  We consider the concept of Stokes-Dirac structures in boundary control theory
proposed by van der Schaft and Maschke. We introduce Poisson reduction in this
context and show how Stokes-Dirac structures can be derived through symmetry
reduction from a canonical Dirac structure on the unreduced phase space. In
this way, we recover not only the standard structure matrix of Stokes-Dirac
structures, but also the typical non-canonical advection terms in (for
instance) the Euler equation.
