Transitions and oscillations in a thermohaline deep ocean circulation model

ABSTRACT

Theoretical 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 $\mathrm{\infty }).$ 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. Results at fixed Ra are presented for numerous values of Raf until either a steady flow or a time-dependent cyclic flow sets in. For Boussinesq flow with Pr < 10, and for seawater flow up to at least Pr = 128, flow oscillates in some parameter ranges. The oscillation of convection cells occurs during a salinity dominated mode with equatorial sinking. This oscillation differs from oscillations of the temperature dominated mode in some climate models and it also differs from oscillations in laboratory experiments for T/S driven convection. In other parameter ranges, flows become steady and hysteresis and multiple states exist for the two modes.

KEYWORDS:

• Thermohaline
• multiple states
• hysteresis
• oscillations
• deep ocean circulation

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Correction

Acknowledgements

I thank Olivier Marcal for helpful discussion and useful suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.