Explorations of non-locality in geomorphic systems
by
Vaughan R Voller(Civil Engineering, University of Minnesota)
→
Europe/Rome
Aula Conversi (Dip. di Fisica - Edificio G. Marconi)
Aula Conversi
Dip. di Fisica - Edificio G. Marconi
Description
Due to the presence of heterogeneities, occurring at
multiple length scales, it is reasonable to consider that the
transport of sediment in geomorphic systems, such as depositional
deltas, will exhibit non-locality, where the value of material flux at
a given point depends of landscape features removed from that point.
If the length scales of the fluvial heterogeneities (e.g. channel
lengths, sand bar dimensions) are power-law distributed, an
appropriate model for non-local transport is a diffusion-like law
expressing the flux at a point in terms of the fractional derivative
of the deposit height above a datum. Through the Caputo fractional
derivative definition, such a law can be interpreted as a weighted sum
(convolution integral) of local fluxes up and down stream of the point
of interest. In understanding the physical nature of such models it is
important to consider the (i)! influence of down verses up stream
weighting and (ii) the form of the local diffusion law. Here i! t is
shown that in order to exhibit physically realistic fluvial surface
predictions there needs to be a clear bifurcation in the direction of
the non-locality weighting between erosional and depositional systems.
Further, it is demonstrated that, in depositional systems, there is a
subtle inter-play between non-local and non-linear realizations of
diffusion transport models; a result that leads to the identification
of experimental tests that may be able to definitively isolate
non-local and non-linear effects in sediment transport systems.
