The preferred roll diameter is examined by a simple three-dimensional numerical model of Bénard convection. We obtained two types of preferred size for the convection roll, which are called the size I and size II. The size I is smaller than the critical size Lc and the size II is larger than Lc, where the critical size Lc is the preferred size at the critical Rayleigh number. The roll with the size I is realized just above the critical Rayleigh number. The roll with the size II is preferable to that with the size I at rather high Rayleigh numbers. The size I corresponds to one predicted in the previous theoretical and numerical works. The preference of the size II to the size I at rather high Rayleigh numbers may explain the discrepancy between the previous theoretical works and experimental works. Furthermore the energy consideration indicates that the inertial terms tend to decrease the roll diameter and the advective terms in the thermodynamic equation have a controlling influence on the selection of the preferred size of the convection.
As an approach to study the development and structure of the tropical cyclone, a numerical experiment is performed with the use of a fine-resolution model in which convective clouds as well as larger-scale motions can be treated explicitly. For simplicity and because of computational limitations, a two-dimensional model is adopted with an assumption of axial symmetry, and a tropical cyclone of very small horizontal scale is treated. An initial condition is taken such that the temperature profile is similar to that of the mean tropical atmosphere in summer but the relative humidity is much higher in the lower atmosphere. The motions are assumed to be at rest and buoyancy perturbations are introduced for the initiation of clouds (and large-scale motions). Results of the numerical experiment indicate that a disturbance develops through its interaction with convective clouds in the conditionally unstable stratification. Except for an extremely small horizontal scale realized, the structures of the disturbance are similar to those of the tropical cyclone; the eye and eyewall structure, realistic tangential and radial velocity fields having inflow concentrated near the surface, and so on. The behaviors and the structures of the disturbance as well as rainfall characteristics are discussed in comparison with those obtained from parameterized models of the tropical cyclone and observations.
Characteristics of two-dimensional heat island convection under general flows are investigated by numerical and laboratory experiments and the results are compared with those of the linear theory in Part 1 (Kimura, 1976). The aim in Part 2 is to examine the effects of 1) self-advection due to the convective motion, 2) vertical shear of the general flow, 3) Prandtl number and 4) ground temperature distribution upon the heat island convection. The main results obtained in the present study are as follows: 1) The self-advection has an effect to concentrate the updraft in a small area at the center of the heat island as stated in Kimura (1975), but the effect is reduced with the increase of the general flow. 2) The vertical shear of the general flow has an effect to increase the height of the inflow region of the perturbation flow field. 3) The small Prandtl number favours the development of the upstream perturbation in the middle layer as speculated in Part 1. 4) In Part 1 maximum values of the perturbation horizontal velocity (umax) decreased monotonously with the increase of the general flow, but in Part 2 it was found that umax is constant or slightly increases under the weak general flow for the more general ground temperature distributions than the form assumed in Part 1. 5) These effects shown in 1)-4), however, are not so significant as to alter the main features of the heat island convection obtained in Part 1.
For the purpose of investigating the general circulation of the atmosphere and Stratospheric-Tropospheric mass exchange, a simplified model was developed and time-integrated for 100 days. The model version is a 10 level primitive-equation model in p-coordinates. The computational domain is limited to 1/6 hemisphere under cyclic condition. Non-adiabatic terms are evaluated by employing the results of observational analyses. The vertical convective mixing and horizontal subgrid-scale diffusion of sensible heat are parameterized as the 6.5 deg/km convective adjustment and the so-called nonlinear viscosity, respectively. Numerical results are presented both from the description of time evolution of the model atmosphere and from a comparison of the period of model-60 days with climatological statistics. The time and zonal mean states of the model atmosphere are similar to the observations for winter more than for annual mean. The subtropical jet, tropical easterlies and meridional three cells are grossly well reproduced. In addition, the model simulates successfully the thermal structure with the tropical and mid-latitude tropopauses. However, the mid-latitude cyclones are less active than those of the real, though the dynamical and synoptic features are qualitatively well presented.
A numerical simulation of Stratospheric-Tropospheric mass exchange was performed by tracing a large number of air particles of the stratospheric origin with a simplified general circulation model. It shows that the most plausible mechanism of outflow of the stratospheric air to the troposphere is cross-tropopause motion associated with the mid-latitude cyclone. The individual process of air particle's movement is that the lowest stratospheric air particles in the rear of the cyclone and around at 60 degrees of latitude most-effectively move downward and equatorward and arrive around at 40 degrees of latitude in the middle troposphere, while many other tratospheric air particles merely flow eastward with north and south meander in the westerlies. Some air particles of the stratospheric origin intruding into the troposphere return toward the original levels to the east side of the cyclone. In spite of the return motion, they eventually descend and merge in the troposphere, since the net downward movement of air particles for a long time is induced by dynamical effects of the cyclone. On the other hand, the model shows the quasi-horizontal outflow of the stratospheric air through the tropopause gap in the subtropics does not take place. Possible general circulation of air particles was discussed and presented in the model. It will be referred to as Lagrangian general circulation of the atmosphere. Its structure shows one cell over a hemisphere with downward and upward branches in higher and lower latitudes, respectively, and coincides with the so-called Brewer-Dobson circulation in the lower stratosphere. Therefore, it may be considered that the individual short-range and statistical long-range mechanisms of Stratospheric-Tropospheric mass exchange are the preferential descending motion in the rear of the cyclone and the Brewer-Dobson type meridional circulation, respectively. The experiment shows that Lagrangian general circulation has the vertical downward velocity of about 100 mb/month at a level of the mid-latitude tropopause, indicating that the magnitude of the residence time needed for the stratospheric air to be completely replaced is of the order half a year. However, since there are some reasons to consider that this value is underestimated by a factor of 2-3, it may be inferred that its magnitude is of the order 1-2 years in the real atmosphere, being in agreement with the results of observational studies.
