The Relationship between Double-Diffusive Intrusions and Staircases in the Arctic Ocean

Abstract

The origin of double-diffusive staircases in the Arctic Ocean is investigated for the particular background setting in which both temperature and salinity increase with depth. Motivated by observations that show the coexistence of thermohaline intrusions and double-diffusive staircases, a linear stability analysis is performed on the governing equations to determine the conditions under which staircases form. It is shown that a double-diffusive staircase can result from interleaving motions if the observed bulk vertical density ratio is below a critical vertical density ratio estimated for particular lateral and vertical background temperature and salinity gradients. Vertical background temperature and salinity gradients dominate over horizontal gradients in determining whether staircases form, with the linear theory indicating that perturbations to stronger vertical temperature gradients are more likely to give rise to a staircase. Examination of Arctic Ocean temperature and salinity measurements indicates that observations are consistent with the theory for reasonable estimates of eddy diffusivity and viscosity.

Double‐Diffusive Layering in the Canada Basin: An Explanation of Along‐Layer Temperature and Salinity Gradients

“…This study contributes to previous studies that have suggested staircase structures are related to intrusions (Bebieva & Timmermans, ; Merryfield, ; Walsh & Carmack, ). Bebieva and Timmermans () showed that either staircases or intrusions can emerge as the result of a perturbation to a background linear vertical stratification in the presence of lateral property gradients. The scenario of intrusions emerging is not inconsistent with the analysis presented here; intrusions develop and then run down to form a staircase.…”

“…The scenario is further complicated by the fact that intrusions are likely advected laterally by the background geostrophic flow in the basin (see, e.g., McLaughlin et al, ). It may be that staircases in the central basin form as the result of a wave‐like perturbation originating from the upstream intrusions at those depths (Bebieva & Timmermans, ). Laboratory lock exchange experiments, for example, indicate velocity perturbations attributed to internal gravity waves far beyond the intrusion front (Ruddick et al, ).…”

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

“…Here we show an example from the Canadian Basin from a yearlong ITP observational record, where mixed layers at the top of the staircase are ≈ 10% as thick as layers toward its bottom (Figure a); layer thicknesses, calculated according to the procedure outlined in Shibley et al (), increase by 1.2 ± 0.1 m for every 10‐m increase in depth in the staircase (Figure b). It is important to note that the thick, lower layers we discuss in the observations should not be conflated with thick layers originating from horizontal intrusions where diffusive convection is not the only mechanism in play (e.g., Bebieva & Timmermans, ).…”

“…These parameters approximately represent the Arctic setting. While molecular values of viscosity and thermal diffusivity in the Arctic Ocean yield σ ≈13, values may be in the range O (0.1 − 1) when turbulence is present (Bebieva & Timmermans, ; Padman, ). Therefore, σ = 7 is a reasonable choice here.…”

“…These have included laboratory experiments and 1‐D models where heat is applied to the bottom of water with a stable linear salinity gradient which then forms a layered system of diffusive convection (e.g., Huppert & Linden, ; Turner, , ). A 2‐D system by way of horizontal thermohaline intrusions which perturb linear gradients in temperature and salinity may also lead to a staircase structure (Bebieva & Timmermans, ; Merryfield, ). Finally, a recent study has described the formation of staircases where the presence of shear in a stably stratified system allows perturbations to buoyancy to grow, leading to a layered system (Radko, ).…”