Interface Migration in Thermohaline Staircases

Dan Kelley Woods Hole Oceanographic Institution, Woods Hole, MA 02543

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Abstract

A theory for the vertical migration speed (e) of interfaces within thermohaline staircases is developed and illustrated with several oceanic examples. It expresses e in terms of layer-to-layer variations in the vertical buoyancy flux (J). We discuss three mechanisms which can induce migration: 1) the nonlinearity of the equation of state; 2) layer-merging (the coalescence of adjacent layers); and 3) interface-splitting (the creation of new layers at the interfaces between existing layers), The theory predicts that migration will be much slower for nonlinearity than for layer-merging and inteface-splitting, because layer-merging and interface-splitting should lead to large O(1) variations in J, while nonlinearity leads to much smaller O(10−2) variations. Even so, the net effect of migration associated with layer-merging and interface-splitting should be small, since the interfaces will not have time to migrate very far before the staircase readjusts to a new, migration-free, equilibrium state.

The large-scale effects of interface migration are predicted to be small, with migration-induced heat and salt fluxes being less than 20% of the double-diffusive fluxes. The migration itself will be difficult to observe: for example, we calculate e∼10−1 m s−1 for Arctic halocline staircases. This is much too small to explain the apparent migration speed, e∼10−4 m s−1, derived by tracking interfaces in CTD Arctic profiles. Therefore, the apparent migration is probably a sampling artifact associated with advection of staircase anomalies having vertical scales of O(1) m (i.e., the layer thickness) and horizontal scales of O(100) m.

Abstract

A theory for the vertical migration speed (e) of interfaces within thermohaline staircases is developed and illustrated with several oceanic examples. It expresses e in terms of layer-to-layer variations in the vertical buoyancy flux (J). We discuss three mechanisms which can induce migration: 1) the nonlinearity of the equation of state; 2) layer-merging (the coalescence of adjacent layers); and 3) interface-splitting (the creation of new layers at the interfaces between existing layers), The theory predicts that migration will be much slower for nonlinearity than for layer-merging and inteface-splitting, because layer-merging and interface-splitting should lead to large O(1) variations in J, while nonlinearity leads to much smaller O(10−2) variations. Even so, the net effect of migration associated with layer-merging and interface-splitting should be small, since the interfaces will not have time to migrate very far before the staircase readjusts to a new, migration-free, equilibrium state.

The large-scale effects of interface migration are predicted to be small, with migration-induced heat and salt fluxes being less than 20% of the double-diffusive fluxes. The migration itself will be difficult to observe: for example, we calculate e∼10−1 m s−1 for Arctic halocline staircases. This is much too small to explain the apparent migration speed, e∼10−4 m s−1, derived by tracking interfaces in CTD Arctic profiles. Therefore, the apparent migration is probably a sampling artifact associated with advection of staircase anomalies having vertical scales of O(1) m (i.e., the layer thickness) and horizontal scales of O(100) m.

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