Non-universality of the turbulence dissipation constant in homogeneous isotropic turbulence and the universal relations which account for it
Seminar Room 1, Newton Institute
The dimensionless dissipation constant of homogeneous isotropic turbulence is equal to the third power of a number which reflects the number of large-scale eddies multiplied by a function of Reynolds number. This function of Reynolds number may tend to a constant in the limit of very high Reynolds number as a result of an eventual balance between a slow growth of the range of viscous length-scales and the increasing non-Gaussianity of the small scales. However, when the turbulence is generated by fractal grids this function of Reynolds number is inversely proportional to the Reynolds number for a very wide range of Taylor length-based Reynolds number up to about 1000 even though the turbulence energy spectrum has a well-defined -5/3 range.
Mazellier, N. & Vassilicos, J.C. 2008 The turbulence dissipation constant is not universal because of its universal dependence on large-scale flow topology. Phys. Fluids 20, 015101
Seoud, R.E. & Vassilicos, J.C. 2007 Dissipation and decay of fractal-generated turbulence. Phys. Fluid 19, 105108