  A perturbative method called beatification is presented for a class of
two-dimensional fluid and plasma theories. The Hamiltonian systems considered,
namely the Euler, Vlasov-Poisson, Hasegawa-Mima, and modified Hasegawa-Mima
equations, are naturally described in terms of noncanonical variables. The
beatification procedure amounts to finding the correct transformation that
removes the explicit variable dependence from a noncanonical Poisson bracket
and replaces it with a fixed dependence on a chosen state in phase space. As
such, beatification is a major step toward casting the Hamiltonian system in
its canonical form, thus enabling or facilitating the use of analytical and
numerical techniques that require or favor a representation in terms of
canonical, or beatified, Hamiltonian variables.
