“Analysis and Simulation of Dune Evolution: from a Dynamical System perspective”

ABSTRACT
Dunes develop whenever there is a source of granular material (like sand), wind of sufficient strength to move this material, and an “obstacle” to induce initial accumulation. These landforms have been found on Earth, Mars, and the Saturnian moon, Titan. However, as common as dunes and dune fields are, the processes associated with their morphology, dynamics, and genesis are not well understood. A thorough understanding is needed for practical reasons, such as the prediction of and fight against desertification or in studies of remotelysensed dunes.

The aim of my research is to construction a simple model which describes granular flow under the influence of wind and gravity, and which will reproduce empirical measurements of sand dunes’ behavior and morphology without impractical computational time requirements. The evolution equations in this two-dimensional dune model include the exchange of sand between “moving” and “static” layers through advective and diffusive terms, which respectively capture the aeolian transport processes and avalanches. An approximation of the wind’s shear stress over multiple interacting dunes is also computed, which is then used to compute the maximal amount of “moving” sand.

The model equations are numerically evolved and resulting dune profiles and migration speeds are compared with empirical measurements. This allows a refinement of the equation setup and evaluation of phenomenological parameters. Additionally, Dynamical Systems techniques are used to find analytical dynamic and steady-state solutions and trends. In the current simulation, sand initially coalesces into pseudo-periodic dunes at the predicted dominant wavelength. However, the lee sides of the dunes steepen quickly and avalanching becomes a dominant process, saturating the downwind slope at the angle of repose and creating an asymmetric semi-steady profile. The smaller dunes eventually run into and up the windward side of the larger dunes, causing eventual coalescence into one large dune. Investigations are continuing regarding which parameters or processes limit the height of dunes.