Double-diffusive depletion of layers in hydrothermal systems

In hydrothermal systems, the circulation of water through the porous matrix is strongly influenced by the joint effects of heat and salinity. Because of phase separation, layers of different salinities and temperature are thought to form, but their stability or their typical lifetime remains unclear. Moreover, the dynamics of heat transport across such a layered system is considerably enriched by double diffusive effects due to the slower diffusion of salinity relative to heat. Here, we study numerically the time evolution of an ideal two-layer configuration where a heavy layer of warm and salty water is overlain by a light layer of cold and fresh water. Thermal convection quickly develops in each layer and maintains a thin diffusive interface between the layers. There is long-standing controversy on the temporal evolution of such a system. Although Griffiths (1981) found experimentally that the sharp interface seemed to persist indefinitely, Schoofs & Hansen (2000) reported via numerical simulations systematic depletion and vanishing of the layers. We resolve this apparently inconsistency. In our simulations, we find systematic depletion of the two-layer initial condition in all cases. However, the timescale over which it occurs depends strongly on the ratio between salinity and temperature contributions to density. When salinity is weakly stabilising, thermal convection and layers are maintained over (very long) diffusive timescales. When salt is strongly stabilising, however, convection becomes quiescent over much shorter times and the sharp interface between layers is quickly diffused away. We determine scalings on the lifetime of the layers in both regimes as a function of the governing parameters.