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

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 g with the density ratio R r . 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 R cr ' 1:7, the authors arrive at an indirect estimate of the characteristic turbulent diffusivity in the subtropical thermocline.

Minimal model for double diffusion and its application to Kivu, Nyos, and Powell Lake

“…Interestingly, these values are very close to the critical value 1.7 for the staircase to form [Radko et al, 2014b], and consistent with observations in the field (e.g., Lake Nyos).…”

“…The literature reports several cases with up to R q 5 10 [e.g., Newell, 1984], while a lower limit of 1.5-1.7 has been proposed [Taylor, 1988;Kelley et al, 2003;Radko et al, 2014b]. The simplicity of the model and the possibility to run a large number of simulations can be exploited to systematically investigate the limiting cases, referring to real large-scale profiles observed in the field or in laboratory, and to the results of stability analyses [Carpenter et al, 2012b].…”

Applicability and failure of the flux-gradient laws in double-diffusive convection

“…The biharmonic model has been used in the past to surmount numerical difficulties associated with the singularity of the double-diffusive flux-gradient laws as m → ∞ (Radko 2005;Radko et al 2014). However, until now, there has been no guidance with regard to the choice of the aberrancy coefficient µ.…”

Permanent Thermohaline Staircases in the Tyrrhenian Sea

“…A necessary and sufficient condition for staircases formation is 1 < R ρ < 1.7 (Radko et al, 2014a). A necessary and sufficient condition for staircases formation is 1 < R ρ < 1.7 (Radko et al, 2014a).…”