Nonlinear Equilibration and Turbulent Cascades in Laboratory Studies of Baroclinic Turbulence

Lead Research Organisation: University of Oxford
Department Name: Oxford Physics


Complex interactions between turbulent convection and stably-stratified flows in the presence of background rotation are important for a wide range of problems in various engineering contexts, in atmospheric and oceanic science, and in stellar and planetary astrophysics. This project will investigate the nature of flows between a heat source and a heat sink that are displaced both vertically and horizontally relative to each other, in the presence of strong background rotation.

In the absence of background rotation, if a heat source is located at a lower altitude than the sink, one would generally expect a strongly convective circulation to result, carrying heat directly and vigorously from the source to the sink. With background rotation, however, evidence from experiments, simulations and in geophysical flows suggest that the resulting circulation may spontaneously partition itself into a convectively unstable/neutral region (where temperature becomes well mixed and doesn't vary much with height) that interacts with a statically stable, so-called baroclinic region (where temperature increases with height and develops a thermal gradient from one side to the other). Wave-like instabilities may develop within this baroclinic zone that may play a crucial role in stabilising the vertical stratification and dominating the transfer of heat and momentum where they occur. Moreover, there is evidence to suggest that if the transport of heat by the instability acts more rapidly than other heat exchange processes, this stabilizing effect may act within a nonlinear feedback loop, somewhat like a thermostat, adjusting the flow back towards a weakly nonlinear/unstable 'critical' state - sometimes referred to as 'self-organized criticality'. Such strongly nonlinear and convective motions are difficult to model accurately, however, so the mechanisms involved, though probably ubiquitous in certain engineering systems and in nature, are not well understood.

We therefore propose to set up an experimental configuration which entails heating a body of fluid in a cylindrical container on a rotating platform along an annular ring at the bottom of the tank close to the outer radius, and cooling it through a circular disk near the centre of the tank at the upper surface. Preliminary numerical simulations and experiments (carried out in my group and with proposed collaborators in the USA and Spain) already suggest that such flows will readily form a statically stable (though baroclinically unstable) zone between convectively unstable regions over/underlying the heated or cooled boundaries. We therefore plan to measure the characteristics of the resulting flows through combinations of in situ thermal sensors and particle image velocimetry (PIV) techniques, including the innovative possibility of using thermochromic liquid crystal particles to determine velocities and temperatures simultaneously within the flow. This will facilitate the determination of flow structures, heat and momentum transports within the flow, and to characterize the development of any kinetic energy cascades that may emerge as more turbulent regimes are explored. The idealised nature of these experiments should ensure that the results obtained will be applicable to a wide variety of problems in various disciplines.

Such a configuration may be seen as an idealisation of a variety of industrial processes (e.g. in rotating semiconductor crystal growth melts, process mixing techniques in chemical engineering, convective flows in turbomachinery etc.), and of a number of geophysical and astrophysical problems in which stably and unstably stratified flows interact in the presence of background rotation. These include the Earth's atmosphere and climate system and its response to variations in its radiative heating and cooling, other planetary atmospheres (notably Mars, Venus and the gas giant planets), and in stellar interiors (e.g. the tachocline region within the Sun).

Planned Impact

Non-academic beneficiaries from the proposed research will include:

- Industrial design engineers in the process engineering industries, turbomachinery and aerospace industries, and in the plasma-confinement fusion power industry. This project will provide new underpinning insights and quantitative constraints to guide engineering design and optimization, and validated enhancements in numerical modelling techniques, for flow systems dominated by convection and rotation. The onset of baroclinic and/or convective instabilities, and the development of complex turbulent flows, can have either adverse or beneficial effects on processes involving heat transfer or chemical mixing and transport, the prediction of which may be crucial to achieving competitive design performance of a variety of devices. It is important that the role of nonlinear self-organized criticality of such instabilities, in determining the way in which instabilities develop and equilibrate, is taken fully into account in designing new devices for greater efficiency or improved control (by suppressing unwanted instabilities), and in evaluating their performance. This project will provide some well controlled case studies in an idealized system, against which modelling techniques can be validated and tested.
- Public sector researchers in government research organizations (notably the UK Met Office and the European Centre for Medium Range Weather Forecasts) and other organizations engaged in making projections of natural and anthropogenically-induced climate change. Benefits are expected to be (a) technological, in leading to quantitative improvements and validated tests of modelling techniques under conditions exhibiting similar complex nonlinear dynamical feedbacks to those encountered in the full Earth climate system, and (b) in relation to influencing public policy decisions both within the UK and beyond in enhancing the credibility of climate model projections as the evidence base for guiding such decisions e.g. in relation to likely effectiveness of mitigation actions, implementation of geoengineering strategies or adaptation to predicted changes.
- Researchers in commercial organizations associated with the energy and insurance industries that make use of projections from climate models for strategic decision-making in relation to the future prosperity of their industries. The future reliability of such decisions will benefit from improved performance of climate prediction models.
- The results of these experiments are likely also to be of interest to the wider general public, in the approach to emulating complex systems in conceptually simple experimental systems, and for the insights offered into some of the complexities of climate science.


