Salt fingering in subsea permafrost: Some stability and energy considerations

Abstract

Salt fingering appears to be a viable mechanism for salt transport in the thawing layer (talik) above ice‐bonded permafrost near the seabed in the Arctic shelves [Baker and Osterkamp, 1988]. These saltwater infusions occur where concentrated brines overlie less concentrated or less dense brines. At least two mechanisms exist which cause this condition near the seabed: first, salts rejected during sea ice growth result in the formation of a concentrated brine layer on the seabed, and second, salts rejected during sediment freezing near the seabed can result in a concentrated brine layer forming within the deeper and yet unfrozen sediments. Unstable salt fingering in a vertical tube containing a porous media is known to develop whenever the density gradient exceeds the critical value: ∂ρ/∂z = 3.390 μk/gkb2 [Wooding, 1959]. This article presents a simple derivation and interpretation of this critical condition in terms of competing time scales. A convective time scale represents the time required for formation of a vertical wedge‐shaped flow due to density differences, and a diffusive time scale represents the time required to diffuse the density difference horizontally across the layer. The critical density gradient is determined from a ratio of these time scales. The stability criterion suggests downward salt fingering whenever the density gradient at Prudhoe Bay exceeds 6.2×10−5 g cm−4 in thawed subsea permafrost sediments. Maximum predicted velocity of the saltwater fingering is about 2 m d−1, and this is consistent with the direction and magnitude indicated by measurements of pressure gradients and numerical modeling in the thawing permafrost. The energy dissipated by viscous forces in the thawed layer balances the potential energy added by the salt fingers caused by concentrated brines on the seabed.