A layer of fluid is confined between two horizontal boundaries which are kept at constant temperatures. An infinitely thin layer at the middle of the fluid is heated uniformly at a constant rate so that a constant negative temperature gradient is maintained in the upper half of the fluid and a constant positive temperature gradient in the lower half. When the rate of internal heating exceeds a critical value, convective motion is given rise. The two-dimensional governing equations with the Boussinesq approximation are transformed to a set of differential equations governing the time variations of the coefficients of Fourier series expanded along the horizontal direction. The system is then truncated by taking into account only a limited number of terms of the Fourier expansions. The equations are then numerically integrated for different values of the Rayleigh number (R) and a fundamental horizontal wavenumber. The result of these numerical integrations indicates that solutions achieve steady states for R smaller than approximately 38 Rc, where Rc is a critical Rayleigh number, and that convection with periodic time-dependency takes place over a narrow range of R, extending to several tens of. The flow in this range consists of successive generations of a pair of plumes and a single plume. The most striking difference between the steady state motion and the periodic motion as revealed by calculation is that the steady flow consists of one mode whereas a few modes having amplitudes of the same order are contributing to produce periodic timedependency. The non-dimensional upward heat flux is found to increase with R to the point where the periodic motion replaces the steady state solution. A sudden decrease of the upward heat flux is observed after this.
An investigation is made of some features of perturbation superimposed in a plane Couette flow with unstable stratification. A set of linearized Boussinesq equations governing the perturbation is solved numerically employing a finite-difference technique. First, stability characteristics of the perturbations are shown. These characteristics are discussed for various Richardson numbers and wavenumbers and are compared with those obtained analytically by Kuo. It is confirmed that constant shear has a stabilizing effect on the perturbation and the effect is striking for perturbations of short wavelength and of transverse modes whose wavelengths in the direction perpendicular to the basic flow are longer than those in the direction parallel to the basic flow. Second, a dynamical structure of unstable perturbations and the associated energy conversions are discussed. Conversion between kinetic energy of the basic flow and that of the perturbation takes place as well as conversion of potential energy to kinetic energy. In particular, vertical transfer of horizontal momentum, which results in conversion between both the kinetic energies of the basic flow and of the perturbation, is crucially controlled by the three dimensionality of the perturbations. The vertical momentum transfer tends to intensify the shear of the basic flow when a perturbation is transverse, while it reverses for a longitudinal pertubation whose wavelength in the direction parallel to the basic flow is longer than that in the direction perpendicular to the basic flow.
Climatic energy sources (or sinks), which consist of local time change of total energy and divergence of total energy flux, are estimated both in the surface layer of the earth and in the atmosphere as residues of the respective energy balance equations over the northern hemisphere for all months. The seasonal variation of the energy sources in the surface layer of the earth shows that extremely strong energy sinks are found in winter and very strong sources in summer both in the Northwest Pacific Ocean and the Northwest Atlantic Ocean. In the Tropical Oceans, there are stationary sources throughout the year, which fact suggests northward energy transport by ocean currents. Energy sources under the ground surface, which consist of the local time change of internal energy and the heat of fusion of ice or snow, have a much smaller amplitude of seasonal varition than that in the oceans. In the high latitudes, the sinks, which are considered to be caused by freezing of soil water, appear in winter and the sources, which are by fusion of ice or snow, appear in summer. The seasonal variation of energy sources in the atmosphere, which means divergence of totalenergy flux by atmospheric motion, shows that strong sources are found in winter and sinks in summer both over the North Pacific Ocean and the North Atlatic Ocean. Over the Tropics there are very strong energy sources through the year. It is found that condensation heat energy mainly contributes to the seasonal variation of energy sources in the atmosphere.
Spectrum analysis of wind, temperature, geopotential height and relative humidity fluctuations in the troposphere of the tropical Pacific is made during the period April through July 1962. As noted by Yanai et al. (1968), the power spectra of the meridional wind component show a peak in the period range 4 to 5 days in the troposphere. The peak in the lower troposphere corresponds to the passage of "easterly waves". There is a weak indication of the corresponding peaks in the spectra of other parameters in the western Pacific. The wavelength of the tropospheric waves with the 4- to 5-day periods is estimated from the phase difference of the meridional wind component between separated stations. The wavelength in the lower troposphere is distinctly different between the eastern Pacific and the western Pacific. The wavelength is 8, 000 to 10, 000km in the eastern Pacific, while it is 5, 000 to 6, 000 km in the western Pacific. The tropospheric wave has a tilt of the wave axis directed from southwest to northeast in the northern hemisphere. The axis is directed from northwest to southeast in the southern hemisphere. The phase lines of the lower tropospheric disturbances are inclined eastward with height and the inclination becomes smaller as the waves progress into the western Pacific. Phase relations between the meridional wind component and other parameters are studied. The coherences among them are relatively large in the western Pacific but they are small in the eastern Pacific. A schematic picture of the structure of the tropospheric wave in the western Pacific is presented. A cold air lies to the east of the wave axis in the lower troposphere and a warm air lies above the cold air. The maximum relative humidity is also situated to the east of the wave axis in the lower troposphere.
Year to year variations of horizontal flux of momentum due to the planetary-scale disturbances in the winter stratosphere are studied based on the 3-month mean statistics throughout five winters from 1963 to 1967 by the use of the gridpoint data of 30mb isobaric heights over the Northern Hemisphere. Computations are made to separate the total momentum transport into the standing eddy flux and the transient eddy flux, as well as into the zonal wave numbers, for the purpose of clarifying the nature of planetary waves. It is likely that the poleward flux of momentum observed in the lower latitudes is caused by the penetration of planetary waves from the middle latitudes into the low-latitude stratosphere. It is also found that, in contrast to Wallace and Newell (1966), the year to year variation of total momentum transport does not necessarily show a direct relation to the quasi-biennial oscillation of the zonal wind in the equatorial lower stratosphere, but that planetary wave activity in the winter stratospheric circulation has, in a broad sense, a close relation to the zonal wind in the tropics.
To clarify the interaction between radioactive ions and condensation nuclei, simultaneous measurements of the concentrations of radioactive ions, radioactive aerosols, condensation nuclei, and small positive ions were carried out on the top of Mt. Norikura and the campus of Nagoya University. The mean life of radioactive ions is 38 sec on the top and 14 sec on the campus, respectively. The concentration of radioactive ions correlates positively with that of small positive ions and negatively with that of condensation nuclei. These correlations may be well expressed by the following simple formulae; q=βnZ and q0=β0n0Z.