  We investigate the effects of advection on the principal eigenvalues of
linear time-periodic parabolic operators with zero Neumann boundary conditions.
Various asymptotic behaviors of the principal eigenvalues, when advection
coefficient approaches infinity, are established in heterogeneous environments,
where spatial or temporal degeneracy could occur in the advection term. Our
findings partially extend the existing results in Chen-Lou [2008 Indiana Univ.
Math. J.] and Peng-Zhou [2018 Indiana Univ. Math. J.] for elliptic operators
and those in Peng-Zhao [2015 Calc. Var. Partial Diff.] for parabolic operators.
