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Main Authors: Dey, Anwesha, Mukherjee, Ritwik, Banerjee, Aikya, Ray, Samriddhi Sankar
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2605.19921
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author Dey, Anwesha
Mukherjee, Ritwik
Banerjee, Aikya
Ray, Samriddhi Sankar
author_facet Dey, Anwesha
Mukherjee, Ritwik
Banerjee, Aikya
Ray, Samriddhi Sankar
contents We investigate two-point velocity-gradient correlation functions in homogeneous isotropic turbulence using exact relations and direct numerical simulations. The second-order gradient correlation is shown to be exactly related to the Laplacian of the velocity correlation, implying inertial-range scaling $C_2^{1,1}(r)\sim r^{-4/3}$. At higher orders, we uncover a parity-dependent organization of gradient correlations: odd-odd correlations exhibit scaling close to $r^{-4/3}$ with weak dependence on order, whereas even-even correlations display systematically different exponents. We show that this distinction originates from the sign structure of the gradient field: sign decorrelation suppresses intermittent contributions in odd-odd sectors, while even-even correlations retain them and remain sensitive to the spatial organization of intense structures. The measured even-even exponents are quantitatively consistent, across two Reynolds numbers, with independently measured box-counting dimensions of intermittent gradient structures. These results identify parity under sign reversal as a fundamental organizing principle for higher-order turbulent correlations and establish a direct connection between sparse intermittent geometry and scaling exponents in turbulence.
format Preprint
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institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Parity-Dependent Scaling of Velocity-Gradient Correlations in Turbulence
Dey, Anwesha
Mukherjee, Ritwik
Banerjee, Aikya
Ray, Samriddhi Sankar
Fluid Dynamics
We investigate two-point velocity-gradient correlation functions in homogeneous isotropic turbulence using exact relations and direct numerical simulations. The second-order gradient correlation is shown to be exactly related to the Laplacian of the velocity correlation, implying inertial-range scaling $C_2^{1,1}(r)\sim r^{-4/3}$. At higher orders, we uncover a parity-dependent organization of gradient correlations: odd-odd correlations exhibit scaling close to $r^{-4/3}$ with weak dependence on order, whereas even-even correlations display systematically different exponents. We show that this distinction originates from the sign structure of the gradient field: sign decorrelation suppresses intermittent contributions in odd-odd sectors, while even-even correlations retain them and remain sensitive to the spatial organization of intense structures. The measured even-even exponents are quantitatively consistent, across two Reynolds numbers, with independently measured box-counting dimensions of intermittent gradient structures. These results identify parity under sign reversal as a fundamental organizing principle for higher-order turbulent correlations and establish a direct connection between sparse intermittent geometry and scaling exponents in turbulence.
title Parity-Dependent Scaling of Velocity-Gradient Correlations in Turbulence
topic Fluid Dynamics
url https://arxiv.org/abs/2605.19921