Flow splitting in numerical simulations of oceanic dense-water outflows

Flow splitting occurs when part of a gravity current becomes neutrally buoyant and separates from the bottom-trapped plume as an interflow. This phenomenon has been previously observed in laboratory experiments, small-scale water bodies (e.g., lakes) and numerical studies of small-scale systems. Here, the potential for flow splitting in oceanic gravity currents is investigated using high-resolution (Δx = Δz = 5  m) two-dimensional numerical simulations of gravity flows into linearly stratified environments. The model is configured to solve the non-hydrostatic Boussinesq equations without rotation. A set of experiments is conducted by varying the initial buoyancy number B₀=Q₀N³/g^′2 (where Q₀ is the volume flux of the dense water flow per unit width, N is the ambient stratification and g′ is the reduced gravity), the bottom slope (α) and the turbulent Prandtl number (Pr). Regardless of α or Pr, when B₀ ≤ 0.002 the outflow always reaches the deep ocean forming an underflow. Similarly, when B₀ ≥ 0.13 the outflow always equilibrates at intermediate depths, forming an interflow. However, when B₀ ∼ 0.016, flow splitting always occurs when Pr ≥ 10, while interflows always occur for Pr = 1. An important characteristic of simulations that result in flow splitting is the development of Holmboe-like interfacial instabilities and flow transition from a supercritical condition, where the Froude number (Fr) is greater than one, to a slower and more uniform subcritical condition (Fr < 1). This transition is associated with an internal hydraulic jump and consequent mixing enhancement. Although our experiments do not take into account three-dimensionality and rotation, which are likely to influence mixing and the transition between flow regimes, a comparison between our results and oceanic observations suggests that flow splitting may occur in dense-water outflows with weak ambient stratification, such as Antarctic outflows.