A model for fastest-growing fingers is developed in which the fingers have finite length and lengthen in time. A finger Richardson number constraint is used to limit the length and fluxes of the fingers. This constraint is equivalent to the collective instability criterion. It is able to reproduce the traditional ΔS4/3 flux law and the laboratory-measured dependence on density ratio, but only if the interface is thin enough (∼30 cm) that individual fingers extend through it. For the 2–5 m thick interfaces that seem to be typical of ocean thermohaline staircases, the model's fluxes depend on interface thickness (unlike the ΔS4/3 flux law) and are over an order of magnitude smaller than ΔS4/3 flux law predictions. This may explain why dissipation rates measured in the thermohaline staircase east of Barbados are thirty times smaller (∼3 × 10−10 W/kg) than ΔS4/3 law predictions (∼80 × 10−10 W/kg).
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