Lagrangian velocity structure functions in Bolgiano turbulence

Single-particle Lagrangian velocity statistics in the Bolgiano--Obukhov regime of two-dimensional turbulent convection is investigated. At variance with flows displaying the classical K41 phenomenology, here, the leading contribution to the Lagrangian velocity fluctuations is given by the largest eddies. This implies a linear behavior in time for a typical velocity fluctuation in the time interval $t$. The contribution to the Lagrangian velocity fluctuations of local eddies (i.e. with a characteristic time of order $t$), whose space/time scalings are ruled by the Bolgiano--Obukhov theory, is thus not detectable by standard Lagrangian statistical observables. To disentangle contributions arising from the large eddies from those of local eddies, a strategy based on exit-time statistics has successfully been exploited. Lagrangian velocity increments in Bolgiano convection thus provide a physically relevant example of signal with \emph{more than smooth} fluctuations.