  In this paper, we first present a Gearhardt-Pr\"uss type theorem with a sharp
bound for m-accretive operators. Then we give two applications: (1) give a
simple proof of the result proved by Constantin et al. on relaxation
enhancement induced by incompressible flows; (2) show that shear flows with a
class of Weierstrass functions obey logarithmically fast dissipation
time-scales.
