Homogeneity and isotropy in a laboratory turbulent ﬂow
Evan A. Variano
Received: 6 February 2013 / Revised: 11 October 2013 / Accepted: 10 December 2013 / Published online: 22 December 2013
Ó Springer-Verlag Berlin Heidelberg 2013
Abstract We present a new design for a stirred tank that
is forced by two parallel planar arrays of randomly actuated
jets. This arrangement creates turbulence at high Reynolds
number with low mean ﬂow. Most importantly, it exhibits a
region of 3D homogeneous isotropic turbulence that is
signiﬁcantly larger than the integral lengthscale. These
features are essential for enabling laboratory measurements
of turbulent suspensions. We use quantitative imaging to
conﬁrm isotropy at large, small, and intermediate scales by
examining one- and two-point statistics at the tank center.
We then repeat these same measurements to conﬁrm that
the values measured at the tank center are constant over a
large homogeneous region. In the direction normal to the
symmetry plane, our measurements demonstrate that the
homogeneous region extends for at least twice the integral
length scale L = 9.5 cm. In the directions parallel to the
symmetry plane, the region is at least four times the inte-
gral lengthscale, and the extent in this direction is limited
only by the size of the tank. Within the homogeneous
isotropic region, we measure a turbulent kinetic energy of
6.07 9 10
, a dissipation rate of 4.65 9
, and a Taylor-scale Reynolds number of
= 334. The tank’s large homogeneous region, com-
bined with its high Reynolds number and its very low mean
ﬂow, provides the best approximation of homogeneous
isotropic turbulence realized in a laboratory ﬂow to date.
These characteristics make the stirred tank an optimal
facility for studying the fundamental dynamics of turbu-
lence and turbulent suspensions.
Homogeneous isotropic turbulence (HIT) is an idealized
ﬂow of special interest because it contains all of the basic
physical processes of turbulence without the complications
commonly found in nature such as mean shear, density
stratiﬁcation, and ﬂuid–solid boundaries (Tsinober 2004).
Thus, HIT is an ideal ﬂow with which to understand some
of the fundamental mechanisms of turbulence that are at
least qualitatively independent of the origin of a speciﬁc
turbulent ﬂow such as internal intermittency (Douady et al.
1991); the self-ampliﬁcation mechanisms of velocity
derivatives (Galanti and Tsinober 2000); inertial range
Eulerian and Lagrangian structure functions (Benzi et al.
2010); and (of particular interest to us) interphase coupling
mechanisms in turbulent suspensions (Poelma and Ooms
2006; Lucci et al. 2010; Balachandar and Eaton 2010;
Toschi and Bodenschatz 2009).
Despite the simplicity of HIT, it is non-trivial to recreate
this condition in a laboratory experiment or in a direct
numerical simulation (DNS). In DNS, turbulence either
decays with time or must be sustained via an artiﬁcial
forcing in space or time that introduce biases in the tur-
bulent statistics (Abdelsamie and Lee 2012; Lucci et al.
2010). Turbulent ﬂows in laboratory experiments, on the
other hand, are intrinsically inhomogeneous because it is
impossible in practice to uniformly distribute turbulent
production. At best, laboratory devices can only approxi-
mate HIT. In doing so, there has typically been a trade-off
between Reynolds number and the size of the HIT region.
Herein, we present a new design for a stirred tank that
G. Bellani (&) Á E. A. Variano
Department of Civil and Environmental Engineering, University
of California, Berkeley, CA 94720, USA
Exp Fluids (2014) 55:1646