Mean-Lagrangian renormalization theory of inhomogeneous turbulent flow

In nature, fluids often show stochastic and disordered behaviors both in time and space. These phenomena are inclusively called the “turbulent flows”. In various circumstances in the real world such that the Reynolds number exceeds some thousands or millions, fluid turbulence plays important roles; it promotes the mixing of the fuel and air in engines, it enhances the drag force on the surfaces of cars, ships or airplanes, it helps the oxygen to dissolve into ocean, it equalizes the temperature of the atmosphere, it diffuses the gigantic magnetic flux in the sun, interstellar gasses or galaxies. Namely, almost everywhere in our universe, there are lots of phenomena which can never be explained without appropriate knowledges about turbulence. Because of its universality and wide applicability, fluid turbulence has been the targets of various scientific fields and the disclosure of its essence should give huge impacts to wide variety of field of both pure and applied science.