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<p>Based on the symmetry-theoretical analysis of the infinite hierarchy of multi-point moment equations, we rigorously derive the self-similar structure of velocity moments of arbitrary order in the turbulent round jet. Therein, we discover the dependency on a new parameter in the axial scaling laws. It has its roots in the statistical scaling symmetry which is connected to intermittency. This new parameter allows different states of self-similarity depending on the inflow condition, as postulated by George (in Arndt, R., George, W.K. (eds), Advances in Turbulence, pp. 39–73, 1989). However, the comparison with data fixes this parameter to zero, i.e. the classical scaling is recovered. Hence, intermittent effects are hidden when only considering the axial scaling laws. However, the influence of intermittency is still visible in the self-similar radial profiles. We find that a Gaussian-type curve fits the self-similar radial profiles of moments of arbitrary order of the axial velocity with high accuracy. The prefactors in the Gauss-function exponent exhibit a clear nonlinear dependency on the moment order, significantly deviating from a dimensional scaling. We attribute this to external or large-scale intermittency, which is likewise visible in the velocity PDF with increasing distance from the axis as we have found in a previous work (Nguyen and Oberlack, Phys. Rev. Fluids. 9(7), 074608, 2024). Furthermore, the statistical scaling symmetry reappears in the symmetry properties of the equations giving rise to the Gaussian profiles.</p>

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Hidden Intermittency in Turbulent Jet Flows

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  • 发表日期：

    2025年7月28日

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  • Cat Tuong Nguyen,
  • Nils Benedikt,
  • Martin Oberlack

摘要

Based on the symmetry-theoretical analysis of the infinite hierarchy of multi-point moment equations, we rigorously derive the self-similar structure of velocity moments of arbitrary order in the turbulent round jet. Therein, we discover the dependency on a new parameter in the axial scaling laws. It has its roots in the statistical scaling symmetry which is connected to intermittency. This new parameter allows different states of self-similarity depending on the inflow condition, as postulated by George (in Arndt, R., George, W.K. (eds), Advances in Turbulence, pp. 39–73, 1989). However, the comparison with data fixes this parameter to zero, i.e. the classical scaling is recovered. Hence, intermittent effects are hidden when only considering the axial scaling laws. However, the influence of intermittency is still visible in the self-similar radial profiles. We find that a Gaussian-type curve fits the self-similar radial profiles of moments of arbitrary order of the axial velocity with high accuracy. The prefactors in the Gauss-function exponent exhibit a clear nonlinear dependency on the moment order, significantly deviating from a dimensional scaling. We attribute this to external or large-scale intermittency, which is likewise visible in the velocity PDF with increasing distance from the axis as we have found in a previous work (Nguyen and Oberlack, Phys. Rev. Fluids. 9(7), 074608, 2024). Furthermore, the statistical scaling symmetry reappears in the symmetry properties of the equations giving rise to the Gaussian profiles.