Conditional eddies in isotropic turbulence

Isotropic turbulence is examined for the existence of conditional flow structures by computing estimates of the velocity u(x + r, t) given that the velocity at (x, t) assumes some specified value, u(x, t). In general, the best mean-square estimate of u(x + r, t) is the conditional average 〈u(x + r, t)| u(x, t)〉. This quantity is approximated in terms of second- and third-order two-point spatial correlations using nonlinear estimation techniques. The estimate predicts conditional eddies that are vortex rings axisymmetric about the direction of u(x, t). Averaging these estimates over all values of u(x, t) yields two-point moments that are correct through third order.