are presented and discussed.

Kathong, Monchai↗

NASA NTRS1982

Theoretical analyses of Baroclinic flows

A stability analysis of a thin horizontal rotating fluid layer which is subjected to arbitrary horizontal and vertical temperature gradients is presented. The basic state is a nonlinear Hadley cell which contains both Ekman and thermal boundary layers; it is given in closed form. The stability analysis is based on the linearized Navier-Stokes equations, and zonally symmetric perturbations in the form of waves propagating in the meridional direction are considered. Numerical methods were used for the stability problem. It was found that the instability sets in when the Richardson number is close to unity and that the critical Richardson number is a non-monotonic function of the Prandtl number. Further, it was found that the critical Richardson number decreases with increasing Ekman number until a critical value of the Ekman number is reached beyond which the fluid is stable.

Antar, B.↗

NASA NTRS1990

Internal structure of Io and the global distribution of its topography

A global topography is presently calculated for two multilayer Io models in which dissipation occurs in a viscous asthenosphere and a solid mantle: (1) a 'thermal swell' model, in which topography and heat flow are positively correlated, and (2) a 'differentiated lithosphere' model, in which topography and heat flow are negatively correlated. Both the polar topography and the hypsometric distribution of elevations in the differentiated lithosphere model are better matched with observations than the thermal swell model. The shift of the equatorial basin-swell pattern indicates a recent zonal rotation of about 25 deg for Io's lithosphere.

Ross, M. N.↗

NASA NTRS1985

A diagnostic study of eddy-mean flow interactions during FGGE SOP-1

Eliassen-Palm (EP) diagrams have been shown to be very useful diagnostics in both the troposphere and the stratosphere. However, the idea that the EP flux divergence is the sole forcing of the mean wind by the eddies can be misleading. A time series of the time rate of change of the zonal mean wind and the EP flux divergence shows that the two quantities were not well correlated during the FGGE special observing period (SOP-1, winter 1979). Calculation of the residual in the zonal momentum equation reveals that considerable negative acceleration (drag) is required to complete the momentum balance in some regions. This residual indicates that not all terms are well represented in atmospheric data sets, and may be largely due to the breaking of vertically propagating gravity waves near the tropopause. Eliassen-Palm diagrams are presented for the FGGE data, as well as Oort's 11-year climatology. The Oort EP diagrams serve as a standard with which to compare other EP diagrams. The FGGE year is shown to be very similar to climatology. A consistent method of displaying the EP flux vectors and divergence is suggested, which has advantages over previous methods.

Baldwin, M. P.↗

NASA NTRS1979

Pseudo-direct solution to the boundary-layer equations for separated flow

This paper describes a procedure for the automatic iteration of an inverse boundary-layer technique to a prescribed pressure distribution in a separated flow. The technique is demonstrated by computation of two transonic airfoil flows and two externally generated shock boundary-layer interaction flows. These results are compared to experimental data and to solutions of the full Navier-Stokes equations. These comparisons indicate that substantial economies can be obtained by applying methods like the present, in lieu of full Navier-Stokes methods, in zonal calculation schemes for design purposes. The optimization technique leading to convergence is described in detail and a table of typical computation time is presented.

Arieli, R.↗

NASA NTRS1978

Turbulent convection within rapidly rotating superadiabatic fluids with horizontal temperature gradients

A model is developed for small scale thermally driven turbulent convection in rapidly rotating systems. The Boussinesq equations of adiabatic and inviscid flow are perturbed about a basic state which is superadiabatic and which contains a horizontal temperature gradient balanced by a geostrophic wind. The growth rates and length scales of the most unstable modes are determined. It is found that these modes are either zonally or latitudinally symmetric, depending on the latitude and the horizontal temperature gradient. The transports of heat and momentum by the modes are computed. The linear amplitudes are assumed to be limited by shear instability. The model predicts a latitude dependent eddy diffusivity. The applicability of the model to astrophysical and planetary bodies is briefly discussed.

