Basin bifurcations, oscillatory instability and rate-induced thresholds for AMOC in a global oceanic box model

The Atlantic Meridional Overturning Circulation (AMOC) transports substantial amounts of heat into the North Atlantic sector, and hence is of very high importance in regional climate projections. The AMOC has been observed to show multi-stability across a range of models of different complexity. The simplest models find a bifurcation associated with the AMOC `on' state losing stability that is a saddle node. Here we study a physically derived global oceanic model of Wood {\em et al} with five boxes, that is calibrated to runs of the FAMOUS coupled atmosphere-ocean general circulation model. We find the loss of stability of the `on' state is due to a subcritical Hopf for parameters from both pre-industrial and doubled CO${}_2$ atmospheres. This loss of stability via subcritical Hopf bifurcation has important consequences for the behaviour of the basin of attraction close to bifurcation. We consider various time-dependent profiles of freshwater forcing to the system, and find that rate-induced thresholds for tipping can appear, even for perturbations that do not cross the bifurcation. Understanding how such state transitions occur is important in determining allowable safe climate change mitigation pathways to avoid collapse of the AMOC.Comment: 18 figure

Evolutionary robotics and neuroscience

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Feedback control of three-dimensional bluff body wakes for efficient drag reduction

The wakes of bluff bodies, such as automotive vehicles, exhibit complex behaviour due to three-dimensionality and high Reynolds numbers, and are furthermore responsible for significant aerodynamic drag. There are significant environmental and economic incentives for reducing drag, however practicalities limit the extent to which this can be achieved through changes to the vehicle shape. This motivates the use of active feedback control methods that modify the flow directly, without significant geometric changes. In this thesis we develop feedback control strategies for two generic three-dimensional bluff bodies, a bullet-shaped body and the widely used Ahmed body. After first applying an extremum-seeking controller to a pre-existing open-loop strategy, we then examine the control of specific coherent structures within the wakes. Two such structures understood to be related to the drag are the static symmetry breaking (SB) mode and the quasi-oscillatory vortex shedding. The former of these is observed as a large-scale asymmetry within the recirculating region. We find, through simultaneous surface pressure and wake velocity measurements, that both the SB mode and vortex shedding may be observed in real-time using practical pressure sensors. Through the use of forcing flaps, we further demonstrate that we are able to strongly interact with both these coherent structures. Statically deflected flaps also prove effective at drag reduction under cross-wind conditions. In order to guide feedback controller design, we develop stochastic models for each of the coherent structures, describing their dynamics and response to forcing. Controllers are then implemented, achieving an efficient drag reduction of 2% when suppressing the asymmetry of the SB mode. Vortex shedding control proved ineffective at drag reduction, despite the suppression of measured fluctuations around the frequency at which oscillations are observed.Open Acces