This work investigates fundamental two-dimensional vortex pair dynamics in
unstratified and stably stratified environments through numerical and
analytical techniques. The study focuses on two main topics: (i) vortex
interaction and merging of co-rotating vortex pairs and (ii) internal wave
generation by co-rotating and counter-rotating vortex pairs.
Two-dimensional vortex merging in a viscous fluid is studied using
numerical simulations. Analysis of the ideal case of two equal co-rotating
vortices (symmetric pair) identifies the basic underlying physics of
vortex merger. Through the interaction of the vorticity gradient and the
mutually induced strain rate near the central hyperbolic point, a tilt in
vorticity contours is established. This leads to core detrainment and the
entrainment of core fluid into the exchange band, which transforms the
flow into a single vortex.
In the case of the asymmetric (unequal strength) vortex pair, the
disparity in the deformation rates between the vortices alters the
interaction. A critical value for a strain rate parameter characterizing
the establishment of core detrainment is determined. The onset of merging
is associated with the achievement of the critical strain by both vortices
and a generalized merging criterion is formulated. A classification
scheme of the various viscous vortex interactions is developed.
Results for the symmetric, horizontally oriented vortex pair in a weakly
stratified fluid provide further insight on vortex merging. The effects of
weak stratification depend on the ratio of the diffusive time scale to the
turnover time, i.e., the Reynolds number. A crossover Reynolds number is
found, above which convective merging is accelerated with respect to
unstratified flow and below which it is delayed.
The generation of internal waves by horizontally orientated co-rotating
and counter-rotating vortex pairs is studied. Linearized inviscid
equations are derived that describe the internal wave, vorticity and
energy fields. These solutions are compared with nonlinear numerical
viscous simulations in moderately and strongly stratified environments.
Through evaluation of the energy field, the time at which the flow reaches
a steady state for strongly stratified flows is found, along with a
characterization of the regimes of strongly and moderately stratified
environments.