Fusion rules in navier-stokes turbulence: First experimental tests

We present the first experimental tests of the recently derived fusion rules for Navier-Stokes turbulence. The fusion rules address the asymptotic properties of many-point correlation functions as some of the coordinates coalesce, and form an important ingredient of the nonperturbative statistical theory of turbulence. Here we test the fusion rules when the spatial separations lie within the inertial range, and find good agreement between experiment and theory. For inertial-range separations and for velocity increments which are not too large, a simple linear relation appears to exist for the Laplacian of the velocity fluctuation conditioned on velocity increments.