Around the Japan Islands, sometimes the cold monsoon from Siberia blows on the warm sea surface in winter. It causes a large amount of snowfall in the mountain region of Central Japan. At this time, the temperature difference between sea surface and air above it is very large and wind velocity is fairly high, so that the transformation of the monsoon air mass is very quick. Perhaps such a meteorological condition is rare all over the world. Previously the author calculated the differences of moistures and those of sensible heat energies in the atmospheric columns between two stations which lie on both sides of the Japan Sea. But marine and upper air data were not very accurate. On this paper, he treats more accurate data at the two stations, Kagoshima and Tango (ship observation), and on the sea surface of the Pacific Ocean. Then he trys to determine the coefficient k in the following evaporation equation used generally; E=k(es-ea)U where E: evaporation, es: saturated vapor pressure at sea surface temperature, ea: vapor pressure in the air, and U: wind velocity. The value of k obtained by this method is in good agreement with that by Jacobs.
The truncation error of difference solutions of the barotropic vorticity equation is considered, and it is shown that the physical phase velocity of the difference solution of the linearized vorticity equation becomes smaller than that of the true solution as an effect of use of the space difference, and larger as an effect of the time difference. And a method eliminating the computational noises which originate from the time difference is given. Some considerations on the truncation error of the non-linear term are also presented. Next, approximate solutions by the perturbation method are considered, and as an example of this method the problems on the energy exchange between the disturbances and general current are discussed. In the case of the long wavelength disturbances good approximate solutions can be obtained, but in the case of the shorter wavelength disturbances it is not. Asnecessary conditions for obtaining the approximate solutions, the laws of the kinetic energy conservation and the momentum transfer on the variation of the general current are adopted.
In order to reduce the errors in numerical calculations of Laplacian and Jacobian, an attempt is made to extend the gridpoint system from 5 to 9 or 25 points. The truncation errors are divided into two kinds; one is symmetrical and the other orientational. The author asserts that in order to get high accuracy of calculation, not only the former error but also the latter must be reduced, which has been apt to be neglected. Taking some examples of patterns, numerical calculation schemes of Laplacian and Jacobian are tested by comparing the numerical with the analytical values.
For solving numerically the Elliptic-type differential equation, the speeds of convergence by various iterative methods are tested. The equations treated are the 2 and 3 dimensional Poisson and Helmholtz-type equations, and the boundary conditions are of the first and of the second kinds. The methods taken up are three Accelerated Liebmann (AL), the Residual Polynomial Generation (RPG) and the Alternating Direction Implicit (ADI) methods. First, the theoretical considerations are made on the optimum value of the overrelaxation coefficient for the AL method and that of the iteration parameter used in the ADI method. Then, taking four practical cases, these methods are tested in various ways using the computing machine IBM 704. The results obtained are that the speed of the ADI method is highest compared with those of other methods, but this method is somewhat complicated in treatment and unstable in convergence. The speed by the RPG method is very low, but it is effective to accelerate the slow method, for instance, the method solving the Helmholtz-type equation of negative coefficient proposed by Matsuno. The AL method is very simple and it needs the fewest memory field, and the computation speed is fairly high, so far as the optimum overrelaxation coefficient is adopted.
It will be necessary to determine the hydrodynamical forces which affect falling snow or snowflake, and to look their falling position, falling trajectory etc. in order to study the collision efficiency between them. In this paper, for preliminary investigation, the method of analysis of these forces and their falling position were shown.