Exact Solutions and Stability Analysis of a Nonlinear Model of Open-Ocean Deep Convection that Allows Multiple Steady States
AbstractWe present analytical solutions of the two-basin model of open-ocean deep convection. Originally suggested by Whitehead [Whitehead, J.A. (2000), Stratiﬁed convection with multiple states, Ocean Modelling, 2(3-4), 109121], the model allows regimes with multiple steady states (multiple equilibria). We provide the full analytical description of the steady states for the particular case of constant surface heat ﬂux from the ocean to the atmosphere, and explore analytically stability of the equilibria within the Lyapunov theory. The results show that, for this particular case, the steady state is unique and stable for all dynamic ﬂow regimes. We also present analytical expressions for dependence of critical values of sea-surface heat ﬂux,at which transitions between the dynamic regimes occur,on the model parameters.