Investigation of the nonstationary Navier-Stokes equations in special domains - transition to turbulence

We regard a general class of boundary-pressure-driven flows of incompressible Newtonian fluids in unbounded layers and in unbounded pipes in R"3 with thickness 2R or radius R, which marginal cases are e.g. plane Couette flows and Poiseuille flows in channels, respectively. We avail the incompressible nonstationary Navier-Stokes equations as description of the physical process. We define energetic Reynolds numbers. Using Galerkin approximations based on Stokes eigenfunctions on open bounded subdomains in R"3 furnished with periodical conditions in the at first unbounded spatial directions, we get an autonomous system of ordinary differential equations for the time-dependent coefficients of the Stokes eigenfunctions from the dimensionless Navier-Stokes equations for the difference u between the velocity and the laminar velocity. For the Galerkin method we utilize fixed periods 2l and the first N(l) Stokes eigenfunctions. We apply the kinetic energy of u as a measure of turbulence. The numerical calculations yield satisfactory results in comparison with measurements keeping in mind the small dimension of our approximation spaces and hope raising results for investigations of bifurcations. (orig.)Available from TIB Hannover: RR 4487(1999,35) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman