The ocean circulation is dominated by an energetic mesoscale eddy field on spatial scales of 10-100 km, analogous to weather systems in the atmosphere. These eddies are unresolved, or at best inadequately resolved, in the ocean models used for long-range climate projections. Thus it is necessary to parameterise the impacts of the missing mesoscale eddies on the large-scale circulation. The vast majority of numerical ocean circulation models employ the Gent and McWilliams "eddy parameterisation" which acts to flatten density surfaces, mimicking the release of potential energy to fuel the growth of the mesoscale eddies. A key parameter in this eddy parameterisation is the "eddy diffusivity", which is critical as it plays a leading order role in setting global ocean circulation, stratification and heat content, the adjustment time scale of the global circulation, and potentially atmospheric CO2. In this project, we will implement a new closure for the Gent and McWilliams eddy diffusivity, derived from first principles, which depends only on the ocean stratification, the eddy energy and a non-dimensional parameter that is less than or equal to 1. If the eddy energy is known, then there is no freedom to specify explicitly any additional dimensional parameters, such as an eddy diffusivity. For this reason, we argue that existing approaches to parameterising eddies in ocean climate models are fundamentally flawed. Our new approach requires solving an equation for the depth-integrated eddy energy. This is a significant challenge and will form a major component of the present project. However, we believe that solving for the eddy energy is tractable as we have some understanding of the key physical ingredients. These key ingredients include the source of eddy energy through instability of the large-scale flow, westward propagation of eddies, diffusion of eddy energy, dissipation of eddy energy in western boundary "eddy graveyards", and dissipation of eddy energy through bottom drag and lee wave generation. Once a consistent eddy energy budget is incorporated, our new eddy parameterisation leads to three highly desirable results, which serve as important proofs of concept: 1. It reproduces the correct dimensional growth rate for eddies in a simple model of instability of atmospheric and oceanic flows for which there is an exact mathematical solution. 2. Assuming perfect knowledge of the eddy energy, it reproduces the eddy diffusivity diagnosed from high-resolution computer simulations of fully turbulent instabilities. 3. It predicts and explains the physics of "eddy saturation", the remarkable insensitivity of the size of the Antarctic Circumpolar Current to surface wind forcing, and a long standing challenge and known deficiency of current eddy parameterisations. The work plan will consist of four inter-related work packages: 1. Implementation and validation of the new eddy parameterisation framework in the NEMO ocean model, used by NERC and the UK Met Office, along with other European partners. 2. Development and refinement of the parameterised eddy energy budget. 3. Quantifying the impact of the new parameterisation on the oceanic uptake of heat and passive tracers in the UK Earth System Model, used for the UK contribution to the Intergovernmental Panel for Climate Change (IPCC) climate projections. 4. Project management, to ensure that the work is delivered fully and in a timely manner.