Lack of self-similarity in transverse velocity increments and circulation statistics in two-dimensional turbulence

We study the statistics of longitudinal and transverse structure functions, as well as velocity circulation in the inverse energy cascade of two-dimensional turbulence. By means of direct numerical simulations of the incompressible Navier-Stokes equations, we show that transverse structure functions exhibit an anomalous scaling, in contrast to the self-similar behavior of longitudinal ones. We argue that the intermittency of transverse structure functions explains the one observed for velocity circulation statistics, although they are driven by different turbulent structures.