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Description A major new experimental facility has been constructed, commissioned and tested. This consists of a large cylindrical tank which is mounted on a rotating table, heated from below and cooled from above over sections of the upper and lower boundaries, in a configuration that emulates the distribution of heating and cooling in a planetary atmosphere such as the Earth's. This has been used to investigate how free convection interacts with baroclinic instability - a fluid process that transfers heat both horizontally and vertically by developing cyclone and anticyclone eddies resembling the large-scale weather systems that dominate the weather at temperate latitudes on Earth. A number of experiments have been completed, showing how the flow produces turbulent convection over the heated region near the outer cylindrical boundary (representing the tropics) while large-scale cyclone/anticyclone waves carry heat towards the cooled plate near the centre of the tank (representing the polar regions). The measurements show how cyclone/anticyclone eddies affect the vertical temperature structure of the large-scale flow at moderate rotation rates to maintain it close to a state of marginal stability. This is believed to emulate to some extent how similar eddies in the Earth's atmosphere control the structure of the atmosphere and hence sustain a locally stable climate, despite changes in radiative forcing. The experiments also allow us to study the properties of turbulence in the presence of density stratification and background rotation in unprecedented detail. Several different types of turbulent regime have been identified and their analysis is continuing. This is fundamental to our understanding of a wide range of problems in nature and in engineering technology.
Exploitation Route Further experiments are being used (in a joint NERC-funded PhD project in collaboration with the Met Office) to evaluate aspects of numerical convection modeling codes, and to test theoretical conjectures concerning mechanisms for the equilibration of convective and baroclinic instabilities. These have a bearing on understanding aspects of the Earth's climate and atmospheric circulation, and in mechanisms of heat transfer relevant to the design of turbo machinery. The latter aspects may be followed up in collaboration with colleagues in university engineering departments and in industry.
Sectors Aerospace, Defence and Marine,Energy,Environment,Transport

Description The experiments we have been carrying out in this project have stimulated some new research with the UK Met Office to adapt their numerical weather forecasting and climate model to be able to accurately simulate complex convective flows that we have measured. This is ongoing work but is expected to lead to new tests of the Met Office model which may eventually feed through to improved weather and climate forecasts for industry, agriculture and public policy.
First Year Of Impact 2016
Sector Agriculture, Food and Drink,Environment,Transport
Impact Types Societal,Policy & public services

Description EUHiT
Amount € 5,000 (EUR)
Funding ID Beta-WTD2 
Organisation European Commission 
Sector Public
Country European Union (EU)
Start 03/2015 
End 05/2015
Description NERC Industrial CASE studentship
Amount £80,000 (GBP)
Organisation Natural Environment Research Council 
Sector Public
Country United Kingdom
Start 10/2015 
End 09/2019
Description Oxford Met-office academic partnership summer intern grant
Amount £2,500 (GBP)
Organisation Meteorological Office UK 
Sector Public
Country United Kingdom
Start 05/2015 
End 07/2015
Description Planetary Science at Oxford Physics 2019
Amount £1,261,196 (GBP)
Funding ID ST/S000461/1 
Organisation Science and Technologies Facilities Council (STFC) 
Sector Academic/University
Country United Kingdom
Start 03/2019 
End 03/2022
Description UK Met Office numerical model development 
Organisation Meteorological Office UK
Country United Kingdom 
Sector Public 
PI Contribution Laboratory measurements of convective flows for comparison with and validation of numerical model simulations.
Collaborator Contribution Provision of access to numerical model codes and technical assistance and advice on adaptation of code to make simulations of our lab experiments. Provision of super-computer resources to carry out simulations. Sponsorship of NERC CASE award for student to work on the model.
Impact Adaptation of Met Office ENDGAME model to simulate flows in cylindrical geometry - work still in progress.
Start Year 2015
Title New 1m diameter rotating annulus experiment with local convective forcing 
Description This new experimental set-up provides a new analogue of the atmosphere circulation and is composed of a rotating annulus convectively forced by local thermal forcing via a heated annular ring at the bottom near the external wall and a cooled circular disk near the centre at the top surface of the annulus. This new configuration is a less thermally constrained variant of the classical thermally-driven annulus where thermal forcing was previously applied uniformly on the sidewalls. In addition, the set-up consists of a much bigger tank. The design and building of the set-up has been carried out from Feb 2014 to January 2016 and the first experimental runs are in working process. 
Type Of Technology Physical Model/Kit 
Year Produced 2016 
Impact Two vertically and horizontally displaced heat sources/sinks are arranged so that, in the absence of background rotation, statically unstable Rayleigh-Bénard convection would be induced above the source and beneath the sink, thereby relaxing strong constraints placed on background temperature gradients in previous experimental configurations to better mimic in fine local vigorous convection events in tropics and polar regions whilst also facilitating baroclinic motion in midlatitude regions in the Earth's atmosphere. This new set-up is also a long-term research facility for the gfd lab. 
Description Public lecture (Oxford) 
Form Of Engagement Activity Participation in an open day or visit at my research institution
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Public/other audiences
Results and Impact An evening talk presented as part of the Oxford Science Ideas Festival (IF) on "Physics from the Lab to your Life". Attended by around 50 people, mostly from the general public and school age people. Led to some stimulating questions and discussion afterwards.
Year(s) Of Engagement Activity 2018
Description Talk to astronomical society (Swindon) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Public/other audiences
Results and Impact A talk on the atmospheres of Jupiter and Saturn, to inform and engage members of the public about recent research. Around 40 people attended a meeting of the Swindon Stargazers, which sparked many questions and discussion afterwards.
Year(s) Of Engagement Activity 2018