Ocean Mixing Parameterisation via Categorisation of Nonlinear Flow Structures - Project 1: Mathematical Model Development

About the project

One of the key challenges for large-scale climate models is to accurately parameterise the mixing which occurs in the oceans. Such mixing occurs at small-scales, well below the grid-resolution of the climate models, and consists of the turbulent exchange of heat and salt between neighbouring regions of fluid. In order to build a robust parameterisation of this mixing, we must take a data-driven approach in which oceanographic data are algorithmically categorised according to the type of dynamics they represent.

Mixing at small scales in the ocean is mediated by a class of flows called stratified shear flows. Within such flows, there are three potential routes, or instabilities, leading to turbulence, each with a distinct degree and vigorousness of mixing. Recently, Dr Tom Eaves proposed a categorisation scheme for oceanographic data taken at a single instant in time, which aims to distinguish between these three instabilities at linear and nonlinear levels (predicting what type of mixing will happen next, and what type of mixing just occurred, respectively).

This project will investigate the fidelity of the categorisation scheme, taking it beyond the simplified flows considered in Dr Eaves’ initial study. We will investigate to what extent the linear and nonlinear categorisation algorithms agree with one another (a prediction at one time about what is about to happen should agree with a prediction at some later time about what just occurred), in addition to probing the mathematics underlying the categorisation schemes to build and interrogate nonlinear flow structures associated with stratified shear flows.

We will make use of a number of computational techniques, including direct numerical simulation of stratified shear flows, an asymptotic high-Reynolds-number contour dynamics model developed by Dr Anirban Guha, and computation of families of exact coherent structures. Dr Guha’s asymptotic model will be compared against the direct numerical simulation results and a suite of parametric experiments led by Dr Alan Cuthbertson (see Project 2) , and then used as a starting point for computing families of nonlinear exact coherent flow structures which emerge from the equations of stratified shear flow.

Key skills developed through the project include the direct numerical simulation of fluid flows, mathematical high-Reynolds-number fluid dynamics, and advanced numerical models and techniques for studying fluid flows.

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