Abstract: In this talk, I will demonstrate a forward stratigraphic model based on depth-averaged governing equations for the flow of submarine turbidity currents over an erodible bed. This model is being used with some success by the Process Stratigraphy team at ExxonMobil to generate stratigraphic models for deepwater environments of deposition. The mathematical model consists of a system of nonlinear hyperbolic PDEs, with an additional so-called Exner equation for modeling the flow-bed sediment exchange and their bedload transport. The Exner equation plays a key role since a (slow time scale) change in the gradient of the bed influences the (fast time scale) momentum of the flow. The transport equations, along with closure models for sediment transport, TKE balance, and water entrainment, are solved using a first-order finite-volume method with a HLLC approximate Riemann solver and integrated using an explicit Euler scheme. The model shows the emergence of self-organized patterns in the deposits, including the creation of bedforms, channel formation, and avulsions, consistent with observations of modern systems and lab experiments. These occur even with uniform boundary conditions and symmetric initial conditions. The initial disturbances that trigger these mechanisms are ostensibly sourced by floating-point roundoff errors. An ensemble of simulations with slightly different initial conditions are used to analyze statistics on shapes of geomorphic elements and grain size distributions. The objective is to assess whether and under what conditions such a numerical model can be predictive and quantify the uncertainty in the results arising due to the irreducible chaos in the dynamical system.
Bio: Ramanathan Vishnampet is a Computational Data Scientist at the Global Business Lines Analytics & Optimization group at ExxonMobil Upstream Integrated Solutions. He graduated with a Ph.D. in Theoretical and Applied Mechanics from the University of Illinois at Urbana-Champaign, where his dissertation focused on an exact and consistent adjoint method for high-fidelity discretization of the compressible flow equations.