
Project Ref: NGCM0104 Available: Yes Supervisor: Davide Lasagna Faculty: FEE Academic Unit: AACE Research Group: Aerodynamics and Flight Mechanics Cosupervisor: Ati Sharma Faculty: FEE Academic Unit: Engineering Sciences Research Group: Aerodynamics and Flight Mechanics Research Area: Computational Engineering Project Description: Recent advances in the understanding of turbulent shear flows highlight the importance of socalled invariant solutions of the NavierStokes 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 wellbehaved 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 dragreducing 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 parallelinspaceandtime 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, fouryear 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): 203225. If you wish to discuss any details of the project informally, please contact Davide Lasagna, Email: davide.lasagna@soton.ac.uk, Tel: +44 (0) 2380 594907 Keywords: Aeronautical Engineering, Applied Mathematics, Applied Physics, Mechanical Engineering Support: All studentships provide access to our unique facilities and training and research support . Project Images 