  We study fluctuations of ergodic averages generated by actions of amenable
groups. In the setting of an abstract ergodic theorem for locally compact
second countable amenable groups acting on uniformly convex Banach spaces, we
deduce a highly uniform bound on the number of fluctuations of the ergodic
average for a class of F{\o}lner sequences satisfying an analogue of
Lindenstrauss's temperedness condition. Equivalently, we deduce a uniform bound
on the number of fluctuations over long distances for arbitrary F{\o}lner
sequences. As a corollary, these results imply associated bounds for a
continuous action of an amenable group on a $\sigma$-finite $L^{p}$ space with
$p\in(1,\infty)$.
