NGCM-104: Sensitivity of turbulent flow to wall roughness – approach based on invariant solutions of the Navier-Stokes equations

Recent advances in the understanding of turbulent shear flows highlight the importance of so-called “invariant solutions” of the Navier-Stokes equations, such as equilibria and periodic orbits [1]. These objects (an example is shown in the accompanying picture) populate the phase space of the system and provide a constitutive scaffold, a skeleton around which long turbulent trajectories sustain and develop. A key feature is that these solutions sometimes reproduce remarkably well the statistics of flow, such as the mean spatial structure. This has contributed to making invariant solutions a prominent basis for decomposing and analysing turbulent flows, and justifies the surge of interest in the last decade.

Recent research at the University of Southampton has proposed that invariant solutions might be the key to tackle challenging design/optimisation problems in turbulence that would otherwise be difficult or extremely computationally intensive to solve. The key enabler is that invariant solutions are a well-behaved proxy for computing the sensitivity of the flow statistics to design parameters of the problem.

In this project we will build upon such advances to design drag-reducing rough surfaces, a subject of intensive research with numerous industrial applications. Significant effort will be dedicated to developing a computational infrastructure to solve partial differential equations using parallel-in-space-and-time algorithms on IRIDIS, the HPC facility of the University of Southampton.

We are looking for an applicant with a background in physics, engineering or applied mathematics and strong interests in high performance computing, numerical analysis, dynamical system theory, optimization and turbulence. One fully funded, four-year studentship is available for UK/EU students. More details on facilities and computing equipment are available http://ngcm.soton.ac.uk/facilities.html

[1] Kawahara, G, Uhlmann, M, and van Veen, L, "The Significance of Simple Invariant Solutions in Turbulent Flows." Annual Review of Fluid Mechanics 44 (2012): 203-225.

If you wish to discuss any details of the project informally, please contact Davide Lasagna, Email: [Email Address Removed], Tel: +44 (0) 2380 594907

This project is run through participation in the EPSRC Centre for Doctoral Training in Next Generation Computational Modelling (http://ngcm.soton.ac.uk). For details of our 4 Year PhD programme, please see http://www.findaphd.com/search/PhDDetails.aspx?CAID=331&LID=2652

For a details of available projects click here http://www.ngcm.soton.ac.uk/projects/index.html