%0 Journal Article %1 bailie2024bifurcation %A Bailie, John %A Krauskopf, Bernd %D 2024 %J Physica D: Nonlinear Phenomena %K moc-box %P 134077 %R https://doi.org/10.1016/j.physd.2024.134077 %T Bifurcation analysis of a conceptual model for vertical mixing in the North Atlantic %U https://www.sciencedirect.com/science/article/pii/S0167278924000289 %V 460 %X The Atlantic Meridional Overturning Circulation (AMOC) distributes heat and salt into the Northern Hemisphere via a warm surface current towards the subpolar North Atlantic, where water sinks and returns southwards as a deep cold current. There is substantial evidence that the AMOC has slowed down over the last century. We introduce a conceptual box model for the evolution of salinity and temperature on the surface of the North Atlantic Ocean, subject to the influx of meltwater from the Greenland ice sheets. Our model, which extends a model due to Welander, parameterises the mixing interaction between a surface box and a deep-water box of constant temperature and salinity, which may be convective or non-convective, depending on the density difference between the boxes. Its two main parameters are the virtual salinity flux μ and the density threshold η, above which the top box becomes sufficiently dense for convective mixing to occur. We use tools from bifurcation theory to analyse two cases of the model: the limiting case of instantaneous switching between convective or non-convective mixing, where the system is piecewise-smooth (PWS), and the full smooth model with more gradual switching. For the PWS model we perform a complete bifurcation analysis by deriving analytical expressions for all bifurcations. The resulting bifurcation diagram in the (μ,η)-plane identifies all regions of possible dynamics, which we show as phase portraits — both at typical parameter points, as well as at the different transitions between them. We also present the bifurcation diagram for the case of smooth switching and show how it arises from that of the PWS case. In this way, we determine exactly where one finds bistability and self-sustained oscillations in both versions of the model. In particular, our results show that oscillations between temperature and salinity on the surface of the North Atlantic Ocean disappear completely when the transition between the convective and non-convective mixing regimes is too slow.

@article{bailie2024bifurcation, abstract = {The Atlantic Meridional Overturning Circulation (AMOC) distributes heat and salt into the Northern Hemisphere via a warm surface current towards the subpolar North Atlantic, where water sinks and returns southwards as a deep cold current. There is substantial evidence that the AMOC has slowed down over the last century. We introduce a conceptual box model for the evolution of salinity and temperature on the surface of the North Atlantic Ocean, subject to the influx of meltwater from the Greenland ice sheets. Our model, which extends a model due to Welander, parameterises the mixing interaction between a surface box and a deep-water box of constant temperature and salinity, which may be convective or non-convective, depending on the density difference between the boxes. Its two main parameters are the virtual salinity flux μ and the density threshold η, above which the top box becomes sufficiently dense for convective mixing to occur. We use tools from bifurcation theory to analyse two cases of the model: the limiting case of instantaneous switching between convective or non-convective mixing, where the system is piecewise-smooth (PWS), and the full smooth model with more gradual switching. For the PWS model we perform a complete bifurcation analysis by deriving analytical expressions for all bifurcations. The resulting bifurcation diagram in the (μ,η)-plane identifies all regions of possible dynamics, which we show as phase portraits — both at typical parameter points, as well as at the different transitions between them. We also present the bifurcation diagram for the case of smooth switching and show how it arises from that of the PWS case. In this way, we determine exactly where one finds bistability and self-sustained oscillations in both versions of the model. In particular, our results show that oscillations between temperature and salinity on the surface of the North Atlantic Ocean disappear completely when the transition between the convective and non-convective mixing regimes is too slow.}, added-at = {2024-02-07T11:30:03.000+0100}, author = {Bailie, John and Krauskopf, Bernd}, biburl = {https://www.bibsonomy.org/bibtex/24e57d50f6a76fc6cf1f74296d82e9ea0/laura.jackson}, description = {Bifurcation analysis of a conceptual model for vertical mixing in the North Atlantic - ScienceDirect}, doi = {https://doi.org/10.1016/j.physd.2024.134077}, interhash = {e5dc14193054cd7221dba97339f0f1b9}, intrahash = {4e57d50f6a76fc6cf1f74296d82e9ea0}, issn = {0167-2789}, journal = {Physica D: Nonlinear Phenomena}, keywords = {moc-box}, pages = 134077, timestamp = {2024-02-07T11:30:03.000+0100}, title = {Bifurcation analysis of a conceptual model for vertical mixing in the North Atlantic}, url = {https://www.sciencedirect.com/science/article/pii/S0167278924000289}, volume = 460, year = 2024 }