How winding is the coast of Britain? Conformal invariance of rocky shorelines

Abstract

[1] We show that rocky shorelines with fractal dimension 4/3 are conformally invariant curves by measuring the statistics of their winding angles from global high-resolution data. Such coastlines are thus statistically equivalent to the outer boundary of the random walk and of percolation clusters. A simple model of coastal erosion gives an explanation for these results. Conformal invariance allows also to predict the highly intermittent spatial distribution of the flux of pollutant diffusing ashore. Citation: Boffetta, G., A. Celani, D. Dezzani, and A. Seminara (2008), How winding is the coast of Britain? Conformal invariance of rocky shorelines, Geophys. Res. Lett., 35, L03615,

Power law statistics of cliff failures, scaling and percolation

“…This makes our model an example of what is called 'self-organized criticality' (see the book by Bak, 1996). Note that the connection between percolation and coast geometries has been recently invoked on totally different grounds by independent studies (Boffetta et al, 2008;Saberi, 2013).…”

Descriptors for sea surface temperature front regularity characterization

“…Though not being perfect as in the example considered by Boffeta et al [9], the fit to the conformally invariant model depicts a satisfactory correlation. It should be stressed that theoretical work addressing turbulence dynamics exploited highresolution observation.…”

“…used this property to show that the rocky shorelines of Brittany are conformally invariant [9]. Though not being perfect as in the example considered by Boffeta et al [9], the fit to the conformally invariant model depicts a satisfactory correlation.…”

Mesoscale coastal complexity and its relationship to structure and forcing from marine processes

“…A substantial amount of research has gone into quantifying coastal complexity (Goodchild and Mark, 1987;Andrle, 1996b;Bishop and Cowell, 1997;Jiang and Plotnick, 1998;Zhu et al, 2000;Bartley et al, 2001;Dai et al, 2004;Finkl, 2004;D'Alessandro et al, 2006;Valvo et al, 2006;Boffetta et al, 2007). Nevertheless, there are many hypotheses as to why some coasts are complex while others are not.…”