David G. Andrews

A Finite-Amplitude Eliassen-Palm Theorem in Isentropic Coordinates

Abstract Isentropic coordinates are used to generalize to finite amplitude the celebrated theorem (1.1) of Eliassen and Palm(1961),under non-acceleration conditions. This primitive-equation result also generalizes the finite-amplitude quasi-geostrophic result of Edmon et at. (1980). A simple physical interpretation is provided, and a set of transformed Eulerian-mean equations arises naturally in the course of the analysis. Isentropes which intersect the lower boundary need special attention; the technique developed to handle them is a generalization of an idea due to Lorenz (1955), and may be of use in other contexts. Mention is also made of a version of the theorem valid for small-amplitude, transient, non-conservative disturbances.

A Conservation Law for Small-Amplitude Quasi-Geostrophic Disturbances on a Zonally Asymmetric Basic Flow

Abstract A quadratic conservation law is derived for small-amplitude quasi-geostrophic disturbances on a wavy basic state. The law may be useful for describing the three-dimensional propagation of disturbances on time-averaged flows. This parallels the use of the generalized Eliassen-Palm theorem in the description of waves propagating on zonally-averaged flows.

Dynamical Evolution of the Northern Stratosphere in Early Winter 1991/92, as Observed by the Improved Stratospheric and Mesospheric Sounder

Abstract Dynamical fields based on temperature measurements from the Improved Stratospheric and Mesospheric Sounder on the Upper Atmosphere Research Satellite are presented for the Northern Hemisphere stratosphere for the period 28 October 1991 through 18 January 1992. Interpretation of these fields gives a picture of the dynamical evolution of this period in terms of the zonal-mean fields and the synoptic structures. Among the features of interest are the movements of the zonal-mean jets and several periods of stratospheric warming, culminating in a near-major warming in January.

On the Direction of the Eddy Momentum Flux in Baroclinic Instability

Abstract The direction of the vertically-integrated horizontal eddy flux of momentum in linear baroclinically unstable modes is investigated in a number of cases where the basic flow contains horizontal, as well as vertical, shear. A general result is presented for slowly-growing modes on a flow with weak horizontal shear. Some special cases are described in which standard baroclinic instabilities of finite growth rate (for an internal jet, Eadys model, and a two-layer model) are perturbed by weak horizontal shear, and some computations for flows with large horizontal shear are also mentioned. A general rule emerging from these calculations is that for flows with horizontal jet structure of broader scale than the radius of deformation, the vertically-integrated momentum flux tends to be into the jet (or upgradient); while for jets narrower than the radius of deformation, momentum fluxes tend to be out of the jet (downgradient), even when the contribution of horizontal curvature to the basic state potenti...

The influence of atmospheric waves on the general circulation of the middle atmosphere

To a first approximation, the basic features of the globally averaged structure of the middle atmosphere (such as the warm stratopause and cold mesopause) can be understood on radiative grounds alone. However, dynamical processes must be invoked if the observed latitudinally varying structures of the zonal-mean temperature and wind fields are to be explained. Particularly large departures from a hypothetical radiatively determined state occur in the winter stratosphere (especially in the Northern Hemisphere) and in the upper mesosphere at the solstices. Simple theoretical models indicate that the primary dynamical mechanisms that drive the middle atmosphere away from radiative balance are wave motions, notably large-scale planetary waves and small-scale gravity waves. Much current research is being devoted to understanding the complex transient and irreversible processes by which such waves can influence the zonal-mean state and also lead to the meridional transport of chemical species.

On the mean motion induced by transient inertio-gravity waves

Using standard ‘two-scaling’ techniques we calculate the Eulerian- and Lagrangianmean flows induced at second order in amplitude by small-amplitude, transient, non-dissipative, vertically-propagating inertio-gravity waves on anf-plane. The example is an idealized one, but illustrates a number of important features that are typical of wave, mean-flow interaction in a rotating, stratified fluid. Physical discussion of the solution is given in Section 4 of the review byMcIntyre (1980), which appears elsewhere in this issue.

A spectral model for simulation of tides in the middle atmosphere. I: Formulation

Abstract A linear spectral tidal model is developed for use in interpreting satellite data for the middle atmosphere. It allows for inclusion of zonal-mean background winds and the parameterization of dissipation processes. In the companion papers (Wood and Andrews, 1996a,b), the model is used to simulate diurnal and semidiurnal tides and comparisons are made with other models and with observations.

Using Different Formulations of the Transformed Eulerian Mean Equations and Eliassen―Palm Diagnostics in General Circulation Models

Abstract Transformed Eulerian mean (TEM) equations and Eliassen–Palm (EP) flux diagnostics are presented for the general nonhydrostatic, fully compressible, deep atmosphere formulation of the primitive equations in spherical geometric coordinates. The TEM equations are applied to a general circulation model (GCM) based on these general primitive equations. It is demonstrated that a naive application in this model of the widely used approximations to the EP diagnostics, valid for the hydrostatic primitive equations using log-pressure as a vertical coordinate and presented, for example, by Andrews et al. in 1987 can lead to misleading features in these diagnostics. These features can be of the same order of magnitude as the diagnostics themselves throughout the winter stratosphere. Similar conclusions are found to hold for “downward control” calculations. The reasons are traced to the change of vertical coordinate from geometric height to log-pressure. Implications for the modeling community, including comp...

Wave–Mean-Flow Interaction in the Middle Atmosphere

Publisher Summary This chapter describes the wave–mean-flow interaction in the middle atmosphere. An important accompaniment to any form of separation of atmospheric quantities into mean-flow and wave parts is the development of a suitable theoretical framework for the diagnosis and interpretation of data that are thus separated. Quantitative information on both aspects of the wave–mean-flow interaction— namely, the influence of the mean flow on the propagation of the waves and the rectified back effect of the waves on the mean flow is required. Ideally, the theoretical formalism should also be capable of providing qualitative physical insights into the two-way process. The stratospheric sudden warming is the most dramatic large-scale dynamical event to occur in the middle atmosphere. It is suggested that the breaking of upward-propagating gravity waves may help to force the mesopause semiannual oscillation. It is found that the significant time-mean zonal flows appear in these regions, as well as the oscillating components and these are likely to influence wave propagation there.

On the available energy density for axisymmetric motions of a compressible stratified fluid

An exact, local expression is obtained for the available energy density for axisymmetric motion of a compressible, stratified fluid. Under certain stated conditions the available energy density is positive definite; this fact can be used to demonstrate the stability of an appropriately defined reference state to finite-amplitude axisymmetric disturbances. The theory extends certain previous results on available energy and axisymmetric stability that are valid only for small-amplitude disturbances.