Oceanic Frontogenesis

Frontogenesis is the fluid-dynamical processes that rapidly sharpen horizontal density gradients and their associated horizontal velocity shears. It is a positive feedback process where the ageostrophic, overturning secondary circulation in the cross-front plane accelerates the frontal sharpening until an arrest occurs through frontal instability and other forms of turbulent mixing. Several well-known types of oceanic frontal phenomena are surveyed, their impacts on oceanic system functioning are assessed, and future research is envisioned.

Frontal Instability and Energy Dissipation in a Submesoscale Upwelling Filament

Based on high-resolution turbulence microstructure and near-surface velocity data, frontal instability and its relation to turbulence are investigated inside a transient upwelling filament in the Benguela upwelling system (southeast Atlantic). The focus of our study is a sharp submesoscale front located at the edge of the filament, characterized by persistent downfront winds, a strong frontal jet, and vigorous turbulence. Our analysis reveals three distinct frontal stability regimes. (i) On the light side of the front, a 30–40-m-deep turbulent surface layer with low potential vorticity (PV) was identified. This low-PV region exhibited a well-defined two-layer structure with a convective (Ekman-forced) upper layer and a stably stratified lower layer, where turbulence was driven by forced symmetric instability (FSI). Dissipation rates in this region scaled with the Ekman buoyancy flux, in excellent quantitative agreement with recent numerical simulations of FSI. (ii) Inside the cyclonic flank of the frontal jet, near the maximum of the cross-front density gradient, the cyclonic vorticity was sufficiently strong to suppress FSI. Turbulence in this region was driven by marginal shear instability. (iii) Inside the anticyclonic flank of the frontal jet, conditions for mixed inertial/symmetric instability were satisfied. Our data provide direct evidence for the relevance of FSI, inertial instability, and marginal shear instability for overall kinetic energy dissipation in submesoscale fronts and filaments.

Simulating the frontal instability of lock-exchange density currents with dissipative particle dynamics

The frontal instability of lock-exchange density currents is numerically investigated using dissipative particle dynamics (DPD) at the mesoscopic particle level. For modeling two-phase flow, the “color” repulsion model is adopted to describe binary fluids according to Rothman–Keller method. The present DPD simulation can reproduce the flow phenomena of lock-exchange density currents, including the lobe-and-cleft instability that appears at the head, as well as the formation of coherent billow structures at the interface behind the head due to the growth of Kelvin–Helmholtz instability. Furthermore, through the DPD simulation, some small-scale characteristics can be observed, which are difficult to be captured in macroscopic simulation and experiment.

Length Scale of the Finite-Amplitude Meanders of Shelfbreak Fronts

Through combining analytical arguments and numerical models, this study investigates the finite-amplitude meanders of shelfbreak fronts characterized by sloping isopycnals outcropping at both the surface and the shelfbreak bottom. The objective is to provide a formula for the meander length scale that can explain observed frontal length scale variability and also be verified with observations. Considering the frontal instability to be a mixture of barotropic and baroclinic instability, the derived along-shelf meander length scale formula is [b1/(1 + a1S1/2)]NH/f, where N is the buoyancy frequency; H is the depth of the front; f is the Coriolis parameter; S is the Burger number measuring the ratio of energy conversion associated with barotropic and baroclinic instability; and a1 and b1 are empirical constants. Initial growth rate of the frontal instability is formulated as [b2(1 + a1S1/2)/(1 + a2αS1/2)]NH/L, where α is the bottom slope at the foot of the front, and a2 and b2 are empirical constants. The formulas are verified using numerical sensitivity simulations, and fitting of the simulated and formulated results gives a1 = 2.69, b1 = 14.65, a2 = 5.1 × 103, and b2 = 6.2 × 10−2. The numerical simulations also show development of fast-growing frontal symmetric instability when the minimum initial potential vorticity is negative. Although frontal symmetric instability leads to faster development of barotropic and baroclinic instability at later times, it does not significantly influence the meander length scale. The derived meander length scale provides a framework for future studies of the influences of external forces on shelfbreak frontal circulation and cross-frontal exchange.

