The Formation of Double‐Diffusive Layers in a Weakly Turbulent Environment

Abstract

Double‐diffusive stratification in the ocean is characterized by staircase structures consisting of mixed layers separated by high‐gradient interfaces in temperature and salinity. These double‐diffusive layers, which flux heat vertically, are observed over a vast region of the Arctic Ocean at the top boundary of the relatively warm and salty Atlantic water layer. In one formalism for the origin of double‐diffusive layers, staircase formation arises when a heat source is applied at the base of water that is stably stratified in salinity. This framework is extended to consider the effect of intermittent shear‐driven turbulence on diffusive‐convective staircase formation. One‐dimensional numerical model results indicate that there is a critical level of intermittent turbulence above which a staircase cannot form. This is framed in terms of a critical diffusivity ratio (ratio of effective salinity diffusivity to effective thermal diffusivity) that cannot be exceeded for a staircase to persist. This critical ratio is not a universal constant but rather differs for each staircase. Model results further indicate that layer thicknesses decrease with height in a staircase, with the variation in thickness over a staircase being more pronounced in the presence of intermittent turbulence. Finally, results suggest that increased diffusivity ratios lead to decreased heat fluxes across interfaces; if a staircase is subject to intermittent turbulence levels (below the critical level), vertical heat fluxes will be smaller than in the absence of shear‐driven turbulence. Findings are related to double‐diffusive staircases, and associated heat fluxes, in the weakly turbulent Arctic Ocean.

Introduction to Special Collection on Arctic Ocean Modeling and Observational Synthesis (FAMOS) 2: Beaufort Gyre Phenomenon

“…Partitioning of kinetic energy into barotropic and baroclinic modes suggests that the halocline structure plays a specific role in limiting the capacity for frictional dissipation at the sea floor. Double-diffusive mixing and layers in the Beaufort Gyre region are studied by Bebieva and Timmermans (2019) and by Shibley and Timmermans (2019). These papers shed light on the origins of various layer types associated with heat and salt transport, as well as the role of turbulence in limiting double-diffusive heat fluxes.…”

“…Doddridge et al, ; Manucharyan & Isachsen, ; Proshutinsky, Krishfield, Toole, et al, ; Regan et al, ); identify the major sources of fresh water and the fresh water pathways from the sources to the Beaufort Gyre region (Kelly, Proshutinsky, Popova et al, ); explain the major patterns and regimes of the surface, Pacific, and Atlantic water layer circulation (e.g. Hu & Myers, ; Spall et al, ; Zhong et al, ); and reveal the physics of mechanical mixing and convection under the influence of wind, internal wave, and tidal forcing (e.g., Bebieva & Timmermans, ; Chanona et al, ; Shibley & Timmermans, ; Zhao et al, ). Other papers in the collection examine the role of sea ice conditions, major features of ice variability, and methods of sea ice prediction in the region (e.g.…”

The Regulation of Sea Ice Thickness by Double‐Diffusive Processes in the Ross Gyre

“…(2) after a staircase is formed, the internal wave field at the depths of a staircase attenuates and therefore background internal-wave-driven turbulent levels are suppressed; (3) reduced upward heat fluxes through a staircase into the surface mixed layer (as compared to the purely turbulent heat fluxes, see, e.g., Shibley & Timmermans, 2019) allow sea ice formation that in turn acts as a buffer limiting further wind energy input into the ocean and reducing internal wave activity in the permanent pycnocline (e.g., Rainville & Woodgate, 2009;Venables & Meredith, 2014). According to our observations and the hypothesis outlined here, the presence of a double-diffusive staircase allows higher rates of sea ice formation in the central Ross Gyre.…”

“…Typical staircase layer thickness varies from 3 to 7 m with temperature and salinity jumps across an interface of ∼0.3 °C and 0.05, respectively. Lateral coherence of the staircase mixed layers is not observed, which might be associated with splitting and merging caused by intermittent turbulent mixing (Shibley & Timmermans, ). In the austral fall (the MRV profiles from March to May are not shown here), a staircase structure alternates in depth with smoother portions of the profile.…”

Analysis of Acoustic Observations of Double‐Diffusive Finestructure in the Arctic Ocean

“…Observations from microstructure profilers or Ice‐Tethered Profilers (ITPs, Krishfield et al., 2008) and theory suggest that staircases may not form above a critical level of turbulence (Guthrie et al., 2017; Rippeth et al., 2015; Shibley & Timmermans, 2019), although the exact nature of staircase persistence is not well understood. While the staircase finestructure may be resolved by microstructure measurements, microstructure surveys consist of individual water column profiles spaced by hours and kilometers and cannot capture staircase variability on shorter scales (Fer et al., 2010; Lenn et al., 2011).…”