Dynamic Morphology of Dissipative and Nondissipative Mechnaics in a Turbulent Pipe Flow

Turbulent flow and its spatial structures in a pipe flow is an unsolved problem. Turbulent flows have been associated with many phenomena such as bifurcation, random motion, local instability, ejections and intermittences etc. Recently, the work on the nondissipative dynamics has shed some lights on the physics and mathematical representation of turbulent flow and its spatial structures and further developments of the theory and experiments are necessary and important. Here, in this study, we introduced the Hausdorff space in order to visualize the dissipative and nondissipative fluids and the Borel -field to represent probability distribution on a spatial topology. In a turbulent pipe flow, the spatial topology is computed by the correlation functions, whose isocontour agrees very well with the measurements by stereoscopic particle image velocimetry (SPIV) when the concept of tunneling is adopted. The dynamic morphology between dissipative and nondissipative fluids is studied with streamwise velocity vectors and the effects of the spatial topology of local resonance on bifurcation, vortex generation, instability, turbulence and intermittences are discussed qualitatively. The consistent validity of the theory of the nondissipative dynamics across multiple subjects is a good verification. The new perspective is expected to provide solutions to the outstanding scientific and engineering problems. We believe that the continuous development and comprehension of the theory of nondissipative mechanics will bring a fresh view of fundamental physics and turbulence and related phenomena.