Turbidity Current Dynamics: 1. Model Formulation and Identification of Flow Equilibrium Conditions Resulting From Flow Stripping and Overspill

Abstract

This study expands the widely used one‐dimensional, four‐equation model for turbidity currents to account for mass, momentum, and energy sinks associated with flow stripping and overspill processes acting upon the turbidity current suspension cloud. The suspension cloud is defined as any portion of the flow extending above the channel levees. The expanded model allows steady turbidity currents to evolve to a uniform, or equilibrium, state where mass, momentum, and energy gained through sediment and clear‐water entrainment processes are balanced by the mass, momentum, and energy lost to flow stripping and overspill. We perform a sensitivity analysis of the expanded model to assess how changes in channel (e.g., slope, channel height, width, bed friction, and radius of curvature) and flow (e.g., sediment grain size, suspension cloud concentration, and turbulence) properties affect the equilibrium flow conditions. By varying the model inputs from half to double their base case values, we find that the equilibrium values can change by up to a factor of 2. We find that the equilibrium conditions, including the flow Richardson number, were generally most sensitive to changes in slope, channel height, grain size, and suspension cloud concentration. Additionally, we identify model parameter space where Richardson subcritical equilibrium flow is possible. The fact that turbidity currents can attain equilibrium, and particularly subcritical equilibrium, might help elucidate the long turbidity current runout distances on low slopes inferred from extensive submarine channel levee systems.

Controls on submarine channel-modifying processes identified through morphometric scaling relationships

“…7), indicating that the stable widths and aspect ratios observed in the upper Bengal 1 channel and the GoM 12 channel may be typical of medial to distal portions of submarine channels. This is consistent with the modeling results of Traer et al (2018aTraer et al ( , 2018b) that suggest turbidity currents can achieve flow equilibrium within the upstream reaches of a channel and maintain it over long distances, producing a flow filtering effect and consistency of flows that traverse the full length of the channel. The dramatic depth decrease at the end of the Bengal 1 channel can be attributed to the channel-lobe transition (see below), which is not mapped in the Amazon 1 and GoM 12 channels.…”

“…11; Conway et al, 2012). Turbidity current modeling efforts by Traer et al (2018aTraer et al ( , 2018b show that currents may take tens to almost 100 km to achieve flow equilibrium (between entrainment and overspill or flow stripping) following a perturbation to channel slope, depth, or other parameters. These findings are consistent with our observations from the Niger 9 channel and suggest that the long adjustment period of flows relative to topographic irregularities and channel length could be reflected in the morphologies documented here.…”

“…We hypothesize that fluvial scaling relationships that arise from terrestrial processes, such as downstream increases in discharge driven by precipitation and overland flow, will be different in submarine systems where such processes do not occur. This study presents a rich data set of submarine channel morphometrics that can be further employed in numerical modeling of turbidity currents (e.g., Sequeiros, 2012;Traer et al, 2015Traer et al, , 2018aTraer et al, , 2018b, offshore energy resource exploration, seafloor infrastructure hazards assessment (e.g., Piper et al, 1999), and marine habitat and ecosystem research (e.g., Vetter and Dayton, 1998). By directly testing whether certain fluvial scaling relationships are also present in submarine channels, we address whether morphological similarities reflect analogous processes, and assess the relevance of fluvial analogs in deep-water systems (Mitchell, 2004;Keevil et al, 2006;Hughes Clarke, 2016).…”

Exploring a new breadth of cyclic steps on distal submarine fans

“…10. Flow stripping plays an important role in regulating turbidity current flow height (Piper & Normark 1983;Traer et al, 2015Traer et al, , 2018, and the overflowing turbidity current can be approximated as a sheet flow moving down the levée.…”

Self-stratifying turbidity currents

“…This artificial boost to the momentum will have significantly altered the predicted dynamics. Traer et al (2018a) proposed a four equation model capturing both mass lost due to lateral overspill by pressure and that lost due to the sinuosity of the current. This model is then extensively investigated in Traer et al (2018b), demonstrating a range of interesting behaviours comparable to those seen in real physical flows.…”