  In this paper we study the dynamical outcome in which black hole (BH)
binary-single interactions lead to two successive gravitational wave (GW)
mergers; a scenario we refer to as a `double GW merger'. The first GW merger
happens during the three-body interaction through a two-body GW capture, where
the second GW merger is between the BH formed in the first GW merger and the
remaining bound single BH. We estimate the probability for observing both GW
mergers, and for observing only the second merger that we refer to as a `prompt
second-generation (2G) merger'. We find that the probability for observing both
GW mergers is only notable for co-planar interactions with low GW kicks
($\lesssim 10^{1}-10^{2}$ kms$^{-1}$), which suggests that double GW mergers
can be used to probe environments facilitating such interactions. For isotropic
encounters, such as the one found in globular clusters, the probability for
prompt 2G mergers to form is only at the percent level, suggesting that
second-generation mergers are most likely to be between BHs which have swapped
partners at least once.
