On the Upheaving Effect of the Stationary and Non-Stationary winds upon the Sea Level

Abstract

In order to avoid the defect of Colding's empirical formula for calculating the elevation of the sea level caused by winds, H. Arakawa and M. Yoshitake discussed the effect of the stationary wind upon the sea level based on an interesting concept. In the present paper, the same method was adopted by the author. Thus, it was shown that the slope of the sea level close to the coast becomes remarkably steep, and that the relation between the elevation of the sea level and the fetch depends upon the topographical features of the sea-bottom. For example, in case of a uniform depth, the elevation is proportional to the fetch itself, while in case of a parabolic depth curve, the elevation is proportional to the square root of the fetch. Moreover, it was shown that if the depth is shallower, the wind-gradient is larger, and if the slope of the sea-bottom is smaller, the elevation becomes higher. Even when the wind does not blow in the neighbourhood of the coast, it can be proved that a considerable amount of upheaval occurs along the shore as long as the wind blows off the shore. In this region of calm, the upheaval caused by the wind off the shore is uniform if the wind is stationary, and not uniform if the wind is not stationary.
In case of non-stationary wind, we can discuss the elevation by the so-called Mass Transport Theory. According to it, we can get the solution for the elevation comparatively easily, even if we can not solve the motion of the sea water explicitly, since we have only to consider the equation of elevation. In this paper, we have discussed the case of the wind velocity increasing exponentially with the time. The equation to be solved is (41), and the boundary conditions are (43), (44) and (45), of which two are independent.
Generally speaking, the sea level in a canal is not reverse-symmetric to the central line of the canal. The sufficient condition of reverse-symmetry is that the distribution of wind velocity is symmetric to the central line with constant wind direction. When the gradient of the wind velocity is positive, the elevation on the lee side is larger than the depression on the windward side, and vice versa. However, owing to the rotation of the earth, the elevation on the lee side is not always positive.
A discussion was also made on the effect of the fetch, depth, wind-gradient and latitude of the place on the elevation of the surfaces of a canal and a semi-infinite ocean. We obtained the solution for the case of the line of discontinuity of wind lying on the sea, and it was concluded that the slope of the sea level also becomes discontinuous along the line of the discontinuity of wind.