Non-Linear Theory of an Equatorial Flow. I

Abstract

(1) A simple model was considered for the equatorial current system on the assumption that pressure gradients and current velocity do not change in the east-west direction. (2) A balance between the Coriolis forces, pressure gradients and field accelerations was assumed, -w(∂u/∂z) and -w(∂v/∂z) being neglected as small compared with -v(∂u/∂y) and -v(∂v/∂y) respectively. The friction due to mixing and thermodynamic process were disregarded. (3) The solution was carried out for a dynamic meridional section, first computing the velocity components at the equator, then extending calculation to higher latitudes of both hemispheres by different procedures. (4) An attempt was made to interpret the significance of Hidaka-Tsuchiya's formula of computing the east-west equatorial velocity. (5) The equatorial undercurrent can be located as an equatorial jet stream of a speed about 85cm/sec confind to a narrow band between 1°S to 1.5°N. (6) The location and size of equatorial countercurrent agree with observations quite well. (7) It can be shown theoretically that the east-west component of velocity is approximately geostrophic even in the 1° intervals next to the equator. (8) Upwelling velocities were determined and found to be an order of -10-3cm/sec. (9) Vertical circulation in a meridional section was determined by constructing the stream function between v and w. (10) A brief discussion was made as to the merit of the inertia terms in hydrodynamical equations of an equational flow.