Fig. 4: Analysis of structure functions.
From: Scaling and intermittency in turbulent flows of elastoviscoplastic fluids
a, Dependence of the longitudinal velocity structure functions S2 (pluses), S4 (squares) and S6 (hexagons) on separation distance r. Symbol colour denotes BiΛ and is the same as in Fig. 2. Dashed lines show scalings predicted by K41, and dash-dotted lines show scalings predicted using the new non-Newtonian scaling E ~ κ−2.3. b, The two scalings collapse onto a single line when we plot the structure functions S4 and S6 in extended self-similarity form, that is, against S2. To easily see changes in gradient, we have normalized the structure functions by their values at r ≈ Λ. The dotted line shows a best fit through the data for BiΛ = 0, which deviates from the K41 prediction (dashed line) due to intermittency. Increasing BiΛ further increases this deviation. The inset in b reports the multifractal spectrum of the energy dissipation rate carried out by the fluid ϵf.
