  Buoyant bubbles of relativistic plasma are essential for active galactic
nucleus feedback in galaxy clusters, stirring and heating the intracluster
medium (ICM). Observations suggest that these rising bubbles maintain their
integrity and sharp edges much longer than predicted by hydrodynamic
simulations. In this study, we assume that bubbles can be modeled as rigid
bodies and demonstrate that intact bubbles and their long-term interactions
with the ambient ICM play an important role in shaping gas kinematics, forming
thin gaseous structures (e.g., H$\alpha$ filaments), and generating internal
waves in cluster cores. We find that well-developed eddies are formed in the
wake of a buoyantly rising bubble, and it is these eddies, rather than the
Darwin drift, that are responsible for most of the gas mass uplift. The eddies
gradually elongate along the bubble's direction of motion due to the strong
density stratification of the atmosphere and eventually detach from the bubble,
quickly evolving into a high-speed jet-like stream propagating towards the
cluster center. This picture naturally explains the presence of long straight
and horseshoe-shaped H$\alpha$ filaments in the Perseus cluster, inward and
outward motions of the gas, and the X-ray-weighted gas velocity distributions
near the northwestern bubble observed by Hitomi. Our model reproduces the
observed H$\alpha$ velocity structure function of filaments, providing a simple
interpretation for its steep scaling and normalization: laminar gas flows and
large eddies within filaments driven by the intact bubbles, rather than
spatially homogeneous small-scale turbulence, are sufficient to produce a
structure function consistent with observations.
