Geometry of intermittency in fully developed turbulence

A geometrical interpretation of intermittency in fully developed turbulence is realized through an hierarchy of fractal structures Omega(p), of dimensions Delta(p) linked each other by the relations Omega(p+1) subset of Omega(p) (i.e Delta(p+1) < Delta(p)) and gamma = (Delta(p+1) - Delta(infinity))/(Delta(p) - Delta(infinity)) with gamma = ((1 + 3/root 8)(1/3) + (1 - 3/root 8)(1/3))(3) and Delta(infinity) = 1 . This is obtained by the introduction of an entropy jump, defined at the scale r, Delta S-p(r) = ( Delta(p+1) - Delta(p)) In ( r/r(0)) characterizing the order level of each sub-structure Omega(p) and verifying a linear relation Delta S-p(r) = y Delta Sp-1(r). (C) 1999 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.