NCED - Working Group: Modeling Surface Evolution

The objective of this workshop is to explore state-of-the-art methodologies for modeling the surface evolution of geomorphic interfaces, focusing on physical systems in which models may be verified through direct field and laboratory observations. The aim is to bring together about 20 people from diverse backgrounds to approach these problems using a combination of mathematical methods, experimental techniques and field observations. We envision that participants will fall roughly into three categories: (1) those with problems, (2) those with solutions, and (3) those with experience in solving similar problems in other fields.

The intended goal is to produce mathematical descriptions of complex morphodynamic systems. The workshop will focus on two problem areas that typify the surface evolution of geomorphic interfaces.

(1) Subaqueous and Eolian Bedforms: Bedforms are the most dynamic of river features, evolving on time scales of minutes, and controlled to a great extent by local interactions of fluid flow, sediment flux and topology.

(2) Movement of Coastlines: How do coastlines change with time in response to sediment and tectonic forcing? In contrast to bed forms coastlines evolve over significantly larger spatial and temporal scales.

Despite the change in scales both of the target systems exhibit autogenic behavior, i.e. internally developed structures and variability. Mathematical techniques that can describe autogenetic behavior will be a critical topic of the workshop. Other questions to be addressed could include: (a) What are the relationships between scale and process, and forcing and response? (b) Can an interface model describe various length scales evolving at different temporal scales? (c) Is characterization of turbulence necessary to understand the sediment/fluid interface? The methods to be considered include, but are not limited to: level set, phase-field, KPZ/BCRE, and front-tracking.

Organization

A list of relevant literature will be forwarded to all participants to allow everyone to acquaint themselves with a contained body of work on these subjects, so that everyone may come to the discussion with a range of ideas that refer to a common framework. This will allow 'people with problems' to bring real data to the workshop to motivate and verify modeling, and will give 'the people with solutions' time to think about using and modifying existing models and methods toward these ends.

Formal presentations will be limited and interactive breakout groups who will formulate problems, construct methodologies, develop solutions and report back to the main group.

At the end, we can reflect on the success of these integrated activities and discuss more general applications from the lessons learned at the workshop. It is our hope that the structure presented here can limit scope without limiting creativity. Using several concrete physical systems to guide model development will hopefully facilitate self-organization rather than chaos.

The MIT Morphodynamics Laboratory has facilities that allow demonstration of subaqueous bed evolution in real time. The workshop will take place on MIT's campus in a computer laboratory with 4 available work stations, and guests are encouraged to bring their own laptop computers. Projectors will be provided. Travel and lodging expenses will be covered by the National Center for Earth-surface Dynamics.

Some suggested reading:

Bouchaud, J.P., M.E. Cates, J. Ravi Prakrash and S.F. Edwards, Hysteresis and metastability in a continuum sandpile model, Phys. Rev. Lett., 74(11), 1982-1985, 1995.

Prigozhin, L. Nonlinear dynamics of Aeolian sand ripples, Phys. Rev. E, 60(1), 729-733, 1999.

Schwammle, V. and H.J. Hermann, A model of Barchan dunes including lateral shear stress, arXiv:cond-mat/0304695 v2 2 May, 2003.

Terzidis, O., P. Claudin and J.P. Bouchaud, A model for ripple instabilities in granular media., Euro. Phys. J. B, 5, 245-249, 1998.