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Stephen B. Fels

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Stephen B. Fels

Abstract

We describe a semianalytical method for calculating solar tides in an atmosphere whose zonal mean velocity need not be close to solid-body rotation, but which varies slowly in the vertical direction. The scheme is closely related to the asymptotic methods developed earlier by others for use in work on terrestrial equatorial waves, and leads to a simple and intuitively appealing formulation of the nonseparable tidal problem as a set of uncoupled ordinary differential equations. The manner in which the meridional structure of the mean state affects the vertical and horizontal tidal structure is especially transparent. The method has been used recently to explain a number of observed features of the Venus semidiurnal tide. The sensitivity of these tidal fields to the structure of the zonal mean wind is briefly discussed, and the Eliasson-Palm flux divergence calculated.

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Stephen B. Fels

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The “trapeze instability” of Orlanski is investigated in the absence of a reflecting lid above the fluctuating layer. An expansion of the exact solution as a power series in a parameter representing the ratio of the fluctuating to the mean stability is made, and the first two terms calculated, both of which grow only for a finite length of time, after which they level off. This is quite unlike what occurs in the closed case. On the basis of a plausible conjecture about the behavior of higher order terms, we conclude that only waves whose vertical wavelength is small compared to the depth of the active layer will be amplified by the trapeze instability. When estimates of the effects of eddy viscosity are included, waves of horizontal wavelength of the order of 200–400 km and a period of two days are expected to be most unstable.

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Stephen B. Fels

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The scattering of two-dimensional, hydrostatic, Boussinesq, internal gravity waves by orographic features is considered, with special attention paid to energy and momentum fluxes.

A general integral equation for the streamfunction is derived from which a special Fourier representation is shown to hold in a well-defined region of the atmosphere. This leads to simple expressions for the energy and momentum fluxes and to a useful form for the energy conservation law. Scattering efficiency functions are defined.

When the topography satisfies certain conditions, analytic approximations can be used to determine the scattering; it is found that the reflected momentum flux is larger than the incident flux. The manner in which viscosity affects this result is discussed.

In the special case that the maximum topographic slope is less than that of the incident wave fronts, a simple integral equation is derived and used to calculate numerically the scattering from several different orographies. In every case, the flux anomaly mentioned above persists. The numerical results show that there is very little interference between nearby orographic features, and suggest that the vertical scale of the topography must be of the order of one-quarter of the incident vertical wavelength to significantly scatter.

On the basis of these results, it is possible that topographic scattering may significantly affect the tidal momentum flux in the Venusian atmosphere.

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Stephen B. Fels

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The mesospheric radiative damping rates for temperature perturbations with vertical wavelengths less than 6 km are calculated, based on previous works of Spiegel and Fels. Effects due to the breakdown of local thermodynamic equilibrium are included, and found to be important above 70 km. The damping calculated is considerably weaker than that found recently by Schoeberl, Strobel, and Apruzese.

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Stephen B. Fels

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No abstract available.

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Stephen B. Fels

Abstract

Analytic functions which approximate six commonly used standard temperature profiles (the AFGL set, and the 1976 U.S. Standard) are described. These provide a uniform way of rounding off the sharp corners of the original models, and have been used in a recent radiation model intercomparison study.

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Stephen B. Fels

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An analysis of the radiative damping of slowly modulated sinusoidal wave disturbances is presented. It is shown that it is possible to incorporate scale-dependent effects in a manner no more difficult than that used in the usual “Newtonian cooling” approximation. Explicit calculations show that these effects can be very important in the middle atmosphere. Detailed graphs of the scale-dependent relaxation times due to CO2 and O3 are given, as well as simple analytical parameterizations.

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Stephen B. Fels and Lewis D. Kaplan

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The dynamical consequences of systematic changes in longwave radiative transfer computations have been investigated using the NCAR six-layer General Circulation Model. The experiments were run for a period of 40 days each: the “control” case with an emissivity computation, and the “test” case using a 19-sepctral-interval calculation, in which the Curtis-Godson approximation is employed. The two calculations lead to substantially different cooling rates when applied to identical soundings, especially in the tropics.

Significant differences are observed in the thermal structure of the two cases, and in the mean meridonal circulations. The total kinetic energy is somewhat higher in the test case, probably due to increased baroclinic activity in latitudes.

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Roelof K. Snieder and Stephen B. Fels

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Because of the requirement of geostrophic balance, mechanical inertia can affect the thermal response of the atmosphere to transient heating. We examine some very simple linear models of this “flywheel effect,” and discuss their possible reference to the Antarctic ozone hole.

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