Levees Formed by Turbidity Currents: A Depth‐Averaged Modeling Treatment

Abstract

The formation of levees with accompanying channels is a ubiquitous feature of turbidity flows both in submarine canyons and on submarine fans. We examine the latter situation using numerical and theoretical calculations based on a depth‐averaged model for subaqueous turbidity currents, introduced by Parker et al. (1986, https://doi.org/S0022112086001404) and reinterpreted by Halsey et al. (2017, https://doi.org/10.1002/2016JC012635). Using a novel similarity solution to these equations, applied to a two‐component sand/mud flow, we show that in a well‐defined limit levees form along rays emanating from the source of the flows, which in our case is the outlet of a submarine canyon. The width of the channel between the levees decreases as particle size increases and increases with increasing slope of the surface. The levees form with a characteristic right‐triangle shape, with the steep slope facing inward toward the channel. The levee height is comparable to the height of the turbidity flow. Levees form even in the absence of preexisting scour. We confirm these analytical results with numerical simulations of the depth‐averaged equations. Further downslope, the formation of levees seems to be inconsistent with an erosion law introduced by Garcia and Parker (1991, 10.1061/(ASCE)0733-9429(1991)117:4(414)), calling the applicability of this law to natural systems into question.

A dimensionless framework for predicting submarine fan morphology

“…Models are solved using a finite volume method with a dynamic time step that is a function of grid spacing, flow velocity, and wave speed. A more detailed description of the depth-averaged theory, governing equations and analyses of their approximate analytical solutions, and a choice of the numerical solver is published in prior studies 29,30 .…”

“…We overcome the direct observational, experimental, and modeling limitations that prevent us from linking properties of turbidity currents to the complex morphologies of submarine fans by leveraging a previously developed, parallel process-based numerical model called EMstrata 29,30 . This model is based on the depth-average approximation of flow parameters in 3D Navier-Stokes equations of fully turbulent flows 31 .…”

A dimensionless framework for predicting submarine fan morphology

“…The amount of morphodynamic work by the head and the body of the turbidity current is controlled by empirical closures [66][67][68] that are function of shear stresses within the flow. A more detailed description of the depth-averaged theory, governing equations and analyses of their approximate analytical solutions, and a choice of the numerical solver is published in prior studies 25,26 .…”

“…We overcome the direct observational, experimental, and modeling limitations that prevent us from linking properties of turbidity currents to the complex morphologies of submarine fans by leveraging a previously developed, parallel process-based numerical model called EMstrata 25,26 . This model is based on the depth-average approximation of flow parameters in 3D Navier-Stokes equations of fully turbulent flows [27][28][29][30] .…”

Numerical Study of the Transport Process of Shallow Heat Carried by Turbidity Currents in Deep‐Sea Environments

“…Ye et al (2018) obtained similar responses of the k − kl, k − ε, and k − ω models for vertical stratification simulations. Halsey and Kumar (2019) presented numerical solutions of the full transient depth-averaged four-equation turbidity current model. Applying a novel similarity solution derived from these equations, analyzed various characteristics of levee growth and structure in a two-component sand/mud flow.…”