How does sustained turbulence first appear?

Turbulence causes substantial friction drag, in other words, it is energetically costly in many applications. To potentially delay or suppress turbulence, we need to understand the nature of its appearance. Since we are concerned with friction, we consider turbulence in flowswith wall boundaries, such as through pipes and channels.

The 'survival' of turbulence depends on the flow rate: 1) At very low flow rates, a patch of turbulence cannot be sustained

and it decays quickly to a smooth flow. 2) At intermediate flow rates, a patch of turbulence can be sustained for

some time then decay suddenly. The sudden decay has the characteristics of a 'memoryless' process. 3) At higher flow rates, turbulence spreads, enabling it to survive indefinitely.

Over the last 10 years there have been landmark studies that have determined the mathematical nature of the transition from 2) to 3). But

at these higher flow rates in any practical setting, turbulence entering a pipe or channel will always survive its full length. In real applications, the transition from 1) to 2) is likely to be more important, i.e. as soon as turbulence can be sustained, it is likely to survive the full length of the pipe or channel in a practical setting. So what causes the first appearance of sustained turbulence? Are there particular 'solutions' to the governing equations that mediate the transition and enable turbulence to be sustained? Can we disrupt the physical mechanism that sustains the turbulence and thereby reduce drag?

A PhD in fluid dynamics would allow you to develop highly transferable skills in analytical thinking, data analysis, scientific computation,

and mathematical modelling. Fluid dynamics is a traditional test-bed for the development of methods of applied mathematics, and beyond your

PhD, fluids appear in a huge range of environmental and industrial applications. You should have a strong mathematical background and be

familiar with the vector calculus. Some training in fluid dynamics would be an advantage, but is not essential.

Fluids Dynamics Group: https://www.sheffield.ac.uk/maths/research/fluid

Application procedures and funding: https://www.sheffield.ac.uk/maths/phd https://www.sheffield.ac.uk/maths/phd/funding