Mathematicians Derive the Formulas for Boundary Layer Turbulence
upstart writes:
Now an international team of mathematicians, led by UC Santa Barbara professor Bjorn Birnir and the University of Oslo professor Luiza Angheluta, has published a complete description of boundary layer turbulence. The paper appears in Physical Review Research, and synthesizes decades of work on the topic. The theory unites empirical observations with the Navier-Stokes equation -- the mathematical foundation of fluid dynamics -- into a mathematical formula.
This phenomenon was first described around 1920 by Hungarian physicist Theodore von Karman and German physicist Ludwig Prandtl, two luminaries in fluid dynamics. "They were honing in on what's called boundary layer turbulence," said Birnir, director of the Center for Complex and Nonlinear Science. This is turbulence caused when a flow interacts with a boundary, such as the fluid's surface, a pipe wall, the surface of the Earth and so forth.
Prandtl figured out experimentally that he could divide the boundary layer into four distinct regions based on proximity to the boundary. The viscous layer forms right next to the boundary, where turbulence is damped by the thickness of the flow. Next comes a transitional buffer region, followed by the inertial region, where turbulence is most fully developed. Finally, there is the wake, where the boundary layer flow is least affected by the boundary, according to a formula by von Karman.
The fluid flows quicker farther from the boundary, but its velocity changes in a very specific manner. Its average velocity increases in the viscous and buffer layers and then transitions to a logarithmic function in the inertial layer. This "log law," found by Prandtl and von Karman, has perplexed researchers, who worked to understand where it came from and how to describe it.
The flow's variation -- or deviation from the mean velocity -- also displayed peculiar behavior across the boundary layer. Researchers sought to understand these two variables and derive formulas that could describe them.
Journal Reference:
Bjorn Birnir, Luiza Angheluta, John Kaminsky, et al. Spectral link of the generalized Townsend-Perry constants in turbulent boundary layers [open], Physical Review Research (DOI: 10.1103/PhysRevResearch.3.043054)
Read more of this story at SoylentNews.