  A general class of linear advective PDEs, whose leading order term is of
viscous dissipative type, is considered. It is proved that beyond the limit of
the essential spectrum of the underlying inviscid operator, the eigenvalues of
the viscous operator, in the limit of vanishing viscosity, converge precisely
to those of the inviscid operator. The general class of PDEs includes the
equations of incompressible fluid dynamics. Hence eigenvalues of the
Navier-Stokes operator converge in the inviscid limit to the eigenvalues of the
Euler operator beyond the essential spectrum.
