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R. A. Plumb

Abstract

General kinematical arguments are used to derive certain properties of eddy fluxes of conserved quantities in a field of small-amplitude waves. The direction of the eddy flux is related in a simple way to wave transience and dissipation; in the absence of local sources and sinks the flux in a steady wave field is directed normal to the background gradient. The flux is expressed as the sum of advective and diffusive terms in addition to a nondivergent contribution.

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R. A. Plumb

Abstract

The properties of forced waves in a two-layer baroclinic fluid are considered. The mean shear is taken to be just smaller than the critical value required for baroclinic instability. A nonlinear evolution equation is derived for the response of the system to weak forcing at a frequency close to resonance. A steady solution exists but under certain circumstances is unstable, in which case the wave undergoes a vacillation cycle, exchanging energy periodically with the mean flow. In general, the wave performs either a small-amplitude vacillation about the steady solution or a larger vacillation akin to that arising from the instability. Which type of solution is chosen depends on forcing amplitude, frequency and initial conditions.

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R. A. Plumb

Abstract

Internal waves propagating through a dissipative fluid interact with the mean flow. In response to forcing by a single wave, the mean flow evolves to a steady solution. In the presence of two (or more) waves such a solution exists but is unstable. The underlying dynamics in the latter case are basically those discussed by Holton and Lindzen (1972) in their theory of the quasi-biennial oscillation. If viscosity is small but nonzero the zonal flow exhibits a long-period oscillation.

This study elucidates the dependence of the period and structure of the oscillation on the imposed parameters, and clarifies the basic dynamics. In particular, the origin of the downward motion of shear zones is discussed in detail following a demonstration (under realistic assumptions) that anomalies in the mean flow structure cannot propagate downward. Thus it is shown that the increase of radiative cooling coefficient with height in the stratosphere is not crucial to the mechanism while the mesospheric semi-annual oscillation is irrelevant for practical purposes. It is also argued that momentum diffusion in the lower stratosphere may be of crucial importance in the momentum budget of the oscillation.

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R. A. Plumb and A. D. McEwan

Abstract

An experiment is described in which a standing internal wave is forced at the lower boundary of an annulus of salt-stratified water. At sufficiently large forcing amplitudes, the wave motion generates a strong mean azimuthal circulation which itself exhibits a long-period oscillation. Theoretical calculations, based on the wave-driven theory of the quasi-biennial oscillation of the tropical stratosphere (with suitable modifications), are performed and compared with the experimental results. Agreement is good and the study thus provides substantial confirmation of the fundamental principles of the theory.

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R. A. Plumb, R. A. Vincent, and R. L. Craig

Abstract

Studies of the quasi-two-day wave show that it is a summertime phenomenon. In the summer of 1983–84 at Adelaide (35°S, 138°E), the main phase of the wave appeared as a pulse in mid-January which lasted about seven cycles (14 days). Coincident with the onset of the pulse a temporary but substantial change occured in the prevailing circulation throughout a deep layer of the upper mesosphere; a perturbation of more than 10 m s&−1 occurred in the northward flow, whereas the change in the zonal flow (about 30 m s−1 westward) actually caused a reversal of the prevailing eastward simulation above 84 km.

It is suggested that these changes in the prevailing circulation were a response to the wave pulse. A simple calculation is performed to estimate the anticipated response to the observed wave event; under plausible assumptions about the magnitude of mean and eddy dissipation processes, predicted circulation changes agree reasonably well with those observed.

It is concluded that such events have a substantial, if temporary, impact on the prevailing circulation in the upper mesospere and may be important in the transport of atmospheric constituents at these heights during summer.

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R. A. Plumb and J. D. Mahlman

Abstract

The GFDL general circulation/tracer model has been used to generate the transport coefficients required in two-dimensional (zonally averaged) transport formulations. This was done by assuming a flux-gradient relationship and then, given gradient and flux statistics from two independent (and contrived) model tracer experiments, to derive the coefficients by inversion of this relation. Given the mean meridional circulation from the GCM, the antisymmetric and symmetric parts of the coefficients tensor determine the advective and diffusive contributions to the net meridional transport in the model. The effective transport circulation thus defined differs substantially from the Lagrangian mean and residual circulations and is in fact a simpler representation of the model circulation than either of these. The diffusive component is coherently structured, comprising the following components:

(i) Strong quasi-horizontal mixing (Dyy ∼ 1 × 106 m2 s−1) in the midlatitude lower troposphere, apparently associated with fronts and the occlusion of synoptic systems.

(ii) A band of strong quasi-horizontal mixing (Dyy ∼ 2 × 106 m2 s−1) stretching across the tropical upper troposphere and the subtropical winter stratosphere. This band follows the band of weak zonal mean winds and is a manifestation in the model of the “surf zone” recently identified by McIntyre and Palmer as a region of breaking planetary waves. Outside the “surf zone,” Dyy ≲ 5 × 105 m2 s−1 in the stratosphere, consistent with other recent estimates.

(iii) Intense vertical mixing (Dzz ≳ 10 m2 s−1) in the troposphere at and near the latitudes of the intertropical convergence zone.

(iv) Vertical (Dzz ∼ 5−10 m2 s−1) through much of the troposphere, a substantial component of which is associated with subgrid-scale mixing (model convective processes).

