Breakdown of Kolmogorov's first similarity hypothesis in grid turbulence

Kolmogorov's first similarity hypothesis (or KSH1) stipulates that two-point statistics have a universal form which depends on two parameters, the kinematic viscosity ν and the mean energy dissipation rate ⟨e⟩. KSH1 is underpinned by two assumptions: the Reynolds number is very large and local isotropy holds. To disentangle the intricacies of these two requirements, we assess the validity of KSH1 in a flow where local isotropy is a priori tenable, i.e. decaying grid turbulence. The main question we address is how large should the Reynolds number be for KSH1 to be valid over a range of scales wider than, say, five Kolmogorov scales. To this end, direct numerical simulations based on the lattice Boltzmann method are carried out in low Reynolds number grid turbulence. The results show that when the Taylor microscale Reynolds number Rλ drops below about 20, the Kolmogorov normalised spectra deviate from those at higher Rλ; the deviation increases with decreasing Rλ. It is shown that at Rλ ≃ 20, the contributi...