Abstract
Analytic solutions of a balloon's response to simultaneous variations of the vertical wind speed and the density are obtained using Fourier expansion methods. It is assumed that density and wind are in phase quadrature. The balloon's response depends on wave period, density and wind amplitudes, and static stability. When density and wind amplitudes are related as in a gravity wave the amplitude of the balloon's velocity response varies from about 75 to 105% of the wind amplitude as the lapse rate condition varies from isothermal to adiabatic, for a typical wave period (13.8 min) and air motion amplitude (30 cm s−1). Further, balloon phase leads air motion phase by ∼30° for adiabatic lapse, but lags the air motion by ∼25° for isothermal lapse conditions at this wave period. For very long period waves the balloon asymptotically approaches a true isopycnic tracer (with some phase shift) for high static stability, but not for low static stability.
