  We introduce the velocity (Vs) of stagnation points as a means to
characterise and measure statistical persistence of streamlines. Using
theoretical arguments, Direct Numerical Simulations (DNS) and Kinematic
Simulations (KS) of three-dimensional isotropic turbulence for different ratios
of inner to outer length scales L/eta of the self-similar range, we show that a
frame exists where the average <Vs>=0, that the r.m.s. values of acceleration
(a'), turbulent fluid velocity (u') and Vs are related by La'/(u'^2) ~
(Vs/u')(L/eta)^(2/3+q) and that Vs/u' ~ (L/eta)^q with q=-1/3 in Kolmogorov
turbulence, q=-1/6 in current DNS and q=0 in our KS. The statistical
persistence hypothesis is closely related to the Tennekes sweeping hypothesis.
