A Continuum Model for Wind-Blown Sand Dune Field Dynamics

The dynamics of fields of wind-blown sand dunes reflects changing pattern characteristics such as spatially varying dune spacing and dune orientation and the impact of evolving aspects of the external environment, such as wind direction, sand supply, groundwater table and vegetation. However, models for patterns within sand dune fields almost exclusively focus on short-to-intermediate morphological dynamics resolved on sub-dune scales , dynamically far removed from the long time scales characterizing evolving patterns of dune fields. To address the disconnect between dune field dynamics and dune field models, I describe a continuum model that includes 1) three primary dune-field variables, crestline orientation, crestline spacing and density of crestline terminations, or defect density, as field variables varying in two-dimensional space and in time; 2) dynamics for these three field variables based on existing models that treat crestline reorientation as resulting from differential migration of oppositely facing crestline terminations, or defects and crestline spacing growth as resulting from migration of defects, moving faster than crestlines, through the dune field; and 3) secondary field variables representing the orientation, spacing and defect density of superimposed dunes that can form on top of large primary dunes. The model reproduces spatial pattern characteristics of the Algodones and White Sands dune fields using hypothesized wind and sand supply histories.