Transitions and oscillations in a thermohaline deep ocean circulation model

ABSTRACTTheoretical ocean convection is a numerically calculated model of the ocean with salt water in a two-dimensional container. The boundary conditions along the top are linearly changing temperature T and flux of salinity S increasing from the model’s pole to equator. The sides and bottom are insulated and impermeable. Diffusivities of T and S are equal so double diffusion is eliminated. Therefore, the focus is upon the consequences of mixed Dirichlet/Neumann conditions upon two-dimensional T/S convection in this deep ocean overturning circulation configuration. Results are calculated over wide ranges of Rayleigh number Ra (0–2 × 106), salinity flux Rayleigh number Raf (0–3 × 106), container length (2–32), and Prandtl number Pr (1–128 and ∞). Two different equations of state are considered: one has constant properties everywhere including constant thermal and salinity density coefficients (the Boussinesq approximation), and the second uses the seawater equation of state in an oceanic T–S range. Resul...