Greenhouse Gases: Emission, Convection and Tipping Points

It is well known that any predictions for the states of the climate system are based on the calculation of the greenhouse gases level, which is appropriate for the future sustainable development of the biosphere. We extend the radiative-convective atmospheric model , taking into account effects connected with greenhouse gas production, chemical degradation of the greenhouse gas molecules, and greenhouse gas diffusion and convection. An original model is similar to Rayleigh–Bénard convection except that thermal radiative transfer is included, thereby altering the basic state temperature profile and introducing radiative damping. Our extended model also describes a greenhouse gas influence on thermal radiative transfer. Although the model proposed is a mathematical idealization, it can be useful as a first approximation, and this model is close to classical models for Rayleigh-Bénard convection, where many linear and nonlinear stability results have been established. Indeed, we show that this model has a large spectrum of bifurcations, including new ones generated by radiation effects and greenhouse gas emissions. Under some natural assumptions, it is possible to obtain a relation for the critical emission level leading to the critical threshold in the climate system. Thus, our analytical approach makes the problem of a greenhouse gases- climate catastrophe more tractable and allows us to describe catastrophic instability in the atmosphere induced by soil greenhouse gas sources.

We also study the dynamics of a system defined by the Navier-Stokes equations for a non-compressible fluid with Marangoni boundary conditions in the two-dimensional case. We found that more complicated bifurcations can appear in this system for a certain nonlinear temperature profile as compared to bifurcations in the classical systems with simple linear vertical temperature profiles. We analytically show that the Marangoni effect can induce an interfacial turbulence through an interaction of slow modes which determine the dynamics and the spatial inhomogeneities in the system.

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The Benard convection cells, which are formed by temperature gradients and the Marangoni patterns are driven by surface tension gradients. Credit: I Sudakow.