ON THE SOLUTIONS OF THE EQUATIONS OF MOTION FOR LINIEAR FIELDS

Abstract

Under the assumption that the geostrophic wind possesses a stream function which is quadratic in x, y, and t, the equations of horizontal motion are solved, neglecting variations of the Coriolis parameter. It is shown that the general solution may be split into two components, called the central and eccentric components. Each of these components satisfies the equations of a linear velocity field. The central field is proposed as a practical approximation to the real wind, to be regarded as a refinement of the geostrophic wind field taking into account the effects of contour curvature, contour convergence, geostrophic shear, and temporal changes of the gradient. The central field is found to be, in a certain sense, a stable approximation. This stability is achieved, however, only by defining the central field by two totally different expressions, these expressions being valid in two mutually exclusive domains of possible quadratic stream functions. The form of the eccentric component of the general solution suggests that horizontal oscillations of the wind may be observable, and the form and period of these oscillations are given.