Optimal Initial Conditions for the Zeroth Law of Turbulence

In this research project, we wish to further understand turbulent flows and the laws that govern them. In particular, we hope to mathematical understand the phenomenon known as “anomalous dissipation” or the “zeroth law of turbulence”. This anomalous dissipation refers to when the viscosity coefficient in a fluid approaches zero, the rate of energy dissipation in the system approaches a nonzero limit. Although this shown been experimental, it is still yet to be understood from a physical and mathematical sense. In this research project, we propose to use an optimization approach to try and further understand this phenomenon. In this approach, we intend on combining the tools of scientific computing and mathematical analysis, to give insight to old-standing open problem. Due to the multidisciplinary nature of turbulent flows, this work will have a significant impact on several fields such as engineering and fluid mechanics.

Faculty Supervisor:

Bartosz Protas

Student:

Partner:

The University of Tokyo

Discipline:

Mathematics

Sector:

Education

University:

McMaster University

Program: