Singular instabilities (collapses) and multifractality of structure functions in turbulence

(Received 4 November 1993, received in final 27 December 1993, accepted 17 January 1994)

Abstract
It is argued that the multifractality of higher order structure functions arises as a result of local singular instabilities (collapses) in 3D-turbulence.The modified Landau approach (with poles) is used for studying supercritical instability in this case. For the simplest situation (pole of order two), the asymptotic behavior of the structure functions is investigated. The arguments are supported by comparison with experimental data from laboratory and geophysical experiments.