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JAMES R. HOLTON

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James R. Holton

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A slight modification of the parameterization suggested by Lindzen (1981) for the zonal drag and eddy diffusion effects generated by breaking internal gravity waves in the mesosphere is tested using a severely truncated midlatitude β-plane channel model. It is found that realistic mean zonal flow profiles with zonal wind reversals above the mesopause can be simulated for both winter and summer radiative heating conditions provided that a gravity-wave spectrum is assumed which includes both stationary waves and waves of relatively large phase speeds (∼ ±20 m s−1). These results contrast greatly with the unrealistic mean wind profiles produced when Rayleigh friction is used to parameterize the effects of small scale motions on the mean flow.

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James R. Holton

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Observational evidence suggests that there may be long-period, large-scale variations in the intensity of the latent heat release in the equatorial zone. In this study a diagnostic numerical model is used to show that a standing wave oscillation of narrow longitudinal extent in the diabatic heat source in the troposphere can generate the global-scale propagating waves observed in the equatorial stratosphere. In particular, a heating oscillation which is symmetric about the equator can account for the eastward-moving Kelvin-wave mode, and a source which is antisymmetric can account for the westward-moving, mixed Rossby-gravity wave mode.

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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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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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James R. Holton

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Vertically stratified stratospheric tracers such as methane and nitrous oxide tend to have constant mixing ratio surfaces that slope downward toward the poles in the meridional plane. The equilibrium tracer slope results from the competition between the slope steepening effects of advection by the diabatic circulation and the slope flattening effects of quasi-isentropic eddy transport and photochemical loss. The diabatic circulation itself is, however, driven primarily by eddy transports, which maintain the departure of stratosphere temperatures from radiative equilibrium. If the eddy transports are weak, the diabatic circulation is also weak and the slope is small. Using a simple beta-plane channel model and an eddy diffusion parameterization for the eddy potential vorticity and tracer transports, we show that the slope is a maximum for a value of eddy diffusion such that the dynamical time scale is between the radiative and chemical time scales.

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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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James R. Holton

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A modification of Saul'ev's finite difference scheme for the heat equation is applied to the vorticity and divergence equation system for a rotating barotropic fluid. The scheme entails the use of two time levels to approximate second space derivatives, plus alternating ascending and descending marches through the grid lattice. The scheme is unconditionally stable in the von Neumann sense. Test integrations are performed for a linearized problem (the response of a barotropic ocean in a bounded basin to a time varying wind stress) and the truncation error is shown to be low, provided that the time step is short compared to the period of the forcing function.

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