  The coarsening and wavenumber selection of striped states growing from random
initial conditions are studied in a non-relaxational, spatially extended, and
far-from-equilibrium system by performing large-scale numerical simulations of
Rayleigh-B\'{e}nard convection in a large-aspect-ratio cylindrical domain with
experimentally realistic boundaries. We find evidence that various measures of
the coarsening dynamics scale in time with different power-law exponents,
indicating that multiple length scales are required in describing the time
dependent pattern evolution. The translational correlation length scales with
time as $t^{0.12}$, the orientational correlation length scales as $t^{0.54}$,
and the density of defects scale as $t^{-0.45}$. The final pattern evolves
toward the wavenumber where isolated dislocations become motionless, suggesting
a possible wavenumber selection mechanism for large-aspect-ratio convection.
