On the Structure of Typhoons (Part 1)

[摘要] There are many theories and hypotheses on the structure of typhoons. Especially the classical theories of F. H. Bigelow W. Wien and Lord Rayleigh are well known. But since the theory of the eddy viscosity had been published, it was difficult to obtain an exact solution referred to the eddy viscosity. While we succeed for the first time, to obtain an approximate solution in the year 1928. Afterward in the year 1935, B. Hauriwtz obtained an exact solution under the conditions that the wind velocity and the pressure gradient are proportional to the distance from the centre of the rotating fluid and that the isobars are circular. Here it will be shown that the new solution is more satisfactory than the previous ones.The equations of motion of a viscous fluid moving symmetrically round a stationary centre expressed in cylindrical coordinates, are where u, v, w are velocities reckoned positive in the directions in which r, θ z increase. Now we shall proceed to a solution of the equation when w=wo Sin 2 m_??_ where w0 and m are constants, puting U=U', v=V+v' and U=u'+iv' ξ=m_??_ and Neglecting the last term, in which A2 is a small quantity of higher order, the equation may be written Now we may assume as a particular solution where The value of c is the same as that which was obtained by Lord Rayleigh and it appears that c is real or complex according as (Ao-1)2 is greater or less than A21 The general possible solution subject to the condition that the ascending velocity can be represented as the same form used by Bigelow and Wien, is therefore given by where C=α+iβ, W is the wind velocity, V is the gradient wind U is the wind velocity induced by the turbulent motion of air, and the equation (7) is expressed in the form of vector.But this solution is not exactly applicable, because the pressure gradient was treated as constant for all heights. On the other hand the pressure gradient varied with height from the observation on high mountain. According to the results of an observation at Mt. Niitaka (3850m above mean sea level), the minimum pressure was 605mb and it was 95smb at Shinko (33m above mean sea level). From these results, we have estimated approximately the gradient winds as follows 25.0m/sec at the distance 28km from the centre and at the height 3850m, 40.0m/sec at the same distance and at the sea level. Thus further investigation is necessary in order to solve the equations of motion in which the gradient is introduced as a certain function of r and z determined by the results of the observation of typhoons.

[学科分类] 大气科学