This project continues the studies of turbulence undertaken previously, combining mathematical analysis, numerical simulations, and methods from dynamical systems. The turbulent flows arise as solutions of the Navier-Stokes equations. The permanent regime for a turbulent flow is related to an attractor in the phase space of the flow. The attractor in turn is approximable by an approximate inertial manifold. Hence development of numerical algorithms that correspond to approximate inertial manifolds is a central theme of the work. Turbulence is a fundamental phenomenon in fluid flows. Such flows arise in describing the behavior of planes, boats, pumps, and engines. A better understanding of turbulence will help to improve the design of these machines.
