  The dynamics in the thin boundary layers of temperature and velocity is the
key to a deeper understanding of turbulent transport of heat and momentum in
thermal convection. The velocity gradient at the hot and cold plates of a
Rayleigh-B\'{e}nard convection cell forms the two-dimensional skin friction
field and is related to the formation of thermal plumes in the respective
boundary layers. Our analysis is based on a direct numerical simulation of
Rayleigh-B\'{e}nard convection in a closed cylindrical cell of aspect ratio
$\Gamma=1$ and focused on the critical points of the skin friction field. We
identify triplets of critical points, which are composed of two unstable nodes
and a saddle between them, as the characteristic building block of the skin
friction field. Isolated triplets as well as networks of triplets are detected.
The majority of the ridges of line-like thermal plumes coincide with the
unstable manifolds of the saddles. From a dynamical Lagrangian perspective,
thermal plumes are formed together with an attractive hyperbolic Lagrangian
Coherent Structure of the skin friction field. We also discuss the differences
from the skin friction field in turbulent channel flows from the perspective of
the Poincar\'{e}-Hopf index theorem for two-dimensional vector fields.
