Nonlinear Equilibration and Turbulent Cascades in Laboratory Studies of Baroclinic Turbulence

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).

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.