Author: David

DPhil (PhD) studentship available to start January 2019

We have a fully-funded DPhil (PhD) studentship available to work on the stability of stratified equatorial ocean jets, a Industrial CASE project joint between , and . You can apply to be based either in Mathematics or in Physics, depending on your preference. Applications to both departments will be considered equally.

Project details:

The instability of zonal flows to small disturbances underpins our understanding of the scales of motion and their predictability in planetary atmospheres and oceans. Numerous papers have explored aspects of this problem since pioneering work in the late 1940s. The quasi-geostrophic formulation is only valid for small Rossby numbers and large Richardson numbers and requires the stratification of the basic state to be independent of latitude. Formulations with more general validity have until recently been restricted to laterally uniform flows neglecting the Earth’s curvature.

Recently, Bell (2018) has described a simple but novel method for studying stability of any zonal flow that is in thermal wind balance: the linearised primitive equations are reduced to a partial differential equation involving only a single variable, the pressure perturbation; the equation is linear in the pressure perturbation, but nonlinear in the complex phase speed which sets the growth rate of the instability. The method can be used to study the stability of jets on a sphere in which the stratification of the basic state varies with height and latitude, the motions can be non-hydrostatic and the fluid can be compressible. Instabilities associated with different types of critical layers and symmetric and Kelvin Helmholz instabilities can be studied. Integral constraints on the instabilities can also be derived.

We will investigate the instability of stratified zonal jets near the equator where the Rossby number is large and the Earth’s curvature of fundamental importance. These flows exhibit a number of instabilities that lead, for example, to the formation of tropical instability waves, the heat transport by which is of fundamental importance in setting ocean structure and heat uptake with widespread impact on tropical climate. Understanding the stability properties of these equatorial flows is therefore crucial for understanding the response of tropical climate to anthropogenic forcing.

The dependence of growth rates on the profile of the mean state will be investigated in a hierarchy of progressively more complex zonal flows. The heat and momentum transports by the unstable waves will be calculated and compared with those of tropical instability waves in NEMO ocean model simulations. Three classes of instabilities within the near-surface ocean mixed layer will be studied: symmetric, baroclinic and Langmuir instabilities. The student will diagnose the instabilities in ocean circulation models, explore numerical solutions for a hierarchy of zonal flows, consider theoretical aspects such as integral constraints on the instabilities and neutral modes which mark stability transitions, and calculate the non-linear or weakly nonlinear development of the instabilities. Preliminary investigations of numerical solutions indicate that the growth rates of some instabilities are overestimated unless very fine vertical grid spacing is used: the student will also investigate the vertical resolution that is required for ocean circulation models to avoid misrepresenting the different classes of instabilities.

This project will suit a student with a strong mathematical/physical science background.

Impacts of Atmospheric Reanalysis Uncertainty on Atlantic Overturning

Helen Pillar‘s paper on Impacts of Atmospheric Reanalysis Uncertainty on Atlantic Overturning Estimates at 25°N has been published in the Journal of Climate and is freely available.

In this study, Helen quantifies the impact of uncertainty in surface fluxes of buoyancy and momentum across different reanalysis products on the modelled Atlantic meridional overturning at 25°N between 19940-2011. Uncertainty in overturning induced by prior air–sea flux uncertainty can exceed 4 Sv within 15 years, at times exceeding the amplitude of the ensemble-mean overturning anomaly. A key result is that, on average, uncertainty in the overturning at 25°N is dominated by uncertainty in the zonal wind at lags of up to 6.5 yr and by uncertainty in surface heat fluxes thereafter, with winter heat flux uncertainty over the Labrador Sea appearing to play a critically important role.

How phytoplankton survive in subtropical ocean gyres

MIT News are running a story on former DPhil student, Ed Doddridge‘s paper, published in the Journal of Geophysical Research: Oceans, on The role of ocean eddies in maintaining biological activity in subtropical gyres. Wind-driven downwelling exports nutrients away from the sunlit zone, preventing phytoplankton from thriving. In this paper, we show that eddies, by opposing this wind-driven downwelling, can change how much fluid is exchanged between the sunlit layer and the homogenous layer below, thereby allowing the nutrient concentration at the surface to increase. See MIT News for the full story and JGR Oceans for the published paper.

Characterising the chaotic nature of ocean ventilation

DPhil student Graeme MacGilchrist‘s paper has been accepted for publication in the Journal of Geophysical Research in which we characterise the chaotic nature of ocean ventilation pathways through a filamentation number. The filamentation number quantifies the extent to which fluid parcels are stretched and folded over, analogous to layers of puff pasty being rolled out and folded by a baker. We find that the filamentation number if large everywhere in the North Atlantic and increases with depth, implying highly chaotic ventilation pathways.

The publication link will be posted once available but in the meantime please email [email protected] for a preprint.

“GEOMETRIC” project funded by NERC!

We’ve received the exciting news from NERC that our proposal “GEOMETRIC: Geometry and Energetics of Ocean Mesoscale Eddies and Their Representation in Climate models” received the highest possible grade and will be funded!

This project will involve implementing, validating and quantifying the impact of our new geometric parameterisation of ocean mesoscale eddies in the NEMO ocean model. We will be working with a number of co-investigators and project partners across the UK including James Maddison (Edinburgh), Xiaoming Zhai (UEA), George Nurser (NOC, Southampton) and Gurvan Madec (UPMC, Paris).


emergent eddy saturation

Emergent eddy saturation with parameterised eddies

A paper led by Julian Mak has just appeared in Ocean Modelling demonstrating that eddy saturation – insensitivity of the volume transport of a circumpolar current to surface wind stress – is an emergent property of our new geometric eddy parameterisation. In effect, we modify the widely-used Gent-McWilliams eddy parameterisation by solving a parameterised eddy energy budget and rescaling the eddy transfer coefficient to match the formderived in Marshall et al. (2012). This is for the same physical reasons as described in our recent paper in Geophysical Research Letters. We are currently working towards implementing this geometric eddy parameterisation in an Ocean General Circulation Model.

emergent eddy saturation

A theory of eddy saturation

Our paper presenting a simple model of eddy saturation – the surprising insensitivity of the strength of the Antarctic Circumpolar Current to surface wind forcing – has been published in Geophysical Research Letters and highlighted as a Research Spotlight in EOS.

The model invokes three ingredients: a momentum budget, an eddy energy budget, and a relation between the “eddy form stress” and eddy energy that we have identified in previous work. The model also predicts that circumpolar transport increases with increased bottom friction, a counterintuitive result that is confirmed in eddy-permitting calculations. These results suggest an unexpected and important impact of eddy energy dissipation, through bottom drag or lee wave generation, on ocean stratification, ocean heat content, and potentially atmospheric CO2.

Validation of geometric eddy diffusivity

Much of our recent work has been building on a geometric framework for parameterising eddy fluxes that we first published in 2012 and 2013. A consequence of this framework is that if the eddy energy and stratification are known, then the eddy diffusivity is determined uniquely aside from a non-dimensional scaling factor that is no greater than 1.

A paper led by Scott Bachman has just appeared in Ocean Modelling in which we use a high-resolution numerical model to diagnose the eddy diffusivity in an unstable front and compare it to several theoretical predictions. Not only does the geometric eddy diffusivity fare better than the competition, but it out-performs our wildest expectations. This is a particularly exciting result as it may allow us to improve the parameterisation of unresolved eddies in the ocean models used for climate prediction.