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Ka Kit Tung

Abstract

Through a critical analysis of the convergence properties of spectral series, it is shown that Clark's method of solution leads to a divergent series; hence all his recent results on quasi-geostrophic wave propagation in distorted background flows are erroneous. A general condition for convergence is derived. The convergent solution (if it exists) to a general second-order recurrence formula is given, which is then applied to Clark's problem, yielding an exact closed form solution. The solution consists of an interacting trio of waves whose wavenumbers add up to zero. With results thus obtained, it is found that the propagation of wavenumber 2 disturbances is not affected by wavenumber 1 finite-amplitude distortions in the background flow, in disagreement with the result of Clark.

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Ka Kit Tung

Abstract

For quasi-geostrophic stationary long waves forced by topography, the nonlinear lower boundary condition is derived in terms of the geopotential height and compared with the linearized version. The common practice of replacing terms describing the flow over and around a mountain by upstream zonal flow over the mountain and evaluating the resulting condition at sea level is found to be a good approximation for the cases considered and does not need to be modified as sometimes suggested. Specifically, it is found that this approximation does not affect, for most cases, the lower boundary condition expressed in terms of the geopotential height provided that the stationary wave is not near resonance. At resonance, the eddy advection terms may become important for large-amplitude waves when dissipation and surface diabatic heating are taken into account

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Ka Kit Tung
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Ka Kit Tung

Abstract

A nongeostrophic theory of zonally averaged circulation is formulated using the nonlinear primitive equations on a sphere, taking advantage of the more direct relationship between the mean meridional circulation and diabatic heating rate which is available in isentropic coordinates. Possible differences between results of nongeostrophic theory and the commonly used geostrophic formulation are discussed concerning (i) the role of eddy forcing of the diabatic circulation, and (ii) the “nonlinear nearly inviscid” limit versus the geostrophic limit.

A set of general diagnostic tools comparable in scope to their geostrophic counterparts is given in Part I, including (i) a generalized definition of Eliassen–Palm flux divergence (without restriction to small amplitudes, to steady state or to adiabatic flows), the vanishing of which is a necessary condition for nonacceleration, (ii) a generalized nonlinear Taylor formula that relates the flux of Ertel's potential vorticity to the Eliassen–Palm flux divergence and (iii) a relationship between the Eliassen–Palm flux divergence and isentropic mixing coefficient, Kyy, used in chemical tracer transport equations in isentropic coordinates. From the mean momentum budget, we give in Part II in estimate of the Eliassen–Palm flux divergence using fitted “observed” field of net radiative heating rate. From this an estimate of the magnitude and latitudinal/seasonal variation of Kyy is also provided.

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Ka Kit Tung

Abstract

A zonally averaged model of stratospheric tracer transport is formulated in isentropic coordinated There are some conceptual and computational advantages, as well as some disadvantages in adopting the potential temperature, instead of pressure, as the vertical coordinate. The main disadvantage is that the “density” (mass per unit coordinate volume) in isentropic coordinates is no longer a constant as in the pressure coordinate system under the hydrostatic approximation. However, it can be shown that this density effect is almost negligible in the calculation of the mean diabatic circulation and the eddy advective transports. What is gained by adopting the new formulation is a conceptually simpler picture of the interplay of diabatic and adiabatic process in the transport of tracers. Mean diabatic heating (cooling) forces a direct rising (descending) mean mass flow. Along the streamlines of this mean mass circulation, tracers are advected in the mean. These surfaces slope downward and poleward in the lower stratosphere. In addition to advection, tracers are also dispersed from their mean path by transient adiabatic processes in a direction parallel to the local isentropic surface. As a result, the lines of mean constant tracer mass mixing ratio slope less steeply than the mean streamlines, but more steeply than the isentropic surfaces. The effect of eddy transport on chemically reacting minor constituent gases is also discussed.

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Ka Kit Tung

Abstract

The problem of barotropic instability of zonal flows to infinitesimal normal-mode perturbations is considered. The zonal flow is assumed to be continuous. but is allowed to be monotonic or nonmonotonic, and can have one or more inflection-points (which are the zeroes of the mean vorticity gradient., the zeroes are allowed to be of any order). A sufficient condition for instability is derived for this general flow profile. The present result complements the condition for stability found by Arnol'd (1965).

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Priscilla Cehelsky and Ka Kit Tung

Abstract

The concept of baroclinic adjustment is reexamined in the context of a fully nonlinear two-layer model on a β-plane. Based on our results we propose a single, conceptually very simple mechanism of the nonlinear equilibration of waves and the mean flow, which we term “nonlinear baroclinic adjustment.” The new concept appears applicable to cases that currently require different explanations, varying from case to case, to account for the equilibration of the mean temperature gradient in the presence of external driving.

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Priscilla Cehelsky and Ka Kit Tung

Abstract

No abstract available

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Jiansong Zhou and Ka-Kit Tung

Abstract

To unmask the anthropogenic global warming trend imbedded in the climate data, multiple linear regression analysis is often employed to filter out short-term fluctuations caused by El Niño–Southern Oscillation (ENSO), volcano aerosols, and solar forcing. These fluctuations are unimportant as far as their impact on the deduced multidecadal anthropogenic trends is concerned: ENSO and volcano aerosols have very little multidecadal trend. Solar variations do have a secular trend, but it is very small and uncertain. What is important, but is left out of all multiple regression analysis of global warming so far, is a long-period oscillation called the Atlantic multidecadal oscillation (AMO). When the AMO index is included as a regressor (i.e., explanatory variable), the deduced multidecadal anthropogenic global warming trend is so impacted that previously deduced anthropogenic warming rates need to be substantially revised. The deduced net anthropogenic global warming trend has been remarkably steady and statistically significant for the past 100 yr.

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Maurizio Fantini and Ka-Kit Tung

Abstract

Results from barotropic stability analyses of strong westerly jets generally tend to conclude that those waves that can extract energy from the shear of the jet are largely trapped by the jet. Therefore, the available shear energy of the flow cannot be transmitted by propagating waves away from the strong zone. We show here that the situation is different if the jet is in the meridional instead of the zonal direction. In this case, unstable waves are generated that are able to propagate energy eastward even in the presence of a realistic dissipation. It is then possible for the shear energy of a western boundary current to be transported large distances into the interior of the ocean.

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