Experimental evaluation of acceleration correlations for locally isotropic turbulence

Abstract

The two-point correlation of the fluid-particle acceleration is the sum of the pressure gradient and viscous force correlations. The pressure-gradient correlation is related to the fourth-order velocity structure function. The acceleration correlation caused by viscous forces is formulated in terms of the third-order velocity structure function. Velocity data from grid-generated turbulence in a wind tunnel are used to evaluate these quantities. The evaluated relationships require only the Navier-Stokes equation, incompressibility, local homogeneity, and local isotropy. The relationships are valid for any Reynolds number. For the moderate Reynolds number of the wind-tunnel turbulence, the acceleration correlation is roughly three times larger than if it is evaluated on the basis of the assumption that velocities at several points are joint Gaussian random variables. The correlation of components of acceleration parallel to the separation vector of the two points is negative near its minimum at spacings close to 17 times the microscale. Its value near this minimum implies that fluid particles at those spacings have typical relative accelerations of one-half that of gravity in the directions toward and away from one another. For large Reynolds numbers, the two-point correlation of acceleration is dominated by the two-point correlation of the pressure gradient. The data verify that the acceleration correlation caused by viscous forces is much smaller than that caused by the pressure gradient.