  In this paper we develop a staggered discontinuous Galerkin method for the
Stokes and Darcy-Forchheimer problems coupled with the
\Red{Beavers-Joseph-Saffman} conditions. The method is defined by imposing
staggered continuity for all the variables involved and the interface
conditions are enforced by switching the roles of the variables met on the
interface, which eliminate the hassle of introducing additional variables. This
method can be flexibly applied to rough grids such as the highly distorted
grids and the polygonal grids. In addition, the method allows nonmatching grids
on the interface thanks to the special inclusion of the interface conditions,
which is highly appreciated from a practical point of view. A new discrete
trace inequality and a generalized Poincar\'{e}-Friedrichs inequality are
proved, which enables us to prove the optimal convergence estimates under
reasonable regularity assumptions. Finally, several numerical experiments are
given to illustrate the performances of the proposed method, and the numerical
results indicate that the proposed method is accurate and efficient, in
addition, it is a good candidate for practical applications.
