Kelvin-Helmholtz instability and induced magnetic reconnection at the Earth’s magnetopause: 3D simulation based on satellite data

A 3D two-fluid simulation, using plasma parameters as measured by MMS on September 8th 2015, shows the nonlinear development of the Kelvin-Helmholtz instability at the Earth’s magnetopause. It shows an extremely rich dynamics, including the development of a complex magnetic topology, vortex merging and secondary instabilities. Vortex induced and mid-latitude magnetic reconnection coexist and produce an asymmetric distribution of magnetic reconnection events. Off-equator reconnection exhibits a predominance of events in the southern hemisphere during the early nonlinear phase, as observed by satellites at the dayside magnetopause. The late nonlinear phase shows the development of vortex pairing for all latitudes while secondary Kelvin-Helmholtz instability develops only in the northern hemisphere leading to an enhancement of the occurrence of off-equator reconnection there. Since vortices move tailward while evolving, this suggests that reconnection events in the northern hemisphere should dominate at the nightside magnetopause.

The influence of far field stratification on shear-induced turbulent mixing

We compare the properties of the turbulence induced by the breakdown of Kelvin–Helmholtz instability (KHI) at high Reynolds number in two classes of stratified shear flows where the background density profile is given by either a linear function or a hyperbolic tangent function, at different values of the minimum initial gradient Richardson number ${{Ri}}_0$ . Considering global and local measures of mixing defined in terms of either the irreversible mixing rate $\mathscr {M}$ associated with the time evolution of the background potential energy, or an appropriately defined density variance dissipation rate $\chi$ , we find that the proliferation of secondary instabilities strongly affects the efficiency of mixing early in the flow evolution, and also that these secondary instabilities are highly sensitive to flow perturbations that are added at the point of maximal (two-dimensional) billow amplitude. Nevertheless, mixing efficiency does not appear to depend strongly on the far field density structure, a feature supported by the evolution of local horizontally averaged values of the buoyancy Reynolds number ${Re}_b$ and gradient Richardson number ${Ri}_g$ . We investigate the applicability of various proposed scaling laws for flux coefficients $\varGamma$ in terms of characteristic length scales, in particular discussing the relevance of the overturning ‘Thorpe scale’ in stratified turbulent flows. Finally, we compare a variety of empirical model parameterizations used to compute diapycnal diffusivity in an oceanographic context, arguing that for transient flows such as KHI-induced turbulence, simple models that relate the ‘age’ of a turbulent event to its mixing efficiency can produce reasonably robust mixing estimates.

On the oxygenation of the Archaean and Proterozoic oceans

Modern-day ocean circulation behaves as a complex forced convective system that is characterized by the decrease in water temperature but increase in water density with depth. The dissolved oxygen content – which initially decreases due to biological oxygen demand – also increases with depth. In contrast to the present-day scenario, we propose that during the Archaean and Proterozoic eons inverted profiles could have developed such that, with depth, ocean water temperature increased and density and dissolved oxygen decreased. These inverted temperature and density profiles resulted in palaeo-ocean circulation behaving as a free convective system. It is proposed that this free convection, which may have been stable, or chaotic and subject to secondary instabilities, hindered the deep oxygenation of the palaeo-ocean. It may not be coincidental that the great oxygenation event (GOE) and Huronian glaciations are contemporaneous, in a similar way that the Neoproterozoic oxygenation event (NOE) is known to have been associated with glaciations. The global-scale external forcing required to switch the natural convective system to its present-day configuration is suggested to have been associated with Neoproterozoic glaciations and the subsequent lowering of ocean water salinity that accompanied them. We propose that this inverted the ocean water density gradient, allowing the oxygenation of the oceans for the first time. It is beyond the scope of this work to model the complex natural convection system, but we hope that geophysicists and numerical modellers will quantitatively evaluate the hypothesis proposed here to validate or refute our proposition.

From primary instabilities to secondary instabilities in Görtler vortex flows

We have studied the transformation process from primary instabilities to secondary instabilities with direct numerical simulations and stability theories (Spatial Biglobal and plane-marching parabolized stability equations) in detail. First Mack mode and second Mack mode are shown to be able to evolve into the sinuous mode and the varicose mode of secondary instability, respectively. Although the characteristics of second Mack mode eventually lose in the downstream due to the synchronization with the continuous spectrum, second Mack mode is found to be able to trigger a sequence of mode resonations which in turn give birth to highly unstable secondary instabilities. In contrast, first Mack mode does not involve in any mode synchronization. Nevertheless, it can still “jump" to a sinuous mode of secondary instability with a much larger growth rate than that of the first Mack mode. Therefore, secondary instabilities of Görtler vortices are highly receptive to the primary instabilities in the upstream, so that one should consider the primary instability in the upstream and the secondary instability in the downstream as a whole in order to get an accurate prediction of the boundary layer transition.