Closure of two dimensional turbulence: the role of pressure gradients

Inverse energy cascade regime of two dimensional turbulence is investigated by means of high resolution numerical simulations. Numerical computations of conditional averages of transverse pressure gradient increments are found to be compatible with a recently proposed self-consistent Gaussian model. An analogous low order closure model for the longitudinal pressure gradient is proposed and its validity is numerically examined. In this case numerical evidence for the presence of higher order terms in the closure is found. The fundamental role of conditional statistics between longitudinal and transverse components is highlighted.