  This is a rather comprehensive study on the dynamics of Navier-Stokes and
Euler equations via a combination of analysis and numerics. We focus upon two
main aspects: (a). zero viscosity limit of the spectra of linear Navier-Stokes
operator, (b). heteroclinics conjecture for Euler equation, its numerical
verification, Melnikov integral, and simulation and control of chaos. Besides
Navier-Stokes and Euler equations, we also study two models of them.
