Disruption of Arctic Staircases by Shear

Numerical simulations have been conducted to examine the structure of diffusive-convection staircases in the presence of vortical-mode-induced turbulent forcing. By modulating the input power $P$ and the background density ratio $R_\rho$ , we have identified three distinct types of staircase structures in these simulations: namely staircases maintained in the system driven by double-diffusion, by turbulence or by a combination of both double-diffusion and turbulence. While we showed that staircases maintained in the double-diffusion-dominated system are accurately characterised by the existing model originally proposed by Linden & Shirtcliffe (J. Fluid Mech., vol. 87, no. 3, 1978, pp. 417–432), we introduced new physical models to describe the staircase structures maintained in the turbulence-dominated system and the system driven by both turbulence and double-diffusion. Our integrated model reveals that turbulence fundamentally governs the entire life cycle of the diffusive-convection staircases, encompassing their formation, maintenance and eventual disruption in the Arctic Ocean's thermohaline staircases. While our previous work of Ma & Peltier (J. Fluid Mech., vol. 931, 2022b) demonstrated that turbulence could initiate the formation of Arctic staircases, these staircases are sustained by both turbulence and double-diffusion acting together after formation has occurred. Strong turbulence may disrupt staircase structures; however, the presence of weak turbulence could lead to unstable stratification within mixed layers of the staircases, as well as enhancing vertical heat and salt fluxes. Turbulence can even sustain a stable staircase structure factor when $R_\rho$ is relatively large, following a similar mechanism to the density staircases observed in laboratory experiments. Consequently, previous parameterisations (e.g. Kelley, J. Geophys. Res.: Oceans, vol. 95, no. C3, 1990, pp. 3365–3371) on the vertical heat flux across the diffusive-convection staircases may provide a significant underestimation of the heat transport by ignoring the influences of turbulence.

Section: Discussionsupporting

confidence: 91%

Diffusive-convection staircases in the polar oceans: the interplay between double diffusion and turbulence

Ma,

Peltier

2024

“…In the spirit of the times, much recent progress in understanding double-diffusive convection has been brought by numerical modelling (e.g. Hieronymus & Carpenter 2016;Yang, Verzicco & Lohse 2016Ouillon et al 2020;Ma & Peltier 2021;Brown & Radko 2022). However, the principal limitation of such efforts lies in the prohibitive computational cost of modelling many realistic configurations.…”

Section: Introductionmentioning

confidence: 99%

“…Many earlier numerical studies reduced the associated computational burden by considering the salt/heat diffusivity ratios τ ≡ k S k −1 T that are much larger than the oceanic value of τ ∼ 0.01 (e.g. Stern et al 2001;Kimura, Smyth, & Kunze 2011;Brown & Radko 2022). While acceptable for preliminary explorations, concerns regarding the ability of such models to accurately represent oceanic processes call for a more cardinal solution to the problem.…”

Section: Introductionmentioning

confidence: 99%

“…Smyth & Kimura 2011; Hieronymus & Carpenter 2016; Yang, Verzicco & Lohse 2016, 2020; Ouillon et al . 2020; Ma & Peltier 2021; Brown & Radko 2022). However, the principal limitation of such efforts lies in the prohibitive computational cost of modelling many realistic configurations.…”

Section: Introductionmentioning

confidence: 99%

“…Stern et al . 2001; Kimura, Smyth, & Kunze 2011; Brown & Radko 2022). While acceptable for preliminary explorations, concerns regarding the ability of such models to accurately represent oceanic processes call for a more cardinal solution to the problem.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The sub-microscale dynamics of double-diffusive convection

Radko

2024

Self Cite

This study investigates the dynamics of fingering convection on scales much smaller than the typical size of individual salt fingers. On such scales, salinity patterns exhibit the spontaneous emergence of sharp fronts induced by finger-scale strain. In contrast, velocity and temperature fields are largely devoid of sub-microscale variability, which is attributed to the rapid molecular dissipation of heat and momentum. The presence of fine salinity structures fundamentally limits the efficiency of direct numerical simulations (DNS) of double-diffusive processes. In the oceanographic context, the computational cost of resolving sub-microscale salinity features exceeds that of temperature-only DNS by up to four orders of magnitude, severely restricting the types of double-diffusive systems that can be studied numerically. To address this complication, we introduce the sub-microscale filtering (SMF) algorithm, which resolves temperature and velocity while parameterizing the sub-microscale dynamics of salinity. The proposed closure draws inspiration from the Smagorinsky scheme, which represents unresolved processes by the downgradient strain-dependent momentum flux. The SMF model is successfully validated through fully resolved simulations.

Turbulence and mixing from neighbouring stratified shear layers

Liu,

Kaminski,

Smyth

2024

Studies of Kelvin–Helmholtz (KH) instability have typically modelled the initial mean flow as an isolated stratified shear layer. However, geophysical flows frequently exhibit multiple layers. As a step towards understanding these flows, we examine the case of two adjacent stratified shear layers using both linear stability analysis and direct numerical simulations. With sufficiently large layer separation, the characteristics of instability and mixing converge towards the familiar KH turbulence, and similarly when the separation is near zero and the layers add to make a single layer, albeit with a reduced Richardson number. Here, our focus is on intermediate separations, which produce new and complex phenomena. As the separation distance $D$ increases from zero to a critical value $D_c$ , approximately half the thickness of the shear layer, the growth rate and wavenumber both decrease monotonically. The minimum Richardson number is relatively low, potentially inducing pairing, and shear-aligned convective instability (SCI) is the primary mechanism for transition. Consequently, mixing is relatively strong and efficient. When $D\sim D_c$ , billow length is increased but growth is slowed. Despite the modest growth rate, mixing is strong and efficient, engendered primarily by secondary shear instability manifested on the braids, and by SCI occurring on the eyelids. Shear-aligned vortices are driven in part by buoyancy production; however, shear production and vortex stretching are equally important mechanisms. When $D>D_c$ , neighbouring billow interactions suppress the growth of both KH instability and SCI. Strength and efficiency of mixing decrease abruptly as $D_c$ is exceeded. As turbulence decays, layers of marginal instability may arise.