A Gradually Varied Approach to Model Turbidity Currents in Submarine Channels

Abstract

We develop a one‐dimensional model to describe the dynamics of turbidity current flowing in submarine channels. We consider the flow as a steady state polydisperse suspension accounting for water detrainment from the clear water‐turbid interface, for spatial variations of the channel width and for water and sediment lateral overspill from the channel levees. Moreover, we account for sediment exchange with the bed extending the model to deal with situations where the current meets a nonerodible bed. Results show that when water detrainment is accounted for, the flow thickness becomes approximately constant proceeding downstream. Similarly, in the presence of channel levees, the flow tends to adjust to channel relief through the lateral loss of water and sediment. As more mud is spilled above the levees relative to sand, the flow becomes more sand rich proceeding downstream when lateral overspill is present. Velocity and flow thickness predicted by the model are then validated by showing good agreement with laboratory observations. Finally, the model is applied to the Monterey Canyon bathymetric data matching satisfactorily the December 2002 event field measurements and predicting a runout length consistent with observations.

Turbulent diffusion modelling of sediment in turbidity currents: An experimental validation of the Rouse approach

“…It can be argued, however, that the approach still holds in cases where the flow changes gradually in time and space, such that the timescales of change are longer than the timescales associated with settling and turbulent mixing (Bolla Pittaluga et al, 2018). Firstly, it relies on the assumption of fully developed flow that is both steady in time and uniform in space.…”

“…This mismatch occurs because modest shear velocity values suffice to homogenously diffuse silt against the pull of gravity over the depth of a current in the Rouse equation (see also Parker et al, 1986). This error has some consequences for studies using Rousean models to predict the composition of the part of turbidity currents that spills over the levee crest (Straub and Mohrig, 2008;Bolla Pittaluga et al, 2018), which is predicted to be too fine. The latter display significant error by underpredicting D 90 of the suspension high in the flow.…”

“…This is required because the Rouse equation depends on the balance between two processes, which takes time to establish. It can be argued, however, that the approach still holds in cases where the flow changes gradually in time and space, such that the timescales of change are longer than the timescales associated with settling and turbulent mixing (Bolla Pittaluga et al, 2018).…”

“…This error is not due to problems in predicting the distribution of coarser material but due to the incorrect prediction of elevated silt content in the upper part of the flow, which reduces the fraction of coarser material and thus draws the 90 th percentile of grain size down ( Figures 7A and 8A). This error has some consequences for studies using Rousean models to predict the composition of the part of turbidity currents that spills over the levee crest (Straub and Mohrig, 2008;Bolla Pittaluga et al, 2018), which is predicted to be too fine. Conversely, flow strength will be overestimated in inverse approaches that use deposit grain size of channel margin or levee deposits to reconstruct flow characteristics (Hiscott et al, 1997;Jobe et al, 2017;, because D 90 is systematically underpredicted in the upper part of turbidity currents (Figures 7A and 8A).…”

“…Consequently, these deposits are increasingly being used as control points for the reconstruction of historic and ancient | 205 EGGENHUISEN Et al. turbidity current flow events in simplified modelling approaches. These approaches commonly rely on the classic equation for suspended sediment profiles in open-channel flow, as proposed by Rouse (1937), to describe grain-size stratification in turbidity currents (Hiscott, 1994;Hiscott et al, 1997;Straub and Mohrig, 2008;Bolla Pittalua and Imran, 2014;Jobe et al, 2017;Bolla Pittaluga et al, 2018). In the Rouse equation, sediment particles are considered to be mixed by turbulence in analogy to heat, momentum and dissolved matter (Rouse, 1937;Vanoni, 1946;Graf, 1971;van Rijn, 1993;Vanoni, 2006;Garcia, 2008).…”