TY - JOUR
T1 - A geometric model for the dynamics of a fluvially dominated deltaic system under base-level change
AU - Lorenzo-Trueba, Jorge
AU - Voller, Vaughan R.
AU - Paola, Chris
PY - 2013/4
Y1 - 2013/4
N2 - We present a geometric model to study the role of base-level change in the dynamics of the alluvial-bedrock transition and shoreline positions in a fluvially dominated deltaic system. The domain of the problem is a sediment wedge in the long-profile cross-section. On assuming that the fluvial surface has a quadratic form, its evolution is determined by imposing an overall volume balance, and conditions for the elevations and slopes at the domain boundaries. This results in a coupled system, involving one ordinary differential equation and one non-linear equation. These equations are solved through an explicit Euler time stepping algorithm to predict the movement of the shoreline and alluvial-bedrock transition boundaries under a wide range of base-level change conditions. The mathematics of the approach are verified by comparing predictions from the geometric model with a closed form solution of a downslope gravity-driven transport model under the specific case of a square-root of time base-level change. Testing with more general base-level change scenarios reveals that this simple geometric mass balance is able to predict system dynamics that are fully consistent with both physical and numerical experiments. Moreover, model predictions under a base-level cycle (fall-rise) suggest a behavior where river incision occurs during the base-level rise stage, a predicted dynamic that has not been previously reported.
AB - We present a geometric model to study the role of base-level change in the dynamics of the alluvial-bedrock transition and shoreline positions in a fluvially dominated deltaic system. The domain of the problem is a sediment wedge in the long-profile cross-section. On assuming that the fluvial surface has a quadratic form, its evolution is determined by imposing an overall volume balance, and conditions for the elevations and slopes at the domain boundaries. This results in a coupled system, involving one ordinary differential equation and one non-linear equation. These equations are solved through an explicit Euler time stepping algorithm to predict the movement of the shoreline and alluvial-bedrock transition boundaries under a wide range of base-level change conditions. The mathematics of the approach are verified by comparing predictions from the geometric model with a closed form solution of a downslope gravity-driven transport model under the specific case of a square-root of time base-level change. Testing with more general base-level change scenarios reveals that this simple geometric mass balance is able to predict system dynamics that are fully consistent with both physical and numerical experiments. Moreover, model predictions under a base-level cycle (fall-rise) suggest a behavior where river incision occurs during the base-level rise stage, a predicted dynamic that has not been previously reported.
KW - Alluvial-bedrock transition
KW - Fluvially dominated
KW - Moving boundary
KW - Shoreline dynamics
UR - http://www.scopus.com/inward/record.url?scp=84875210344&partnerID=8YFLogxK
U2 - 10.1016/j.cageo.2012.02.010
DO - 10.1016/j.cageo.2012.02.010
M3 - Article
AN - SCOPUS:84875210344
SN - 0098-3004
VL - 53
SP - 39
EP - 47
JO - Computers and Geosciences
JF - Computers and Geosciences
ER -