  The evolution of a localized vortex in stably stratified flow, within the
Boussinesq approximation, is analyzed using the fluid impulse concept. The set
of equations describing the temporal development of the fluid impulse has an
integro-differential character where the terms representing the effect of
stratification appear as convolution integral of the component of the fluid
impulse and time-depended 'memory' functions. These functions are calculated
for the case where the external parallel shear flow varies only in the
direction gravitational force and is subjected to localized two- and
three-dimensional disturbances. As follows from the solution of evolution
equations, in both cases there is a range of Richardson numbers where the fluid
impulse associated with the disturbance grows exponentially. The upper limit of
this range for two- and three-dimensional cases are Ri ~ 1.23 and Ri ~ 0.89.
Both cases are also characterized by a critical value of the Richardson number
(around Ri ~ 0.3 for both cases), beyond which the solution exhibits
oscillatory behavior. Indeed, this oscillatory behavior has been observed in
turbulent flows and, as is shown in the present study, it is an inherent
feature of a non-wavy localized vortex embedded in a stably stratified shear
flow. The paper was written in 2001 and published now without changes and new
additions.
