Heat transport through diffusive interfaces

Abstract

[1] We perform a series of 3-D Direct Numerical Simulations (DNS) to assess the vertical heat transport through thermohaline staircases in the Arctic Ocean. The diagnostics of DNS, performed for the first time in the realistic parameter range, result in vertical fluxes exceeding those of extant "four-thirds flux laws" by as much as a factor of 2 and suggest that the 4/3 exponent may require downward revision. Through a series of equivalent 2-D DNS, we show that they are consistent with their more resource-intensive 3-D counterparts for sufficiently large density ratio (R r ) but underestimate heat transport for low R r . Finally, we examine the role of boundary conditions in controlling the vertical heat transport. Rigid boundaries-a necessary ingredient in laboratoryderived flux-laws-are shown to reduce the estimates of heat fluxes relative to the corresponding periodic boundary conditions.

Double‐diffusive interfaces in Lake Kivu reproduced by direct numerical simulations

“…For R ρ < 3, <F H,mol,DNS > strongly depends on the rejection criterion for disturbed interfaces, which can lead to overestimates (as here, by 29%) as well as underestimates (without rejecting, 20%) of <F H,tot,DNS >. We note that Flanagan et al [2013] showed that at R ρ = 2, 2-D simulations result in a factor of 1.5 smaller heat fluxes than the corresponding 3-D simulation. This questions, in general, the validity of the 2-D DNS in accurately capturing fluxes at small R ρ .…”

“…With increasing computation power, direct numerical simulations (DNS) are becoming more attractive to study complex fluid behavior such as double diffusion [Kimura and Smyth, 2007;Simeonov and Stern, 2008;Niino, 2010a, 2010b;Traxler et al, 2011;Carpenter et al, 2012a;Flanagan et al, 2013]. However, DNS are still limited by the size and dimensions of the computational domain at sufficient grid resolution and rely on choices of the boundary conditions that may not be representative of natural staircases.…”

Thermohaline layering in dynamically and diffusively stable shear flows

“…Despite the profound importance of staircases for high-latitude ocean dynamics (Turner, 2010;Flanagan et al, 2013) the physical cause of diffusive layering has not been fully explained (Kelley et al, 2003;Radko, 2013). It is generally accepted that staircases are ultimately produced and maintained by double-diffusive processes.…”

Double-Diffusive Recipes. Part II: Layer-Merging Events

“…While the appearance of well-defined staircases has been firmly linked to double diffusion (e.g., Schmitt 1994), the mechanics of their generation and equilibration are still debated [see the review in Radko (2013)]. Theories proposed to explain the origin of staircases include the collective instability mechanism (Stern 1969), which attributes layering to the interaction between waves and double diffusion, and the suggestion that steps in temperature and salinity profiles represent intrusions evolving into a staircase (Merryfield 2000).…”

“…Comprehensive discussions of both phenomena are offered in Schmitt (1994) and Radko (2013). The salt-finger regime is realized when warm and salty water overlies cold and fresh-conditions that are typical for the subtropical thermocline.…”