Research Associate

University of Sheffield - Faculty of Science / School of Mathematics and Statistics

Contract Type: Fixed-term for 36 months.

Summary:

The School of Mathematics and Statistics is seeking to appoint a Research Associate to work with Prof K. Ohkitani at the University of Sheffield, partly in collaboration with Prof J. Gibbon at Imperial College and Prof P. Constantin at Princeton, to investigate the statistical property of the Navier-Stokes turbulence, with the goal to develop new insights on the statistics of turbulence at the fundamental level. They also collaborate with Dr Y. Li and Dr A.P. Willis, in particular on the numerical aspects. The position is funded by EPSRC.

This project aims to combine operational calculus handling of the statistical Navier-Stokes equations with the numerical verifications. The problem of fluid turbulence deals with phenomena ubiquitous in our daily life, yet its complete understanding, let alone its control, is way far beyond our current capability. Turbulence is also regarded as a big open problem in classical physics. While a suitable description of turbulence should be inevitably statistical in nature, a satisfactory theory has not yet been developed.

Even for deterministic solutions of the fluid dynamical equations, there is still room for smooth solutions to break down. Such a potential blow up is connected with statistical solutions, as it can trigger a transition from deterministic to statistical descriptions.

The team will study (1) the long-standing problem of statistical solutions of the incompressible Navier-Stokes equations. Statistical solutions of the Navier-Stokes equations are governed by a functional differential equation (FDE), the Hopf equation. We will introduce a novel systematic method of approximations based on operational calculus and test its performance against numerics.

We will also study (2) the regularity issue of the fluid dynamical equations with generalised dissipativity, based on the recent mathematical results of blowup criteria with critical norms.

Turbulence with finite total energy in the whole space will also be investigated to see whether and how the nonlocal effects affect turbulence characteristics. The postholder will be occupied with problems 1) and 2).

You will hold a PhD or will be close to completing a PhD in Mathematics/Engineering or Physics with knowledge of Fluid Mechanics (or equivalent experience). You will be competent in performing numerical simulations and will be skilled in computer programming languages and operating systems, such as Fortran, Matlab and Unix.

The post is available immediately on a fixed-term basis for 36 months.

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Northern England