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Editorial: Scaling the Turbulence Edifice.

Jérémie Bec1,2, Giorgio Krstulovic3, Takeshi Matsumoto4

  • 1Université Côte d'Azur, INRIA, CNRS, CEMEF, Sophia-Antipolis, France.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|January 17, 2022
PubMed
Summary
This summary is machine-generated.

A microscopic theory of turbulence remains elusive, but new interdisciplinary approaches combining physics and mathematics offer hope. This work explores these complementary strategies for understanding fluid dynamics.

Keywords:
intermittencyscaling lawsturbulenceweak solutions

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Area of Science:

  • Fluid Dynamics
  • Mathematical Physics
  • Applied Mathematics

Background:

  • Turbulence is a fundamental phenomenon studied across physics, mathematics, and engineering.
  • A complete microscopic theory of turbulence, derived from basic hydrodynamic equations, is still lacking.
  • Despite its long history, turbulence remains one of science's oldest unsolved problems.

Purpose of the Study:

  • To unite emerging research directions at the intersection of physics and mathematics concerning turbulence.
  • To highlight the complementary nature of physicists' and mathematicians' approaches to turbulence.
  • To contribute to the ongoing effort of 'solving' the problem of turbulence.

Main Methods:

  • This article is part of a two-part theme issue focusing on new directions in turbulence research.
  • It emphasizes the integration of diverse methodologies from physics and mathematics.
  • The focus is on the interface between these disciplines to tackle the complexity of turbulence.

Main Results:

  • New research avenues at the physics-mathematics interface have emerged in the last decade.
  • These directions strengthen the prospect of developing a comprehensive theory of turbulence.
  • The complementarity of different scientific approaches is crucial for progress.

Conclusions:

  • Interdisciplinary collaboration between physicists and mathematicians is key to advancing turbulence theory.
  • The ongoing research presented offers a promising platform for future breakthroughs.
  • Understanding turbulence requires a unified approach that leverages insights from multiple scientific fields.