Zonal harmonic analyses were applied to 5-day mean heights, 25-day mean heights, departures from 25-day mean heights, depatures from the normal and tendency fields on the 500-mb level. It was found that the first and second harmonics for transient waves at 70° and 60°N generally move westward. The mean westward phase velocities are about a quarter of the wave-length per five days, i. e., about 20° and 10° longitude per day for the first and second harmonics respectively. The westward movement was not pronounced at lower latitudes mainly due to the small amplitudeof transient waves. The frequency distributions of phase velocities of transient waves for the third harmonic are nearly uniform and the third harmonic does not reveal mean westward or eastward movements. The fourth harmonic moves eastward with a mean phase velocity of about 6° longitude per day at 70° and 60°N. On the contrary, the fourth harmonic at low latitudes has a tendency to move westward in summer. The mean phase velocities of the first two harmonics are nearly the same for each season, and the amplitudes of transient waves are large in winter and small in summer. As the present study is based on the data for 20 years or more, namely more than 1460 cases for each harmonic, the results obtained are statistically significant. Several examples of travelling waves were presented for the first four harmonics at 60°N.
During the 4-day period of project observation, July 8-July 12, 1968, the “Baiu front” activity was prevailing almost steadily over the Far East.Therefore the averaged fields of various meteorological elements in the vicinity of “Baiu front” are examined. The most remarkable structure is found not in the thermal stratification but in the wind field with a low-level jet which is considerably ageostrophic. The existence of low-level jet stream seems to be deeply related with the precipitation and, therefore probably, with the connective activity. Along the concentrated zone of strongly baroclinic field, lower tropospheric disturbances of wave lengths less than 1, 000km were generated and moved east-northeastwards successively, bringing a large amount of precipitation periodically at an interval of about 20 hours. The associated thermal field indicated the existence of indirect circulation, but, nevertheless, disturbances did develop. The energy conversion processes among three different scales of motion, i. e., general synoptic scale, intermediate scale (frontal disturbances) and small scale (convection) are studied. It is suggested that the kinetic energy of intermediate-scale disturbances is transformed from the kinetic energy of convective-scale motion.
A theory is developed which appears to explain the flatness of the convection cells that has been observed from satellites. Rayleigh's thermal convection theory, which describes the transition from conduction to convection of a horizontal layer of fluid heated from below, is studied in conjunction with the thermal boundary condition which is more applicable to the atmosphere than the boundary condition of constant temperature. The thermal boundary condition is expressed by a linear combination of the vertical temperature gradient and the temperature itself. For hydrodynamical boundary condition, two cases are studied, one is “slip” and the other is “non-slip”. The eigenvalues of the governing differential equation are obtained numerically at the marginal state. The results show that the eigenvalues are largely influenced by a nondimensional number γ which is the ratio of the vertical temperature gradient term to the temperature term at the boundaries. The critical Rayleigh number Ray decreases as the ratio decreases and Rαy approaches a value of approximately 120 as γ approaches zero. Dependency of the eigenvalues upon γ is large for the lowest eigenvalue, but γ exerts small effect on the other eigenvalues. A non-dimensional number a, defined by kd where d is the depth of convection layer and k is the horizontal wave number, decreases also as γ decreases. Since a represents a ratio of the vertical to horizontal dimensions of a cell, the result indicates that the flat convection cells common in the atmosphere are developed when γ is small at the boundaries. Furthermore, the Rayleigh number becomes nearly uniform at its lowest value over a wide range of a, showing that cellular convection can set in with a rather broad variety of cell dimensions. The dynamical boundary conditions, slip or non-slip, however, are found to exert only small influences upon a as compared with the thermal boundary condition.
Non-geostrophic and non-hydrostatic effects on the stability of Eady's baroclinic model are studied in the range of small Richardson numbers (Ri). The latitudinal as well as the longitudinal variations of wave perturbations are included. There are two growth rate maxima, one is that of the ordinary baroclinic instability on the l (latitudinal wave number)=0 axis, and the other is that of a symmetric instability on the k (longitudinal wave number)=0 axis and |ι|→∞ when Ri<1.There appears an unstable mode destabilized by the inertial effect. The non-hydrostatic effect supresses the appearance of Helmholtz type instability in the range of positive Ri. There is little difference between eigenvalues in the case (k, ι) and (k, -ι), but the structure of perturbations in the two cases differs greatly with the increase of |l| . The effect of the β-term is also studied under non-geostrophic and non-hydrostatic conditions.