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Timothy J. Dunkerton

Abstract

The decelerating effect of enhanced upper tropospheric wavedriving (DF) in winter and early spring induces a “reverse” component of the residual mean meridional circulation in the polar lower stratosphere opposite to that induced by radiative cooling. The cooling, in turn, is maintained by the decelerating effect of stratospheric DF. If the upper-tropospheric wavedriving is increased, and the stratosphere wavedriving is sufficiently reduced, the change in the mean circulation will include upwelling in the polar lower stratosphere. Analytic and numerically derived properties of this generalized residual mean “body form” circulation are discussed.

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Timothy J. Dunkerton

Abstract

Inertial instabilities on the equatorial beta-plane may take the form of a zonally nonsymmetric disturbance while preserving their centrifugal character. Numerical experiments at finite zonal wavenumber suggest a preferred mode of instability with zonal wavenumber between the symmetric value and a short-wave cutoff in linear cross-equatorial shear. Zonal nonsymmetric results in a slight reduction of the marginally stable shear in the presence of second-order diffusion.

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Timothy J. Dunkerton

Abstract

Observations of ascending water vapor anomalies in the tropical lower stratosphere—the so-called tape recorder effect—have been used to infer profiles of vertical mean motion, vertical constituent diffusivity, and lateral in-mixing rate in this region. The magnitude of vertical wave flux required to drive the quasi-biennial oscillation (QBO) in the presence of mean upwelling, along with other related aspects of QBO dynamics, is examined in light of the tape recorder results using a simple one-dimensional model. As found in a previous study, it is necessary that wave fluxes significantly exceed the “classic” values associated with long-period Kelvin and Rossby-gravity waves; the extra fluxes are presumably associated with a continuous spectrum of short-period gravity and inertia–gravity waves. Larger wave fluxes, when used in connection with traditional wave-transport parameterizations developed for the QBO, require a larger vertical diffusivity of momentum in order to prevent the formation of unrealistically strong vertical wind shear. The profile of constituent diffusivity derived from the tape recorder effect, however, is much smaller everywhere than the momentum diffusivity assumed in previous QBO modeling studies.

Realistic shear is obtained in the model using a momentum-conserving “shear adjustment” scheme representing the effect of unresolved shear instabilities and other processes not included in the wave-transport parameterization. This device, together with a QBO amplitude profile based on the equatorial-wave phase speeds, motivates an (otherwise inviscid) analytic QBO solution in the underdamped, quasi-compressible case. The simple analytic solutions replicate most aspects of the numerical solution, display a similar dependence on wave flux at the lower boundary, and provide reasonably accurate estimates of QBO period in the inviscid limit.

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Timothy J. Dunkerton

Abstract

Internal gravity waves, and the stress divergence and turbulence induced by them, are essential components of the atmospheric and oceanic general circulations. Theoretical studies have not yet reached a consensus as to how gravity waves transport and deposit momentum. The two best-known theories, resonant interaction and Eikonal saturation, yield contradictory answers to this question. In resonant interaction theory, an energetic, high-frequency, low-wavenumber wave is unstable to two waves of approximately half the frequency and is backscattered by a low-frequency wave or mean finestructure of twice the vertical wavenumber. By contrast, the Eikonal saturation model, as it is commonly used, ignores reflection by assuming a slowly varying basic state and does not question the longevity of the primary wave in the presence of local Kelvin–Helmboltz or convective instabilities. The resonant interaction formalism demands that the interactions be weakly nonlinear. The Eikonal saturation model allows strong, “saturated” waves but ignores reflection and eliminates nonlinear instability with respect to other horizontal wavenumbers by invoking the linear or quasi-linear assumption.

To help bridge the gap between the two theories, results from prototype, nonlinear numerical simulations are presented. Attention is directed at the nonlinear instability of gravity waves in a slowly varying basic state. Parametric instability theory yields a group trajectory length scale for the primary wave expressed in terms of the dominant vertical wavelength and degree of convective saturation. This result delimits the range of validity for the Eikonal saturation model: a low-amplitude wave introduced into an undisturbed slowly varying basic state easily traverses many vertical wavelengths; conversely, a convectively neutral wave soon undergoes decay through nonlinear instability provided that some noise is present initially or created in situ by off-resonant interactions.

The numerical results establish the existence of a cascade in wavenumber space, which for hydrostatic waves proceeds toward both higher and lower horizontal wavenumbers, in accord with theory. Substantial reductions in momentum flux are found relative to the linear values.

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Timothy J. Dunkerton

Abstract

It is shown that slowly varying linear equatorial Rossby-gravity waves in a barotropically neutral mean-wind profile near the equator accelerate the mean flow in a stabilizing sense there. This indicates that the Rossby-gravity wave, believed to be the driving force in the easterly acceleration phase of the quasi-biennial oscillation, cannot force a barotropically unstable mean flow near the equator. Mean flows generated near the equator in the easterly phase of the oscillation in then context of these approximations will therefore resemble or be approximately bounded by a parabola of curvature β, where β is the planetary vorticity gradient. This result does not depend upon a “barotropic adjustment” process, although the latter has been suggested in the past and would yield the same result, but over a broader latitudinal area.

