Instabilities of geophysical flows
The dynamics of geophysical flows are characterised by various fascinating instability mechanisms responsible for the limited predictability of such systems. Instabilities are usually associated to exchanges of energy across scales.
We approach the problem of bringing together the mathematical and physical characterisation of such phenomena using the formalism of covariant Lyapunov vectors (CLVs), which allow for associating physical modes to well-defined rates of exponential growth (and decay) of perturbations. CLVs have proved useful for studying the baroclinic instability of quasi-geostrophic flows and in providing a new characterisations of blocking events.
Response to perturbations
It is possible to roughly divide the response of geophysical systems (and not only) to perturbations into three broad classes:
- smooth behaviour, as described by the Ruelle response theory
- rough dependence of the system on small changes of its parameters, taking place near critical transitions and related to the existence of the Ruelle-Pollicott resonances
- critical transitions associated to qualitative changes in the properties of the system.
We explore the interplay of these scenarios in order to be able to study the properties of the climate systems across a wide range of parametric modulations, including anthropogenic climate change and tipping points.
Parameterisation of unresolved processes
Geophysical flows feature variability over such a large range of scales that any reasonable approach based on numerical simulation requires dealing with the problem of coarse graining.
Given the nature of such systems, simplifying hypothesis as time scale separation are not fully convincing and more sophisticated approach are needed in order to construct parameterisations of unresolved processes. Such parameterisations unavoidably include stochastic and non-Markovian components.