Flasar, F. M.↗

NASA NTRS1981

Numerical model of long-lived Jovian vortices

The extension of the measured zonal velocity profile into the adiabatic interior of Jupiter, while eddies and large oval structures are confined to a shallow stably-stratified upper layer, are assumed in a nonlinear numerical model of long-lived Jovian vortices. In agreement of the observed flows of Jupiter, each vortex is stationary with respect to the shear flow at a critical latitude that is close to the latitude of the vortex center. The solutions obtained are strongly nonlinear, in contrast to the solitary wave solutions that are the weakly nonlinear extensions of ultralong linear waves. The merging of two stable vortices upon collision, rather than the non-interaction predicted by solitary wave theory, is in keeping with Jovian vortex observations. It is suggested that long-lived vortices maintain themselves against dissipation by absorbing smaller vortices produced by convection.

Ingersoll, A. P.↗

NASA NTRS1986

Interaction of the Asian summer monsoon and the Southern Hemisphere

The possible role that divergent circulations emanating from regions of large scale organized convection may have on the rotational motions of the subsiding branch of the resulting overturnings is considered. Correspondence is found between the cross-equatorial flow emanating from regions of organized convection in the Northern Hemisphere, and the subtropical jet in the vicinity of Australia. The difference field also reveals a good correspondence between changes in the meridional gravity wave component and changes in the intensity of maximum zonal wind. The results are consistent with the picture of a local ageostrophic Hadley overturning in the entrance region of subtropical jets, and they show the importance of adequate resolution of tropical divergent modes.

Paegle, Julia N.↗

NASA NTRS1989

A simplified self-adaptive grid method, SAGE

The formulation of the Self-Adaptive Grid Evolution (SAGE) code, based on the work of Nakahashi and Deiwert, is described in the first section of this document. The second section is presented in the form of a user guide which explains the input and execution of the code, and provides many examples. Application of the SAGE code, by Ames Research Center and by others, in the solution of various flow problems has been an indication of the code's general utility and success. Although the basic formulation follows the method of Nakahashi and Deiwert, many modifications have been made to facilitate the use of the self-adaptive grid method for single, zonal, and multiple grids. Modifications to the methodology and the simplified input options make this current version a flexible and user-friendly code.

Davies, C.↗

NASA NTRS1990

A simple inertial model for Neptune's zonal circulation

Voyager imaging observations of zonal cloud-tracked winds on Neptune revealed a strongly subrotational equatorial jet with a speed approaching 500 m/s and generally decreasing retrograde motion toward the poles. The wind data are interpreted with a speculative but revealingly simple model based on steady gradient flow balance and an assumed global homogenization of potential vorticity for shallow layer motion. The prescribed model flow profile relates the equatorial velocity to the mid-latitude shear, in reasonable agreement with the available data, and implies a global horizontal deformation scale L(D) of about 3000 km.

Allison, Michael↗

NASA NTRS1995

A Zonal Approach for Prediction of Jet Noise

A zonal approach for direct computation of sound generation and propagation from a supersonic jet is investigated. The present work splits the computational domain into a nonlinear, acoustic-source regime and a linear acoustic wave propagation regime. In the nonlinear regime, the unsteady flow is governed by the large-scale equations, which are the filtered compressible Navier-Stokes equations. In the linear acoustic regime, the sound wave propagation is described by the linearized Euler equations. Computational results are presented for a supersonic jet at M = 2. 1. It is demonstrated that no spurious modes are generated in the matching region and the computational expense is reduced substantially as opposed to fully large-scale simulation.

Shih, S. H.↗

NASA NTRS1975

Study to define unsteady flow fields and their statistical characteristics

Preliminary estimates of space shuttle fluctuating pressure environments were made based on analyses of wind tunnel data, and empirical prediction techniques. Particular emphasis was given to the external tank and solid rocket boosters for the transonic speed regime during launch of a parallel-burn space shuttle configuration. Predicted environments are presented as space-averaged zonal profiles with progressive shading from zone to zone to illustrate spatial variations in the magnitude of the fluctuating pressure coefficient over the surfaces of the external tank and solid rocket boosters. Predictions are provided for the transonic Mach number range from 0.8 equal to or less than M sub infinity equal to or less than 1.5, and for supersonic Mach numbers of 2.0 and 3.0.

Robertson, J. E.↗