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A multifractal equivalent of the Beaufort scale for sea‐state
Author(s) -
Kerman Bryan R.
Publication year - 1993
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/93gl00049
Subject(s) - multifractal system , fractal , statistical physics , singularity , physics , gravitational singularity , mathematics , mathematical analysis
It is reported here that the ocean surface under a sufficiently high wind is a multi‐fractal process, consisting of breaking wave singularities. It has been argued elsewhere that the singularity strength associated with individual breaking waves implies a distinct energy state within a continuum of such states whose entropy is associated with a fractal dimension. When the multi‐fractal process is modelled in the simplest, non‐trivial multiplicative energy flux cascade – as a Besicovitch‐Cantor process – 3 independent variables are required for a full description. It is shown that when a closure assumption is invoked which relates the 2 sub‐process energy fluxes as a power‐law in their respective receiving areas (the process' support), the 2 exponents involved are remarkably constant within the experimental variation arising from different aircraft imaging sorties over different sea states. The result is a reduction of complexity from 3 to just 1 independent variable to describe any realization; this parameter is referred to as the multi‐fractal equivalent of the Beaufort scale.