  The relationship between crystal structures and superconducting critical
temperatures has attracted considerable attention as a clue to designing
higher-$T_{\rm c}$ superconductors. In particular, the relationship between the
number $n$ of CuO$_2$ layers in a unit cell of cuprate superconductors and the
optimum superconducting transition temperature $T_{\rm c}^{\rm opt}$ is
intriguing. As experimentally observed in layered cuprates, $T_{\rm c}^{\rm
opt}$ increases when $n$ is increased, up to $n=3$, and, then, decreases for
larger $n$. However, the mechanism behind the $n$ dependence of $T_{\rm c}^{\rm
opt}$ remains elusive although there have been many studies on the $n$
dependence. In this paper, we studied a bilayer $t$-$t'$ Hubbard model to
clarify the effects of the adjacent CuO$_2$ layers on the stability of the
superconductivity by using a many-variable variational Monte Carlo method. We
calculate the superconducting correlation at long distance and zero
temperature, and the amplitude of the superconducting gap functions estimated
from the momentum distribution as the observables correlated with $T_{\rm
c}^{\rm opt}$. It is found that the in-plane superconducting correlation is not
enhanced in comparison with that in the single-layer $t$-$t'$ Hubbard model.
The superconducting correlations of the bilayer Hamiltonian are significantly
small in the overdoped region in comparison with those of single-layer
Hamiltonian, which is attributed to the van Hove singularity. In addition, we
found that the amplitude of the superconducting gap functions is also similar
in both the single-layer and bilayer $t$-$t'$ Hubbard model at the optimal
doping. Therefore, we conclude that the adjacent Hubbard layers are not
relevant to the enhancement of $T_{\rm c}^{\rm opt}$ in the bilayer cuprates.
Possible origins of the enhanced $T_{\rm c}^{\rm opt}$ other than the adjacent
layers are also discussed.
