Many-Body Chaos in Fully Developed Turbulence

Banerjee, Aikya (2025) Many-Body Chaos in Fully Developed Turbulence. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS Dissertation of Aikya Banerjee (20MS104)) 20MS104_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (2MB)

Abstract

The nature of many-body chaos in fully deleveloped turbulence is perhaps one of the most celebrated question in last few decades. Turbulent flows stand out from other instances of classical many-body systems exhibiting chaotic behaviour because they are ubiquitous in the natural world. Thus, it should come as no surprise that physicists working on problems in oceanography, atmospheric sciences, astrophysics, and fluid dynamics must take into account the fundamentally chaotic character of such flows [1]. This prevalence is not unexpected, as the fundamental Navier-Stokes equation in all of these systems leads to turbulent solutions in the limit of small viscosities [2]. While mathematical and engineering tools remain indispensable, the ideas of statistical physics provide the basis for much of our understanding of turbulence, especially in its most general form where the flow is homogeneous and isotropic. In particular, chaos along with the other fingerprint of fully developed turbulence, namely intermittency, and their dependence inter alia the Reynolds number Re, forms a major challenge in a complete understanding of turbulence [2]. Thus, this continues to be a fundamental problem in the areas of statistical physics of non-equilibrium, driven-dissipative systems and for many the holy grail in fully developed turbulence.

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