Numerical Simulations of Gravity Driven Reversible Reactive Flows in Homogeneous Porous Media

The effect of reversibility on the instability of a miscible vertical reactive flow displacement is examined. A model, where densities and/or viscosities mismatches between the reactants and the chemical product trigger instability, is adopted. The problem is governed by the continuity equation, Darcy’s law, and the convection-diffusion-reaction equations. The problem is formulated and solved numerically using a combination of the highly accurate spectral methods based on Hartley’s transform and the finite-difference technique. Nonlinear simulations were carried out for a variety of parameters to analyse the effects of the reversibility of the chemical reaction on the development of the flow under different scenarios of the frontal instability. In general, faster attenuation in the development and growth of the instability is reported as the reversibility of the chemical reaction increases. However, it was observed that reversibility is capable of triggering instability for particular choices of the densities and viscosities mismatches. In addition, the effect of the reversibility in enhancing the instability was illustrated by presenting the total relative contact area between the reactants and the product.

Eddy-Driven Exchange between the Open Ocean and a Sub–Ice Shelf Cavity

The exchange between the open ocean and sub–ice shelf cavities is important to both water mass transformations and ice shelf melting. Here, the authors use a high-resolution (500 m) numerical model to investigate to which degree eddies produced by frontal instability at the edge of a polynya are capable of transporting dense high-salinity shelf water (HSSW) underneath an ice shelf. The applied surface buoyancy flux and ice shelf geometry is based on Ronne Ice Shelf in the southern Weddell Sea, an area of intense wintertime sea ice production where a flow of HSSW into the cavity has been observed. Results show that eddies are able to enter the cavity at the southwestern corner of the polynya where an anticyclonic rim current intersects the ice shelf front. The size and time scale of simulated eddies are in agreement with observations close to the Ronne Ice Front. The properties and strength of the inflow are sensitive to the prescribed total ice production, flushing the ice shelf cavity at a rate of 0.2–0.4 × 106 m3 s−1 depending on polynya size and magnitude of surface buoyancy flux. Eddy-driven HSSW transport into the cavity is reduced by about 50% if the model grid resolution is decreased to 2–5 km and eddies are not properly resolved.

FRONTAL INSTABILITY OF LOCK-EXCHANGE GRAVITY CURRENTS

In this work we address the frontal instability of gravity currents. The planar laser-induced fluorescence (PLiF) flow visualization is utilized to analyze the detailed dynamics of the current, which are generated in a lock-exchange Perspex tank. We believe that two dominant modes of instability determine the complex structures at the head of the flow. The first one resembles Kelvin–Helmholtz instability, which results in Kelvin–Helmholtz billows rolling up in the shear zone above the head. The other, categorized as convective instability known as "lobes and clefts", which stems from ground friction as well as unstable inverse density stratification, and is considered to be the cause for the disruption of the span-wise symmetry of Kelvin–Helmholtz billows. Moreover, our observations indicate that the convective instability also contributes to a secondary instability associated with Kelvin–Helmholtz vortex breakdown. These instabilities not only play a central role in shaping the three-dimension characteristics of the currents, but also govern the mixing and entrainment mechanisms. Therefore, more precise measurement of the positions of the frontal instability and the flow structures, especially the turbulent structures is indeed necessary.

Linear Fluctuation Growth during Frontogenesis

Near-surface, two-dimensional (2D) baroclinic frontogenesis induced by a barotropic deformation flow enhances the growth of three-dimensional (3D) fluctuations that occur on an ever smaller scale as the front progressively sharpens. The 3D fluctuation growth rate further increases with a larger deformation rate. The fluctuations grow by a combination of baroclinic and barotropic energy conversions from the 2D frontal flow, with the former dominating for most of the situations examined, ranging from small to 𝒪(1) values of the Rossby and Froude numbers and nondimensional deformation rate. Averaged 3D fluctuation buoyancy fluxes resist the 2D frontogenesis by a frontolytic tendency. They also augment the buoyancy restratification and potential-to-kinetic energy conversion tendencies of the 2D frontogenesis itself, and the 2D frontogenetic and 3D eddy-induced secondary circulations are mostly reinforcing (unlike in turbulent baroclinic jets). This shows that frontal instability coexists with, and potentially may even overcome, active frontogenesis; this conclusion is contrary to some previous studies. Frontal instability thus can augment frontogenesis in accomplishing a forward cascade of energy from oceanic mesoscale eddies into the submesoscale regime en route to finescale dissipation.