  This article aims to understand the behavior of the curvature operator of the
second kind under the Ricci flow in dimension three. First, we express the
eigenvalues of the curvature operator of the second kind explicitly in terms of
that of the curvature operator (of the first kind). Second, we prove that
$\a$-positive/$\a$-nonnegative curvature operator of the second kind is
preserved by the Ricci flow in dimension three for all $\a \in [1,5]$.
