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Details of Grant 

EPSRC Reference: EP/S023100/1
Title: Deterministic and stochastic aspects of fluid mixing
Principal Investigator: Coti Zelati, Dr M
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department: Dept of Mathematics
Organisation: Imperial College London
Scheme: EPSRC Fellowship
Starts: 01 September 2019 Ends: 31 August 2024 Value (£): 951,288
EPSRC Research Topic Classifications:
Continuum Mechanics Fluid Dynamics
Mathematical Analysis
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:
Panel DatePanel NameOutcome
23 Jan 2019 EPSRC Mathematical Sciences Fellowship Interviews January 2019 Announced
28 Nov 2018 EPSRC Mathematical Sciences Prioritisation Panel November 2018 Announced
Summary on Grant Application Form
The basic mathematical models that describe the behaviour of fluid flows date back to the eighteenth century, and yet many phenomena observed in experiments are far from being well understood from a theoretical viewpoint. For instance, especially challenging is the study of fundamental stability mechanisms when weak dissipative forces (generated, for example, by molecular friction) interact with advection processes, such as mixing and stirring. The goal of this project is to develop new mathematical tools that may be used to make progress towards outstanding open problems in the theory of the Navier-Stokes and Euler equations of incompressible fluids, such as the stability of vortices and laminar flows, the appearance of coherent structures in turbulence and atmosphere/ocean dynamics, and the statistical description of turbulent flows.

In general, mixing refers to a cascading mechanism that transfers information (such as energy, enstrophy, ...) to smaller and smaller spatial scales, in a way that is time reversible and conservative for finite times but results in an irreversible loss of information at infinite time. The precise definition of mixing really depends on the physics of the problem under study, and its quantification for infinite-dimensional systems is fundamental to deeply understand the dynamics. It is fairly accurate to think of mixing as a stabilising mechanism for certain stationary structures, generating damping effects: in kinetic theory this is known as Landau damping, while in fluid dynamics it is called inviscid damping.

In many cases, mixing acts to enhance the dissipative forces, giving rise to what we refer to as enhanced dissipation: this can be understood by the identification of a time-scale faster than the purely diffusive one, and its detection precisely relies on the understanding of the interactions between diffusion and advection. In this case, the cascading behaviour from large length-scales to small length-scales is vaguely analogous to, but much simpler than, that which occurs in turbulence.

This project aims at granting solid mathematical foundations to this theory that has been a consistent source of mathematical ideas since the 1830's. Phenomena such as the transition from laminar to turbulent states in fluids (observed in the famous Reynolds' 1883 experiments), the formation of coherent, meta-stable, vortex-like structures in large-scale atmospheric dynamics (hurricanes being the most dramatic) and the rapid decay of the electric field in hot plasmas close to equilibria (Landau damping, with implications in engineering and astrophysics) have mixing as a common stabilising effect.

In the course of this project, we propose to employ one research associate for three years and a PhD student, who will enhance and complement the PI's skills in tackling probabilistic and dynamical systems aspects of this program. The proposal envisions a great deal of dissemination work in universities and international conferences world-wide, along with the attraction of specialists through a dedicated workshop on ``Stability and long-time dynamics in incompressible flows'' and short visits by leading experts in mathematical fluid mechanics: J. Bedrossian (University of Maryland), T. Elgindi (UC San Diego), G. Crippa (University of Basel), and V. Vicol (Courant Institute).
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Organisation Website: http://www.imperial.ac.uk