Consider a homogeneous static equilibrium with g=0.
In the ideal equations, there are 2 normal modes with
w=0 which are convective cells where k x u is non zero,
k and u being vectors.

Find w for these same convective cells if your equations
are the NS eqns.   NS eqns are first order correct in lambda << L,
thus to lowest order you should be able to recover the w=0 cells.