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James R. Holton

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JAMES R. HOLTON

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James R. Holton

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JAMES R. HOLTON

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A model for shallow cumulus convection is formulated in which the vertical momentum equation and horizontal divergence equation are combined to produce a diagnostic equation for the perturbation pressure field. These equations, together with the first law of thermodynamics and equation of continuity of water substance, are averaged horizontally over the cloud area (a cylinder of constant radius). The resulting set can be integrated in time to study the life cycle of a nonprecipitating cumulus initiated by release of a small buoyant element. The results indicate that the perturbation pressure field plays an essential role by reducing the extremely sharp gradients in velocity near the cloud top, which are common to most other one-dimensional models. Inclusion of the pressure field also makes it possible to predict the radial scale at which the maximum cloud growth rate will occur.

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James R. Holton

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A time-dependent primitive equation model for an equatorial channel is used to study the interaction of equatorial Kelvin and mixed Rossby-gravity waves with the mean flow. The model employs a semi-implicit time-differencing scheme and a finite-difference grid in the meridional plane. The zonal dependence is represented by the mean plus a single Fourier wave component. The wave modes are forced by specified geopotential perturbations at the lower boundary. Initial mean wind profiles with westerly (easterly) shear with height are used for cases with Kelvin (mixed Rossby-gravity) wave forcing. Both mechanical and thermal dissipation are included to generate wave-driven mean flow modification. Integrations are carried forward for 60 days after initiation of the boundary forcing. As expected, the wave-mean flow interaction process leads to the development of intense downward moving shear layers centered at the equator. However, contrary to some previous suggestions, latitudinal mean shears antisymmetric with respect to the equator tend to be reduced rather than amplified by the wave-driven mean flow accelerations. Thus, both Kelvin and mixed Rossby-gravity waves tend to produce mean flow profiles symmetric with respect to the equator which are qualitatively in accord with observations.

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James R. Holton

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The response of an unbounded ocean to circularly symmetric time varying wind stresses is analyzed. A continuously stratified ocean is first considered. The model includes bottom friction, but the Coriolis parameter is a constant. It is shown that in a stratified ocean both barotropic and baroclinic currents are generated by wind stresses. The barotropic current, however, has its amplitude limited by bottom friction, so that the baroclinic mode dominates for long period forcing. A simple analytic approximation to the depth dependence of static stability in the oceans is introduced and shown to give more realistic results than a constant static stability model. A two-layer model including both a variable Coriolis parameter and bottom friction is analysed. This simple model indicates that both bottom friction and the variation of the Coriolis force enhance the baroclinic mode.

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James R. Holton

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The Charney-Pedlosky theorem on the trapping of unstable baroclinic waves is generalized to show that unstable waves which satisfy a condition analogous to the Charney-Drazin condition for the trapping of neutral planetary waves are trapped even in the presence of a local energy source provided by vertical shear of the mean zonal wind. This generalization provides a depth scale for the trapped waves which, unlike that derived by Charney and Pedlosky, does not become infinite as the growth rate of the unstable waves goes to zero.

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James R. Holton

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The equatorial stratospheric quasi-biennial oscillation (QBO) in zonal wind and temperature is observed to be symmetric about the equator. The QBO in column ozone, although it is believed to be caused primarily by vertical displacements due to the meridional circulation associated with the equatorial temperature QBO, is asymmetric with respect to the equator, and is strongly linked to the phase of the annual cycle. In this note a simple one-layer model is used to demonstrate that the gross features of the observed QBO in total ozone can be attributed to meridional advection of the ozone perturbation by the annually reversing mean meridional Hadley circulation. This advection causes a displacement of the equatorial ozone anomaly towards the winter hemisphere, and thus products an asymmetry with respect to the equator. It also modulates the amplitude of the ozone QBO, since the phase of the equatorial wind QBO with respect to the annual cycle may produce either constructive or destructive interference between the effects of the annually reversing meridional transport and the vertical advection by the equatorial wind QBO.

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James R. Holton

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James R. Holton

The linear theory for stationary Rossby waves excited by flow over long ridges is reviewed. The traditional “textbook” model, in which there is no disturbance of the potential temperature surfaces or streamlines upstream of the ridge, is shown to be inadequate. For both the β-plane and the f-plane cases, pressure forces cause lifting of the isentropes and a cyclonic turning of the streamlines upstream of the ridge. The β-plane and f-plane solutions are, however, totally different for long ridges owing to the resonant excitation of stationary Rossby waves and the vertical propagation of the long-wave components in the β-plane case. Curiously, the vertical displacement of the isentropic surfaces is nearly identical in the β-plane and f-plane solutions in the lower troposphere where the response is dominated by the short-wave vertically decaying components.

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