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posted by Fnord666 on Friday December 13 2019, @02:32AM   Printer-friendly
from the you-want-cream-with-that? dept.

What if engineers could design a better jet with mathematical equations that drastically reduce the need for experimental testing? Or what if weather prediction models could predict details in the movement of heat from the ocean into a hurricane? These things are impossible now, but could be possible in the future with a more complete mathematical understanding of the laws of turbulence.

University of Maryland mathematicians Jacob Bedrossian, Samuel Punshon-Smith and Alex Blumenthal have developed the first rigorous mathematical proof explaining a fundamental law of turbulence. The proof of Batchelor's law will be presented at a meeting of the Society for Industrial and Applied Mathematics on December 12, 2019.

[...] Since its introduction in 1959, physicists have debated the validity and scope of Batchelor's law, which helps explain how chemical concentrations and temperature variations distribute themselves in a fluid. For example, stirring cream into coffee creates a large swirl with small swirls branching off of it and even smaller ones branching off of those. As the cream mixes, the swirls grow smaller and the level of detail changes at each scale. Batchelor's law predicts the detail of those swirls at different scales.

The law plays a role in such things as chemicals mixing in a solution, river water blending with saltwater as it flows into the ocean and warm Gulfstream water combining with cooler water as it flows north. Over the years, many important contributions have been made to help understand this law, including work at UMD by Distinguished University Professors Thomas Antonsen and Edward Ott. However, a complete mathematical proof of Batchelor's law has remained elusive.

"Before the work of Professor Bedrossian and his co-authors, Batchelor's law was a conjecture," said Vladimir Sverak, a professor of mathematics at the University of Minnesota who was not involved in the work. "The conjecture was supported by some data from experiments, and one could speculate as to why such a law should hold. A mathematical proof of the law can be considered as an ideal consistency check. It also gives us a better understanding of what is really going on in the fluid, and this may lead to further progress."

"We weren't sure if this could be done," said Bedrossian, who also has a joint appointment in UMD's Center for Scientific Computation and Mathematical Modeling. "The universal laws of turbulence were thought to be too complex to address mathematically. But we were able to crack the problem by combining expertise from multiple fields."

Journal References:

  1. Jacob Bedrossian, Alex Blumenthal, Samuel Punshon-Smith. Almost-sure exponential mixing of passive scalars by the stochastic Navier-Stokes equations. submitted to arXiv, 2019 [link]
  2. Jacob Bedrossian, Alex Blumenthal, Samuel Punshon-Smith. Almost-sure enhanced dissipation and uniform-in-diffusivity exponential mixing for advection-diffusion by stochastic Navier-Stokes. submitted to arXiv, 2019 [link]

Original Submission

 
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  • (Score: 0) by Anonymous Coward on Friday December 13 2019, @05:37AM

    by Anonymous Coward on Friday December 13 2019, @05:37AM (#931645)

    I managed to read the summary of your first link okay. I even understood most of the words up until I hit "white-in-time". After that things got iffy. Thanks for the links, by the way.