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Timothy J. Dunkerton

Abstract

For barotropic flow in spherical geometry, the ideal potential vorticity staircase with flat steps and vertical risers exhibits a relationship between prograde jet strength and spacing such that, for regular spacing, the distance between adjacent jets is given by a suitably defined “Rhines scale” multiplied by a positive constant equal to . This result was obtained previously by the author in the equatorial limit of spherical geometry and by others in periodic beta-plane geometry. An improved asymptotic method has been devised to explain the strength–spacing relationship in sphere-filling solutions. This analysis explains the approximate validity of the equatorial asymptotics and yields new insight on minimum energy states and staircase mode transitions simulated in the presence of random, persistent energy inputs at high horizontal wavenumber.

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Timothy J. Dunkerton

Abstract

The variability of zonally averaged stratospheric circulation is examined using daily gridded analyses from the U.K. Met. Office for 1991–99, corresponding to the period observed by the Upper Atmosphere Research Satellite. Application of rotated principal component analysis to the dataset reveals dominant modes of variability consisting of annual, semiannual, and quasi-biennial oscillations, together with intraseasonal and interannual variability in the winter hemisphere. In the upper stratosphere during northern winter, poleward propagating zonal wind anomalies at the stratopause and a sudden deceleration of the subtropical mesospheric jet in each midwinter are observed. The high-latitude flow is more variable, and the data suggest two contrasting types of wintertime evolution in the polar stratosphere. One is characterized in high latitudes by relatively strong flow in early winter and a significantly weakened flow after solstice, the other by relatively weak flow in early winter and a strong positive flow anomaly after solstice. In both, the subtropical deceleration is accompanied by high-latitude acceleration. In the second type, polar westerlies remain long after solstice, decaying gradually, while in the first type, polar easterlies appear after 10–30 days. In two winters of the first type, the subtropical deceleration is unusually abrupt, followed by brief reacceleration of the polar vortex and a spectacular breakdown after 30 days. Multivariate EOF analysis incorporating temperature data separates deceleration events in northern winter affecting the subtropical jet, with midlatitude warming, from those affecting the polar night jet, with polar warming.

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Timothy J. Dunkerton

Abstract

When the time-averaging operator is applied to the Generalized Lagrangian Mean equations of motion there results a conservation law involving a total static energy invariant which contains the so-called “pseudoenergy”. This invariant is analogous to the Kelvin or Bjerknes circulation which is conserved as an invariant in the zonal averaging case. An approximate pseudoenergy is also derived which is applicable in cases where quadratic “available” potential energy is of interest.

In the small-amplitude limit, the pseudoenergy may be evaluated as an Eulerian diagnostic in terms of the perturbation potential vorticity and entropy fields.

As in the zonal averaging case, the Lagrangian time mean leads to conservation laws not containing any kind of artificial conversion of energy which appears in the conventional Eulerian mean formulation. Hence the Lagrangian mean provides a static energy invariant analogous to the Kelvin or Bjerknes circulation which may be of use in the study of nonlinear waves on time-mean flows in the lower atmosphere.

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Timothy J. Dunkerton

Abstract

A theory of inertial instability on the equatorial beta-plane is developed with application to the inertial stability of the equatorial middle atmosphere at the solstices. It is shown that the stability of this region depends primarily on two unknowns. First, there is the question of whether eddy diffusion can be regarded as stabilizing, or whether this diffusion actually arises from the instability itself. Second, because the diabatic circulation would appear to induce a cross-equatorial shear much greater than that observed, or than that modeled in Holton and Wehrbein (1980), it appears that the gravity wave-induced decelerations would he crucial to the stability of this flow. Unfortunately, the parameterization scheme of Leovy (1964) designed to mimic this effect obscures the issue, since this “frictional drag” concept is invalid on a local basis (Lindzen, 1981).

The expected structure and vertical wavelength of the equatorial inertial instability is discussed in the context of this simple model. Predicted vertical wavelengths also depend on the unknown factors listed above. The greatest likelihood of an observable inertial instability would be in the winter tropical mesosphere, within 10° of the equator.

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Timothy J. Dunkerton

Abstract

Selective transmission of gravity waves into the upper mesosphere and lower thermosphere leads to the generation of mean flows opposite to those below. This interaction is addressed in the context of a simplified transient, stochastic, conservative wave model. The dominant phase speed in the spectrum appears to determine the magnitude of the upper level flow, while the height of interaction is determined by the forcing amplitude. Observed features of the upper atmosphere are efficiently explained by this model, and the results compare very well to recent steady wave models, despite the differing formulations.

The model also provides a tentative explanation of the semiannual oscillation in the tropical upper mesosphere.

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