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UBC Theses and Dissertations

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UBC Theses and Dissertations

Non-smooth dynamics in the Stommel model of the thermohaline current Griffith, Cody

Abstract

We analyzed the non-smooth dynamics for the Stommel model for thermohaline circulation with additional mechanisms like slowly varying bifurcation parameters and high frequency oscillatory forcing. Our goal was to find an analytic approximation to the tipping point and forced bifurcation induced by the new features in the model. We first analyze a simpler one component model that has similar structure to the Stommel model and gradually build in more complexity into the one component problem and study the effects on the tipping point.In this context, we compare the relative strengths of the non-smooth effects on the tipping point to the smooth effects which has been previously studied. With the one component model understood, we then apply similar methods to the Stommel model and study thee ffects on the non-smooth tipping points and forced bifurcations. With these results we have the ability to fully describe the hysteresis found in the Stommel model.

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Attribution-NonCommercial-NoDerivatives 4.0 International