  The decay of homogeneous isotropic turbulence in a variable viscosity fluid
with a viscosity ratio up to 15 is analyzed by means of highly resolved direct
numerical simulations (DNS) at low Reynolds numbers. The question addressed by
the present work is how quantities such as the kinetic energy and the
associated dissipation rate, as well as the inter-scale transport mechanism of
turbulence are changed by local fluctuations of the viscosity. From the
one-point budget equation of the turbulent kinetic energy, it is shown that the
mean dissipation rate is nearly unchanged by variable viscosity effects. This
result is explained by a negative correlation between the local viscosity and
the local velocity gradients. However, the dissipation is a highly fluctuating
quantity with a strong level of intermittency. From a statistical analysis it
is shown that turbulent flows with variable viscosity are characterized by an
enhanced level of small-scale intermittency, which results in the presence of
smaller length scales and a modified turbulent mixing. The effect of variable
viscosity on the turbulent cascade is analyzed by a budget equation for the
velocity structure function. From DNS it is shown that viscosity gradients
contribute to the inter-scale transport mechanism in the form of an inverse
transport, where information propagates from the small scales to the large
scales.
