FRACTAL BOUNDARY LAYER AND ITS BASIC PROPERTIES

In this paper, the fractal calculus is introduced to study a non-smooth boundary layer of a viscous fluid, and a fractal-fractional modification of the Blasius equation is suggested and solved analytically. The results show that the non-smooth boundary might lead to smaller friction, this can explain well the lotus effect, the waving sand dune and Fangzhu's water collection. The fractal boundary layer theory has opened the path for a new way to optimal design of a high moving surface with the minimal friction.

Automated summary

This paper introduces the application of fractal calculus in studying the non-smooth boundary layer of a viscous fluid, and proposes a fractal-fractional modification of the Blasius equation, which is solved analytically. The results show that a non-smooth boundary may lead to smaller friction, which can explain phenomena such as the lotus effect, waving sand dunes, and water collection on Fangzhu's leaf. The fractal boundary layer theory opens up a new approach to optimizing the design of highly moving surfaces with minimal friction.