Self-similar long profiles of aggrading submarine leveed channels: Analytical solution and its application to the Amazon channel

Many submarine fans are coursed by well-defined leveed channels constructed by turbidity currents. The channels aggrade in time, typically accumulating sandy deposits in their beds and muddy deposits in their levees. Periodic channel avulsion acts to build up the fan as a whole. Here a first theory for the long profile of leveed channels is offered. The theory is based on the assumption that there exists a time period, well after channel initiation but before incipient avulsion, during which the channel and its levees are in a quasi-equilibrium state, concurrently aggrading and prograding onto the surrounding fan. The currents are assumed to deposit sand on the channel bed and mud on the levees. The formulation uses a steady uniform flow assumption and a sediment transport relation inherited from rivers and yields a partial differential equation for the evolution of the channel starting from any initial condition. For the ideal case of a channel forming on an initially unchannelized sloping fan, the theory predicts self-similar long profiles for the down-channel variation of channel bed slope, bed elevation, and width, as well as flow discharge and sand/mud discharges. The time evolution of the channel then amounts to a simple rescaling of the self-similar profile as it aggrades and progrades down fan. The theory, when tested against data from the Amazon channel of the Amazon Submarine Fan, shows encouraging comparisons. The generality and shortcomings of the model assumptions are discussed based on a comparative study of mud-rich and relatively sand-rich submarine fan systems.