The validity of the flux-gradient relation as a parameterization of eddy transport processes was tested by implementing the parameterization in a two-dimensional model, using these derived coefficients. In comparison experiments it was found that at the two-dimensional model could reproduce well the zonally-averaged evolution of tracers in the GCM; the quantitative errors that were found may in part result from the finite model resolution, rather than from errors in formulation. Therefore, although the flux-gradient relation is formally justified only in the small-amplitude limit, it appears to be a useful practical description of large-scale transport by finite-amplitude eddies.

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R. Hide, P. J. Mason, and R. A. Plumb

Abstract

Detailed studies of the azimuthal structure of fully developed waves in a differentially heated rotating fluid annulus have been carried out with the aid of instrumentation capable of providing frequent determinations of the temperature variation around a circle concentric with the walls of the annulus. Owing to the cyclic nature of the data they are conveniently analyzed in terms of azimuthal Fourier modes. The time-averaged azimuthal spectra thus obtained show that in the regular regime, where the flow is dominated by a single mode of wavenumber M, say, significant “energy” is found not only in the harmonics required to describe the jet stream structure of the flow but also in the sideband modes of wavenumber M=1 which describe the observed azimuthal modulations in the amplitude and/or phase of the wave. At the high-wavenumber end of those spectra for which an inertial subrange can be resolved the “spectral energy” follows a (wavenumber)−3 law.

The time-dependent behavior of the phases of the sidebands and the main baroclinic mode, &phisM−1, ϕM+1 and ϕM respectively, is such that the value of ϕ≡2ϕM−ϕM−1−ϕM+1, remains nearly constant (and close to π), implying that a frame of reference can be found in which the average intrinsic frequencies of the main mode and its side bands are equal. This special frame is fixed relative to the rotating apparatus when the waves are only weakly dispersive, but it can be altered by sloping the endwalls of the apparatus so as to introduce dispersion and returned to the apparatus frame by introducing irregular topography. The theoretical implications of these results are explored with simple wave-interaction theory, which suggests that the sidebands interact strongly with baroclinically stable long waves, but in such a way that in equilibrium the net energy transfer into the long waves is small.

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A. H. Sobel, R. A. Plumb, and D. W. Waugh

Abstract

Existing quantitative calculations of material transport across the stratospheric polar vortex edge are difficult to interpret. This is because what is actually calculated has not been clearly shown to be irreversible transport, because of ambiguities inherent in defining the vortex edge, and (relatedly) because the uncertainties in the various sorts of calculations have not been quantified. The authors discuss some of the conceptual and technical difficulties involved in such calculations. These typically use a tracer coordinate, so that an air parcel’s “position” is defined as a function of some tracer that it carries. Also examined is the sensitivity to noise of a method that has been used in several prior studies, which the authors call the “contour crossing” method. When contour crossing is implemented with no explicit threshold to discriminate noise from signal, a realistic amount of noise in the tracer data can cause apparent transports across the vortex edge in the range of ten percent to several tens of percent of the vortex area per month, even if the true transport is zero. Moreover, contour crossing does not discriminate between dynamically driven transport and that due to large-scale nonconservative effects acting upon the tracer used to define the coordinate. The authors introduce a new method, which is called the “local gradient reversal” method, for estimating the dynamically driven component of the transport. This method is conceptually somewhat similar to contour surgery but applies to gridded fields rather than material contours. Like contour crossing, it can thus be used in conjunction with the reverse domain filling advection technique, while contour surgery is used with contour advection or contour dynamics. Local gradient reversal is shown to be less sensitive to noise than contour crossing.

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D. W. Waugh, R. A. Plumb, and L. M. Polvani

Abstract

The nonlinear response of a barotropic, nondivergent, spherical flow representative of the upper troposphere (but without a tropical Hadley cell) to localized, extratropical topographic forcing is examined using high-resolution contour surgery calculations. The response is shown to vary greatly with forcing amplitude and can be significantly different from the linear response. At large amplitude, Rossby wave breaking occurs in the tropics irrespective of the direction of the equatorial winds, and leads to small-scale stirring and the formation of a “tropical surf zone,” which inhibits the meridional propagation of the disturbance.

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Aditi Sheshadri, R. Alan Plumb, Erik A. Lindgren, and Daniela I. V. Domeisen

Abstract

Stratosphere–troposphere interactions are conventionally characterized using the first empirical orthogonal function (EOF) of fields such as zonal-mean zonal wind. Perpetual-winter integrations of an idealized model are used to contrast the vertical structures of EOFs with those of principal oscillation patterns (POPs; the modes of a linearized system governing the evolution of zonal flow anomalies). POP structures are shown to be insensitive to pressure weighting of the time series of interest, a factor that is particularly important for a deep system such as the stratosphere and troposphere. In contrast, EOFs change from being dominated by tropospheric variability with pressure weighting to being dominated by stratospheric variability without it. The analysis reveals separate tropospheric and stratospheric modes in model integrations that are set up to resemble midwinter variability of the troposphere and stratosphere in both hemispheres. Movies illustrating the time evolution of POP structures show the existence of a fast, propagating tropospheric mode in both integrations, and a pulsing stratospheric mode with a tropospheric extension in the Northern Hemisphere–like integration.

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