Mechanics of merging events for a series of layers in a stratified turbulent fluid

Abstract

This study attempts to explain the evolutionary pattern of a series of well-mixed layers separated by thin high-gradient interfaces frequently observed in stratified fluids. Such layered structures form as a result of the instability of the equilibrium with uniform stratification, and their subsequent evolution is characterized by a sequence of merging events which systematically increase the average layer thickness. The coarsening of layers can take one of two forms, depending on the realized vertical buoyancy flux law. Layers merge either when the high-gradient interfaces drift and collide, or when some interfaces gradually erode without moving vertically. The selection of a preferred pattern of coarsening is rationalized by the analytical theory -the merging theorem -which is based on linear stability analysis for a series of identical layers and strongly stratified interfaces. The merging theorem suggests that the merger by erosion of weak interfaces occurs when the vertical buoyancy flux decreases with the buoyancy variation across the step. If the buoyancy flux increases with step height, then coarsening of a staircase may result from drift and collision of the adjacent interfaces. Our model also quantifies the time scale of merging events and makes it possible to predict whether the layer merging continues indefinitely or whether the coarsening is ultimately arrested. The merging theorem is applied to extant one-dimensional models of turbulent mixing and successfully tested against the corresponding fully nonlinear numerical simulations. It is hypothesized that the upscale cascade of buoyancy variance associated with merging events may be one of the significant sources of the fine-scale (∼10 m) variability in the ocean.

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

“…For instance, Merryfield (2000) suggested that staircases represent the ultimate state of thermohaline interleaving, which is, in turn, induced by lateral temperature and salinity gradients. Radko (2003) on the other hand argued that doublediffusive layering is likely to be caused by the so-called gamma instability, which is driven by variations in the ratio of the turbulent heat and salt fluxes:…”

“…To model staircases, several distinct scales must be resolved: (i) fingering interfaces (;1 m), (ii) the vertical thermocline scale (;1 km), and (iii) the lateral basin-scale circulation patterns (;1000 km). Theoretical arguments (Radko 2005) suggest that while the initial layers form rather rapidly (within weeks), the evolution and ultimate equilibration of staircases occur on the time scale of decades. Computational capabilities have only recently reached the level of resolving such a wide range of spatial and temporal scales.…”

“…Our study addresses both challenges by performing simulations at unprecedented vertical resolution (Dz 5 1 m) and by adopting a recent parameterization of finger-induced diapycnal fluxes (Radko and Smith 2012). The Radko and Smith (2012) mixing model is based on a suite of DNS and, importantly, it reflects the systematic variation of the flux ratio with the density ratio.…”

Generation of large-scale intrusions at baroclinic fronts: an analytical consideration with a reference to the Arctic Ocean

“…Furthermore, it is worth not-ing that the 2-D models of double-diffusive interleaving, as applied to typical baroclinic fronts in the ocean, are able to forecast intrusive layers with vertical length scale of no more than 10 m (Kuzmina and Rodionov, 1992;May andKelley, 1997, 2001;Kuzmina and Zhurbas, 2000;Kuzmina and Lee, 2005;. Therefore, despite the proven-by-simulation hypothesis of intrusions of small vertical scale merging into larger structures (Radko, 2007), new approaches to the mathematical description of the formation of large intrusions in the area of baroclinic fronts become relevant.…”

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

“…So far, most of these models have focused on the properties of the interfaces between layers, such as their thickness, the heat and mass flux through them, and the characteristic dimensionless ratios. Attempts to determine the conditions for the formation of double-diffusive layers, the layer thickness and their stability [Huppert, 1971;Kelley, 1984] have been proposed for the diffusive and the salt finger regimes [Radko, 2003[Radko, , 2005, and theoretical considerations have been formulated to explain the layer merging mechanisms [Radko, 2007;Noguchi and Niino, 2010b;Radko et al, 2014a]. However, coupling local dynamics and largescale effects in the description of the process by which the typical staircase structure forms and evolves is still an unresolved task.…”