By applying the theory of random walk to a turbulent flow, the frequency distribution functions of wind speed and wind direction are derived. The turbulence in the flow is assumed to be homogeneous and isotropic in the horizontal, and further the phase angles of each component of the Fourier series of the finite variable wind speed are assumed to be at random and independent of each other. Further by using the frequency distribution functions of wind speed, the diffusivity in the horizontal is obtained. Because there is no conclusive Lagrangian correlation function, we discussed the diffusivity using some correlation functions. The theory is tested by using the records obtained in the Research Institute of Atomic Energy in Tokai Mura, Ibaraki Prefecture.
To describe the turbulent character in plant canopies, a simple model is assumed, and from conditions of the turbulent flow consisting at the boundary of two spaces, i. e. over and under a plant canopy, a relation is deduced which connects d (zero-plane displacement), z0 (roughness length) and H (roughness height). It is made clear that when the wind rises, i. e. H decreases, there are several cases of variation of d against z0. The experimental results appearing very complicated at first sight is shown as expected from the theory. A diagram is given which illustrates the relation between d, z0, H and (u/ν∗)z=H and in which any rough surface is represented by a single point, being specified by not only the surface is smooth or rough, but also its roughness is dense or sparse. Also the so called skin-friction coefficient is discussed, and it is shown that the coefficient generally does not have a simple relation with d or z0, but it increases when the rough surface becomes more dense.
By making use of a two-level, quasi-geostrophic model without friction or heat sources, the rates of change of disturbances with time are discussed. In case of using the technique of the linearized perturbation theory, where the disturbances are considered to be small perturbations superimposed on a zonal basic current, the amplitudes of disturbances are not uniquely determined, while the rates of amplification of amplitudes with time are obtained as the exponential type in relation with the wave length of disturbance and the vertical shear of the basic current. In this paper, the second-order effects on the zonal current and also on the mean static stability of the domain we concerned with due to the presence of very simple unstable baroclinic waves are considered. In this discussion, it is qualitatively shown that the small amplitude perturbation grows at first and later the zonal current is modified by the action of the northward eddy transport of sensible heat, while the vertical eddy transport of entropy changes the mean static stability. Both effects controll the exponential amplification of amplitude of unstable disturbance with time. Basing upon the qualitative considerations which are obtained theoretically from the simple model, we perform the numerical experiment where the time changes of disturbances are presented quantitatively.
The breakdown of the polar vortex in the stratosphere is considered as a barotropic instability process of an irregularly shaped vortex. Numerical tests are carried out based on the observed height patterns of 50 mb level in the cases of 15 November 1957, 15 January 1958, and 20 January 1958 as initial value problems for artificially introduced small disturbances. Kinetic energy of disturbances remains constant for the former two, but in the case of 20 January 1958, just a few days before the occurrence of breakdown, the kinetic energy increases. The patterns of disturbance thus computed were similar to the observed height changes for the latter two cases.
Under the assumption that a convective system with an updraft in the downshear side and a downdraft in the upshear side is already formed in the conditionally unstable atmosphere, the effects of the prevailing wind with vertical shear on the system are studied by numerical integration of hydrodynamic and thermodynamic equations in which the formation, the evaporation and the fall of water drops are taken into consideration. From computations of two cases which are different only in the intensity of vertical shear, following results are obtained. In the case with stronger vertical shear, larger amount of raindrops evaporates in broader region on the way of their falls than in the case with weaker shear and the cooling due to the evaporation is more intensive in the whole atmosphere. However, the downdraft in the former case cannot develop so much as in the latter case mainly because the cooling is not concentrated in the main part of the downdraft. Strong vertical shear weakens the cold-front-like action of the air diverging from the downdraft on the warm air in low level, as it prohibits the development of the downdraft and it causes streamlines in the downdraft region to be unfavorably inclined. Further, it inhibits also the development of the updraft. These prohibiting effects of strong vertical shear are also made clear from the view-point of energy-conversion. Following conclusions can be deduced from these results, the previous work of the author (1965) being taken into account ; that is, vertical wind shear does not intensify a connective system itself, but organizes the release of convective instability-energy by maintaining the convective system and causing it to propagate. There is a criterion in the intensity of vertical shear which is favorable for the maintenance of the convective system. This criterion will be dependent upon the degree of the development of the convective system.
The boundary errors in numerical integrations of hydrodynamical equations are discussed. If the advective type equation is solved on an open domain, adopting centered difference scheme, an extra boundary condition is needed at the outflow point and it brings some errors. It is shown that these errors result from the false reflection of a computational mode wave, synchronized with the incident physical wave. By assuming the situation that in a semi-infinite domain, the incident physical wave and the reflected suprious wave are in balanced state, the rate of reflection of the computational mode is estimated. It was found that if the quantity at the outflow boundary point is extrapolated from the interior of the domain with l-th order continuity, the reflection rate is tan (l+1)(p/2), +where p is the wave number of the incident wave measured in grid unit. The same method of analysis is applied to the examination of boundary conditions of primitive equations. It was revealed that adopting some boundary conditions, the reflection rates of computational mode of gravity wave exceed unity, while a certain condition does not bring artificial reflection at all. Discussions are made about the differences between the Platzman's analyses (1954) and the present results.