  The linear Rossby wave instability (RWI) in global, 3D polytropic discs is
revisited with a much simpler numerical method than that previously employed by
the author. The governing partial differential equation is solved with finite
differences in the radial direction and spectral collocation in the vertical
direction. RWI modes are calculated subject to different upper disc boundary
conditions. These include free surface, solid boundaries and variable vertical
domain size. Boundary conditions that oppose vertical motion increase the
instability growth rate by a few per cent. The magnitude of vertical flow
throughout the fluid column can be affected but the overall flow pattern is
qualitatively unchanged. Numerical results support the notion that the RWI is
intrinsically two dimensional. This implies that inconsistent upper disc
boundary conditions, such as vanishing enthalpy perturbation, may inhibit the
RWI in 3D.
