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Double-Diffusive Recipes. Part I: Large-Scale Dynamics of Thermohaline Staircases

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  • 1 Department of Oceanography, Naval Postgraduate School, Monterey, California
  • | 2 Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts
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Abstract

Three-dimensional dynamics of thermohaline staircases are investigated using a series of basin-scale staircase-resolving numerical simulations. The computational domain and forcing fields are chosen to reflect the size and structure of the North Atlantic subtropical thermocline. Salt-finger transport is parameterized using the flux-gradient formulation based on a suite of recent direct numerical simulations. Analysis of the spontaneous generation of thermohaline staircases suggests that thermohaline layering is a product of the gamma instability, associated with the variation of the flux ratio with the density ratio . After their formation, numerical staircases undergo a series of merging events, which systematically increase the size of layers. Ultimately, the system evolves into a steady equilibrium state with pronounced layers 20–50 m thick. The size of the region occupied by thermohaline staircases is controlled by the competition between turbulent mixing and double diffusion. Assuming, in accordance with observations, that staircases form when the density ratio is less than the critical value of , the authors arrive at an indirect estimate of the characteristic turbulent diffusivity in the subtropical thermocline.

Corresponding author address: T. Radko, Department of Oceanography, Naval Postgraduate School, 833 Dyer Road, Bldg. 232, Room 328, Monterey, CA 93943. E-mail: tradko@nps.edu

Abstract

Three-dimensional dynamics of thermohaline staircases are investigated using a series of basin-scale staircase-resolving numerical simulations. The computational domain and forcing fields are chosen to reflect the size and structure of the North Atlantic subtropical thermocline. Salt-finger transport is parameterized using the flux-gradient formulation based on a suite of recent direct numerical simulations. Analysis of the spontaneous generation of thermohaline staircases suggests that thermohaline layering is a product of the gamma instability, associated with the variation of the flux ratio with the density ratio . After their formation, numerical staircases undergo a series of merging events, which systematically increase the size of layers. Ultimately, the system evolves into a steady equilibrium state with pronounced layers 20–50 m thick. The size of the region occupied by thermohaline staircases is controlled by the competition between turbulent mixing and double diffusion. Assuming, in accordance with observations, that staircases form when the density ratio is less than the critical value of , the authors arrive at an indirect estimate of the characteristic turbulent diffusivity in the subtropical thermocline.

Corresponding author address: T. Radko, Department of Oceanography, Naval Postgraduate School, 833 Dyer Road, Bldg. 232, Room 328, Monterey, CA 93943. E-mail: tradko@nps.edu
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