An asymptote is a streamline upon which other streamlines merge or diverge from. When the flow is not a simple wave as above and areas of confluence or diffluence exist, it can often be captured by drawing asymptotes.
A confluent asymptote is a streamline on which other streamlines converge. Confluent asymptotes are commonly analyzed in the vicinity of cyclonic circulations and along fronts, but may also be found elsewhere. See the red streamline below for an example. *Note: red is a standard coloring for indicating confluence/convergence in military streamline analyses, while blue is used for difluence/divergence. Other analysis sources may use these convections, or use all black streamlines.
A diffluent asymptote is a streamline from which other streamlines diverge. diffluent asymptotes are typically analyzed emerging from anticyclonic circulation centers, in flow transitions and in other areas. An example is below.