  This study aims to research on dynamics of two quantized vortices in miscible
two-component Bose--Einstein condensates, trapped by a circular box potential
by using the Gross--Pitaevskii equation. We consider a situation in which two
vortices belong to different components and they are initially close. Their
dynamics are significantly different from those of a vortex pair in a
single-component condensate. When two vortices are initially co-located, they
are split by dynamical instability or remain co-located depending on their
intercomponent interaction. If the two split vortices have the same sign of
circulation, they rotate around each other. Then, the angular velocity can be
given as a function of the distance between two vortices, which is understood
through the equations of motion and their interaction. If the circulations of
two close vortices have different signs, however, they move in the same
direction initially, then overlap during the dynamics. This subsequent overlap
can be categorized into two types based on the initial distance between them.
The mechanism of this overlapping can be understood from the interaction
between the vortex and its image vortex, which makes the two vortices close to
each other even if the intrinsic interaction between them is repulsive.
