https://ogma.newcastle.edu.au/vital/access/ /manager/Index ${session.getAttribute("locale")} 5 https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:39305 n of the longitudinal velocity increment, (𝛿𝑢), can be described by a simple power-law 𝑟^𝜁𝑛, where the scaling exponent ζ_n depends on n and, except for 𝜁₃(=1), needs to be determined. In this Letter, we show that applying Hölder's inequality to the power-law form (𝛿𝑢)³⎯⎯⎯⎯⎯⎯⎯⎯ ∼(𝑟/𝐿) ^𝜁𝑛 (with 𝑟/𝐿≪1; L is an integral length scale) leads to the following mathematical constraint: 𝜁_2𝑝=𝑝𝜁₂. When we further apply the Cauchy–Schwarz inequality, a particular case of Hölder's inequality, to |(𝛿𝑢)³⎯⎯⎯⎯⎯⎯⎯⎯| with 𝜁₃=1, we obtain the following constraint: 𝜁₂≤2/3. Finally, when Hölder's inequality is also applied to the power-law form (|𝛿𝑢|)³⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ ∼(𝑟/𝐿)^𝜁𝑛 (this form is often used in the extended self-similarity analysis) while assuming 𝜁₃=1, it leads to 𝜁₂=2/3. The present results show that the scaling exponents predicted by the 1941 theory of Kolmogorov in the limit of infinitely large Reynolds number comply with Hölder's inequality. On the other hand, scaling exponents, except for ζ₃, predicted by current small-scale intermittency models do not comply with Hölder's inequality, most probably because they were estimated in finite Reynolds number turbulence. The results reported in this Letter should guide the development of new theoretical and modeling approaches so that they are consistent with the constraints imposed by Hölder's inequality.]]> Tue 09 Aug 2022 11:22:16 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:18223 Sat 24 Mar 2018 08:04:39 AEDT ]]>