  Let $G$ be a simple algebraic group over an algebraically closed field $K$
with Lie algebra $\mathfrak{g}$. For unipotent elements $u \in G$ and nilpotent
elements $e \in \mathfrak{g}$, the Jordan block sizes of $\operatorname{Ad}(u)$
and $\operatorname{ad}(e)$ are known in most cases. In the cases that remain,
the group $G$ is of classical type in bad characteristic, so
$\operatorname{char} K = 2$ and $G$ is of type $B_{\ell}$, $C_{\ell}$, or
$D_{\ell}$.
  In this paper, we consider the case where $G$ is of type $C_{\ell}$ and
$\operatorname{char} K = 2$. As our main result, we determine the Jordan block
sizes of $\operatorname{Ad}(u)$ and $\operatorname{ad}(e)$ for all unipotent $u
\in G$ and nilpotent $e \in \mathfrak{g}$. In the case where $G$ is of adjoint
type, we will also describe the Jordan block sizes on $[\mathfrak{g},
\mathfrak{g}]$.
