An Analytical Study of Nonlinear Responses of Rising Balloons to Horizontal Winds

Abstract

Solutions of the nonlinear, coupled equations of horizontal and vertical balloon motions are obtained using standard expansion methods. Comparison of the results of these solutions with those from numerical integration and from solutions of the approximate, linear versions of the equations of motion shows that 1) the linear solutions provide reliable estimates of the transfer function for horizontal air motions, and 2) the nonlinear solution provides the salient features of coupling between horizontal and vertical motions. For example, a balloon's mean ascent rate will diminish slightly if the horizontal winds are fluctuating rapidly, while in no case do the nonlinear effects lead to significant frequency mixing of horizontal balloon motions.