  We present the simulation results of merging harmonically confined rotating
Bose-Einstein condensates in two dimensions. Merging of the condensate is
triggered by positioning the rotation axis at the trap minima and moving both
condensates towards each other while slowly ramping their rotation frequency.
We analyze the dynamics of the merged condensate by letting them evolve under a
single harmonic trap. We systematically investigate the formation of solitonic
and vortex structures in the final, unified condensate, considering both
non-rotating and rotating initial states. In both cases, merging leads to the
formation of solitons that decay into vortex pairs through snake instability,
and subsequently, these pairs annihilate. Soliton formation and decay-induced
phase excitations generate sound waves, more pronounced when the merging time
is short. We witness no sound wave generation at sufficiently longer merging
times that finally leads to the condensate reaching its ground state. With
rotation, we notice off-axis merging (where the rotation axes are not aligned),
leading to the distortion and weakening of soliton formation. The
incompressible kinetic energy spectrum exhibits a Kolmogorov-like cascade
[$E(k) \sim k^{-5/3}$] in the initial stage for merging condensates rotating
above a critical frequency and a Vinen-like cascade [$E(k) \sim k^{-1}$] at a
later time for all cases. Our findings hold potential significance for atomic
interferometry, continuous atomic lasers, and quantum sensing applications.