Power spectra and vertical structure of transient planetary waves are investigated using a space-time cross spectrum analysis. From the analysis of pressure-heights of three levels (30, 100 and 300mb) in the Northern Hemisphere for two winters, it is found that for the shorter period (around 15 days) waves in the stratosphere westward moving component prevails for the zonal wavenumber 1 while for the wavenumber 2 and 3 only eastward components have a significant power. It is also found that an eastward moving wave of wavenumber 1 with a period of about 30 days is present in the stratosphere which have no corresponding wave in the troposphere. The vertical structure of eastward moving waves of the wavenumber 2 exhibits the characteristics of upward propagation whereas the westward moving waves of the wavenumber 1 exhibit somewhat complex features. In the latter half, the characteristics of the vertical propagation of traveling planetary waves into the stratosphere are examined. The plausible vertical and meridional distribution of the mean zonal wind and the periodic amplification of waves at a lower boundary are prescribed. We select 6, 12, 24 and 48 days as the period of forcing. It is revealed that the planetary waves which have periods of either 12 or 24 days can penetrate into the upper stratosphere. As to wavenumber 2, the eastward moving modes with a period of 10-20 days become dominant at the 30km. On the other hand, as to wavenumber 1, the dominance of either eastward moving or westward moving depends upon the period of the wave. For periods longer than 20 days, eastward moving waves are more propagatable while for the period about 12-15 days, the westward moving wave becomes predominant at higher levels. All these waves have a westward tilt between the 15 km and 30 km levels. Thus, apart from the structure of the westward moving mode of wave 1, the agreement between the observa- tion and computation is quite good. Especially, for the eastward moving mode of wavenumber 2, its transient features may be interpreted to be a manifestation of “selective propagation” due to the gross field of westerly shear flow and the phase velocity of wave itself.
The present study will treat two intermediate-scale disturbances developing on the Baiu front with a wavelength of about 2, 500km and of about 1, 000km. Three-dimensional structure of the longer wave is analyzed with the aid of the vertical-longitudinal cross sections by means of the harmonic analysis of 6-hourly data, and the shorter wave by meansof composite technique. The results show that these disturbances with a shallow vertical extension below the400-mb level are of warm-core type and the vertical structures are different between northof and in the mean Baiu frontal zone. North of the front, it is cold in the trough, which has a slightly forward tilt. In the frontal zone it is warm in the trough, the axis of which tilts backward vertically. On the horizontal map, the trough line runs NW-to-SE in the northern part and SW-to-NE in the southern part. Velocity divergence and vertical component of relative vorticity have a magnitude of the same order. The disturbance developed in a narrow zone of strong gradient of a Richardson number in the one-week mean field. As it develops, a warm core in the upper layer of the low becomes intense through the latent heat release.
Rainfall at Hilo, Hawaii was studied by the character of inversion height and strength, which has a strong relation with movement of the upper cyclone. The electric field, satellite pictures, and general meteorological parameters such as upper wind, temperature and humidity profiles obtained by radiosonde were referred to for the rain classification. August rain was studied in detail as typical of trade-wind rain, and for another month, rain with ice phase was studied to compare with the rainfall pattern from warm rain. The types of rain are subdivided into: a) morning and evening rain, caused by land and sea breezes when the inversion is low; b) intense, all-day rain, occurring when the inversion is high; c) weak but continuous rain, occurring when there are double inversions. There is no rain when the inversion height is less than 1.7km. Winter time cool rain is also studied. It is characterized by long-lasting, heavy rainfalls accompanied by high electrical activity and usually by lightning. This contrasts with warm rain, heavy but short-lasting falls with weak, negative electricity. It seems that although the presence of ice crystals does not contribute to high rainfall intensity from deep cloud, it is important for the generation of high electrical activity and for maintaining heavy rain.
θThe present paper deals with the spatial structures of atmospheric turbulence in terms of the coherence and the phase of velocity fluctuations between two points. It is shown by reanalyzing the observed wind data that the decay factor of coherence is not constant, but function of both separation distance l and wind-anemometer line angle θ. However, for a longitudinal direction, the decay factor appears to be constant and the phase is obtained like that as deduced from Taylor's hypothesis. The following empirical formula of the decay factor is obtained at the height of 41.5m in high wind condition: kl=acosθ+b(lsinθ/z)Csinθ where a, b and c are constants and z is a height of observation level. At the height of 41.5m in high wind conditions, estimated value of a is nearly equal to 2.6 or 3.8 and those of b and c are 14 and 0.45, respectively. The decay factors for lateral separations seem to decrease with increasing roughness length. Space correlations are computed as function of the wind-anemometer line angle by using the experimental formulae of power spectrum, coherence and phase. The calculated results agree well with the experimental ones within the range of their scattering.