The thin blue line: A review of shoreline dynamics across time scales and environments

A major thread of theoretical research on the response of shorelines to changing boundary conditions has adapted the moving-boundary approach from heat transfer and solidification/melting. On sufficiently short time scales, shorelines respond to changes in relative sea level in a simple, geometrically predictable way. On longer time scales, their behaviour becomes far more complex and interesting, because the surface over which the shoreline moves is itself continually modified by morphodynamics that depend sensitively on shoreline location. This makes the shoreline the archetype of moving-boundary problems in morphodynamics, and subject to potentially counterintuitive behaviours over time scales on which the sediment surface modifies itself as relative sea level changes. We review existing moving-boundary theories and propose two significant extensions to allow inclusion of first-order effects of waves and tides. First, we show how wave effects can be included via planform diffusion linked to river-mouth location, which results in shoreline smoothing during delta-lobe growth and localized transgression after channel abandonment. Tides produce a low-gradient region in which the sea and land overlap; we show how this can be treated in a moving-boundary framework by replacing the shoreline with a ‘mushy region' so that the handoff from land to water occurs over a zone rather than a line. We also propose that the moving-boundary approach can be readily generalized to other dynamic moving boundaries, such as those separating different regimes of river transport. The shoreline thus serves as a prototype for modelling dynamic facies boundaries along the whole source–sink system.