Björn Birnir
November 22, 2021

Award Date: November 22, 2021

 

Update: This research is featured in a new article in Scientific American!

 

An international team of mathematicians, led by UCSB Professor Björn Birnir, has published a complete mathematical description of boundary layer turbulence. The paper, published in the journal Physical Review Research, synthesizes decades of work on the topic to provide a mathematical formula describing the turbulance caused when flow of water, air, or other fluids interacts with a boundary such as a pipe wall or the surface of the earth. Boundary layer interactions are important to many scientific and engineering fields, from meteorology to optimizing the aerodynamics of cars and aircraft.

 

 

A Clear Description of Turbulent Water

 

 

Mathematicians derive the formulas for boundary layer turbulence 100 years after the phenomenon was first formulated
 
Update: This research is featured in a new article in Scientific American!
 
 
(Santa Barbara, Calif.) — Turbulence makes many people uneasy or downright queasy. And it’s given researchers a headache, too. Mathematicians have been trying for a century or more to understand the turbulence that arises when a flow interacts with a boundary, but a formulation has proven elusive.
 
Now an international team of mathematicians, led by UC Santa Barbara professor Björn 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 Kármán 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.