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Details of Grant 

EPSRC Reference: EP/R024952/1
Title: A Universal "Sound-Proof" Fluid Model
Principal Investigator: Wood, Dr T
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department: Sch of Maths, Statistics and Physics
Organisation: Newcastle University
Scheme: New Investigator Award
Starts: 01 September 2018 Ends: 31 August 2020 Value (£): 174,577
EPSRC Research Topic Classifications:
Continuum Mechanics Fluid Dynamics
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:
Panel DatePanel NameOutcome
29 Nov 2017 EPSRC Mathematical Sciences Prioritisation Panel November 2017 Announced
Summary on Grant Application Form
One of the greatest challenges in Applied Mathematics is to understand and predict the complex, turbulent, large-scale fluid flows in the Earth's atmosphere and oceans, as well as those in the Sun and other astrophysical objects. A major difficulty is the enormous range of timescales involved, and nearly all models are forced to make some approximation in order to "filter out" dynamics taking place on timescales that are much shorter than those of interest. This filtering is essential in computer simulations of large-scale fluid flows, because otherwise the majority of the computational power would be wasted resolving the "fast" dynamics that is of no scientific interest.

The most important example of this problem comes from sound waves, which are waves of rapid expansion and compression that are ubiquitous in real fluids, yet generally play a negligible role in the fluid's dynamics. Most fluid flows are only weakly compressible, because the flow speed is much slower than the speed of sound, and we would therefore like to filter sound waves out of the fluid equations, yielding a "sound-proof" model. There are several existing methods to achieve this filtering, but these methods often violate certain physical laws that the real system must obey, such as conservation of energy, and in many cases this produces unphysical results.

We propose an alternative framework for obtaining a general sound-proof model, using the techniques of Lagrangian and Hamiltonian mechanics. This type of mathematics, which is frequently used in discrete mechanics and classical field theory, is underutilised in fluid mechanics, but offers two crucial advantages. First, the filtering of sound waves can be achieved in a simple and intuitive way, by imposing particular constraints on the dynamics. Second, with this method the conservation laws are built in from the outset, avoiding the unphysical behaviour that can arise with other methods.

As well as providing a general methodology for filtering sound waves, which has applications across a wide range of physical applications, we will develop an efficient algorithm to simulate sound-proof flows computationally, and use this to study two problems for which traditional methods are inadequate: thermal convection in a rapidly rotating fluid, and the generation of strong magnetic field within the Sun.
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