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. Using 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 derive an analytical relation that shows that the scaling exponents of transverse structure functions and velocity circulation are related in two-dimensional turbulence.