The quasi-linear and non-linear growth of disturbances induced in a stably stratified layer with hyperbolic tangent shear is systematically examined based on shape assumption and by direct integrations. By the calculations based on the shape assumption, we obtain the maximum values of the velocity fluctuations, the time needed for the disturbances to attain the maxima and the averaged growth rate for various Richardson numbers and wavenumbers. The averaged growth rate offers somewhat smaller value than that derived by the direct integrations. But the difference is not significant. Comparison with the wind tunnel experiment shows rough justification for the shape assumption. Development of Kelvin-Helmholtz waves is examined by direct numerical integrations. The time evolutions of the stream function, the velocity and the potential temperature are obtained by a non-linear system which includes five harmonic components. At early stages of the time evolution, there are little differences among non-linear systems of any degree including the quasilinear one because the higher harmonics are too small to affect the fundamental mode. But with lapse of time, discrepancies of wave pattern among the systems become significant. Namely in the non-linear systems of relatively lower degree including the quasi-linear system, periodic behavior is predominant while in the higher degree systems, such a behavior tends to disappear. Some characteristic features of Kelvin-Helmholtz instability are discussed based on the results obtained by the numerical integrations. Considerations about reduction mechanism of Richardson number in the atmospheric planetary boundary layer, reradiation of internal gravity waves by Kelvin-Helmholtz instability and decay processes of Kelvin-Helmholtz billows are also proposed with reasonable speculations.
An analysis was made of planetary-scale variations of temperature and wind fields in the summertime stratosphere and mesosphere by the use of meteorological rocket and satellite observations. From the vertical time-section analysis of temperature and wind at Cape Kennedy (28N, 81W) and other rocket stations in subtropics of the Northern Hemisphere, it is found that the oscillation with a period of about 15 days is predominant above 30km. To describe the nature of wind and temperature oscillation in more detail, a power spectral analysis was made of the time series rocket data during the period of three months from July to September in 1969 and 1970. The result suggests that the oscillation as revealed by the analysis for indivisual observation station is a reflection of the horizontal movement of planetary-scale wave disturbances embedded in the mesospheric easterlies. The presence of traveling planetary waves in the summertime stratosphere was confirmed by means of a zonal harmonic analysis of ITOS-D VTPR retrieval data and Nimbus-5 SCR radiance data for the Southern Hemisphere in 1972/1973 summer, and the wavenumber-frequency relation is given in a quantitative manner.
The mean motions induced around a planetary wave packet surrounding longitudinally a rotating sphere and propagating meridionally on it are discussed by using a simple model situation of two dimensional motion of an incompressible fluid. It is shown that the wave packet conserves its angular momentum during the meridional propagation on a sphere, while it conserves its momentum under the beta-plane approximation. It is also shown that the wave packet induces the change of mean angular momentum in case of propagation on a sphere and the magnitude of the induced mean angular momentum is just equal to the wave action which is defined by the ratio of the wave energy and the westward drift angular velocity of the wave packet. Under the beta-plane approximation, this is reduced to the result that the induced mean zonal momentum is just equal to the wave momentum which is defined by the ratio of the wave energy and the ‘local’ westward phase velocity given by Rossby formula. It is concluded from these results that the photon analogy to such a wave packet is allowed. Finally, some comments are made upon the origin of westerlies found in the mid-latitudinal regions.
The effects on the semidiurnal lunar tide of the meridional temperature gradient and the associated zonal winds are discussed by a linear theory with a numerical method. It is shown that the zonal wind, its horizontal shear, and its vertical shear affect the latitudinal distributions and the vertical wave length of the oscillation considerably. For instance, the amplitude becomes larger in westerly winds than in easterly winds, and the vertical wave length is reduced by equator-symmetric easterly winds, but is lengthened by equator-symmetric westerly winds. It is also shown that the effect of the meridional temperature gradient itself is also considerable, especially in the upper atmosphere. It is suggested that the seasonal variation of the zonal wind system may be one of the important causes for the statistically observed seasonal variation of the lunar tide.
The distributions of monthly-mean zonal root mean square (r.m.s.) relative geostrophic vorticity, ξg, are useful in determining the locations, seasonal migrations and other properties of jet streams, and hence are valuable in general circulation studies, as shown by Srivatsangam (1974). In this paper the distributions of zonal r.m.s. ξg as obtained from radiosonde and Satellite Infra Red Spectrometer (SIRS) data are compared. The differences between the two distributions are shown to be partially due to the over-estimation of geopotential heights made by the SIRS observations in the presence of clouds, and the under-estimates made in the clear regions. The estimation errors result from the nature of the least squares regression method used in deriving geopotential heights from radiosonde data, as well as the subsequent interpolation of clear-area data into cloudy areas (where no SIRS-derived data are often available).
A equation of precipitation-element size distribution will be proposed in this paper. It is represented by the normal distribution of liquid water content per unit volume of air with size. The conventional distributions (e.g. Marshall-Palmer (1948) and Best (1950)) and the characteristic distributions observed and computed as reported in the writer's previous paper (Shiotsuki, 1974) are fitted by this equation. Furthermore, the melted drop-size distributions for snowflakes and graupels are also represented by such normal distribution. The most. usefulness of the proposed equation is that it is applicable to almost all kinds of size distribution of various types of precipitation. The new equation is determined by the space liquid water content (M) and the mean diameter (D) and the standard deviation of i t (a) of the normal distribution of liquid water content. Thus the present equation also needs some parameters which may be dependent on precipitation type, as well as the conventional equations. But those three parameters of the present equation can be easily determined by observing the data of radar reflectivity (Z), precipitation intensity (R) and number flux of precipitation particles (N).