Statistics of homogeneous isotropic decaying turbulence with variable viscosity*

  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). The question 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.  The comparison is performed with respect to the decaying homogeneous isotropic turbulence with constant viscosity (CV), equal to the mean value of the variable viscosity (VV). It is shown that VV leads to an enhanced level of small-scale intermittency with respect to CV flow, which results in the presence of smaller length scales.  The effect of VV on the turbulent cascade is analyzed by a budget equation for the velocity second-order structure function. Viscosity gradients contribute to the inter-scale transport mechanism in the form of an inverse transport. The phenomenology is discussed in the context of closures of the transport term, based on  a Lagrangian approach.  The latter  takes into account contributions from the variable-viscosity interfaces.