  A flow generator is described in which homogeneous axisymmetric turbulent air
flows with varying and fully controllable degrees of anisotropy, including the
much studied isotropic case, are generated by the combined agitations produced
by 32 acoustic mixers focusing at the center of the system. The axisymmetric
turbulence in a central volume of the size of the inertial scale is shown to
have negligible mean and shear. The Taylor Reynolds number is about 480.
  The influence of large scale anisotropy on the turbulence is examined from
three aspects, namely the velocity structure functions, the velocity
correlation functions, and the integral lengths. The directional dependence of
two different second order transverse structure functions, in which one of them
has separations stretched along the axis of symmetry of the turbulence and the
other one normal to it, is studied. It is shown that the inertial range scaling
exponents, determined using the extended-self-similarity procedure, and the
Kolmogorov constants of the two structure functions are unaffected by the
direction in which the structure functions are measured.
  Finally, it is found that, except in the isotropic case, the second order
transverse velocity correlation functions deviate from each other at the large
scale with increasing anisotropy. A self-similarity argument similar to one
found in the study of critical phenomena is proposed. It is shown that the
argument leads to a power-law relationship between the large scale velocity
fluctuation and the correlation length, with an exponent that depends on the
inertial range scaling exponent of the turbulence. The data collapse predicted
by the self-similarity hypothesis is verified. It is demonstrated that the
value of the power-law exponent is consistent with the value of the inertial
range scaling exponent.
