  Here we present a numerical method for finding non-hydrostatic
coastal-trapped wave and instability solutions to the non-hydrostatic
Boussinesq equations in the presence of a background flow and complicated
coastal topography. We use spectral methods to discretise the two-dimensional
eigenvalue problem and solve the resulting discrete problem by standard
methods. Our approach is applied to three examples and shown to be consistent
with previous numerical and analytical results. In particular, we show that our
method is able to reliably identify coastal-trapped wave solutions that
correspond to waves seen in realistic simulations of the Southeast Greenland
shelf.
