  We present an experimental investigation of intense turbulence generated by a
class of low-blockage space-filling fractal square grids. We confirm the
existence of a protacted production region followed by a decaying region, as
first reported by Hurst & Vassilicos (Physics of Fluids, 2007). We show that
the centerline streamwise variation of most of the statistical properties of
the turbulent flow can be scaled by a wake interaction length-scale $x_*$. We
also confirm the finding of Seoud and Vassilicos (Physics of Fluids, 2007) that
the ratio of the integral length-scale $L_u$ to the Taylor micro-scale
$\lambda$ remains constant in the decaying region whereas the Reynolds number
$Re_\lambda$ strongly decreases. As a result the scaling $L_{u}/\lambda \sim
Re_{\lambda}$ which follows from the $u'^{3}/L_u$ scaling of the dissipation
rate in boundary-free shear flows and in usual grid-generated turbulence does
not hold here. However, we show that the ratio $L_u/\lambda$ is an increasing
function of the inlet Reynolds number $Re_0$. This extraordinary decoupling is
consistent with a self-preserving single length-scale decaying homogeneous
turbulence proposed by George & Wang (Physics of Fluids, 2009) with which our
results are compared.
