  We prove that the eigenvalues of a certain highly non-self-adjoint operator
that arises in fluid mechanics correspond, up to scaling by a positive
constant, to those of a self-adjoint operator with compact resolvent; hence
there are infinitely many real eigenvalues which accumulate only at $\pm
\infty$. We use this result to determine the asymptotic distribution of the
eigenvalues and to compute some of the eigenvalues numerically. We compare
these to earlier calculations by other authors.
