We examine the convergence characteristics of iterative methods based
on a new preconditioning operator for solving the linear systems
arising from discretization and linearization of the Navier-Stokes
equations. With a combination of analytic and empirical results, we
study the effects of fundamental parameters on convergence. We
demonstrate that the preconditioned problem has an eigenvalue
distribution consisting of a tightly clustered set together with a
small number of outliers. The structure of these distributions is
independent of the discretization mesh size, but the cardinality of
the set of outliers increases slowly as the viscosity becomes smaller.
These characteristics are directly correlated with the convergence
properties of iterative solvers.