Hines <1997a, b> has developed a Doppler spread parameterization (DSP) for the deposition of small-scale gravity wave (GW) momentum and energy in the middle atmosphere. We have incorporated this DSP into the two-dimensional (2-D) version of the numerical spectral model (NSM) of Chan et al. <1994a, b> which is applied to the Earth's middle atmosphere. With a globally uniform flux of (quasi) isotropically propagating GW emanating from the troposphere, the NSM has been integrated for several model years to describe seasonal variations and equatorial oscillations. Here, after a review of the NSM and DSP, we discuss numerical results that describe the temperature and wind fields during solstice and equinox conditions, emphasizing the role played by the GW spectrum. That spectrum is filtered as it ascends through the stratosphere and provides, at the solstices, a highly anisotropic wave and momentum flux at mesospheric heights. Upon further filtering there, with attendant momentum deposition, the waves decelerate and then reverse the zonal circulation. In quasi-geostrophic balance latitudinally, this reversal is accompanied by a reversal of the latitudinal temperature gradient, one that leads to a temperature minimum in the summer polar mesopause region, as is observed. Corresponding results for equinox are obtained, and all are discussed. Our results differ only in detail from those of similar analyses that employ other GW parameterizations. They are presented here in part to exhibit the success of the DSP at this elementary level and in part to provide a point of departure against which future refinements may be judged. Our first extension of the modeling concerns the semiannual and quasi-biennial oscillations that are produced by the DSP in the NSM at equatorial latitudes with the same, constant and uniform, incident GW flux. Initial results are presented in the companion paper and are compared there with observations. ¿ 1997 American Geophysical Union