Reduction of Triadic Interactions Suppresses Intermittency and Anomalous Dissipation in Turbulence

Abstract

We investigate how the defining statistical features of three-dimensional turbulence respond to systematic reductions of the Fourier-space triadic interaction network. Using direct numerical simulations of both fractally and homogeneously decimated Navier-Stokes dynamics, we show that progressive thinning of the set of active modes leads to a systematic suppression of intermittency and, most strikingly, to the vanishing of the mean dissipation rate in the large-Reynolds-number limit. Structure-function exponents collapse onto their dimensional values, the multifractal singularity spectrum contracts, and the analyticity width extracted from the exponential spectral tail increases monotonically with decimation-each indicating a substantial regularization of the velocity field. Together, these results provide direct evidence that anomalous dissipation in incompressible turbulence is not a generic property of the Navier-Stokes equations, but instead requires the full combinatorial richness of their triadic nonlinear interactions.

Figures (6)

• Figure 1: Pseudo-color plots of the energy dissipation field $\varepsilon$ on a two-dimensional slice for (a) the undecimated case $\rho=1$ and (b) a homogeneously decimated flow with $\rho=0.5$, shown on a logarithmic color scale. Decimation suppresses the intense filamentary structures characteristic of intermittent three-dimensional turbulence, resulting in a smoother dissipation field. (c) Probability density functions of $\langle \varepsilon \rangle$ for increasing decimation, showing a transition from log-normal to exponential tails. (Inset) PDFs of the longitudinal strain-rate component $S_{xy}$ approaching a Gaussian form with increasing decimation.
• Figure 2: Mean dissipation rate $\varepsilon$ versus the Taylor-scale Reynolds number $Re_\lambda$ for different levels of Fourier decimation, compared with the undecimated three-dimensional Navier--Stokes case. With increasing decimation, $\varepsilon$ decreases systematically with $Re_\lambda$, indicating a breakdown of dissipative anomaly. The black dashed line represent the parameterized dissipative anomaly curve DONZIS_SREENIVASAN_YEUNG_2005Cannon_Marco_2024. (Inset) Probability density functions of the vorticity--strain interaction (vorticity production) for selected decimation levels, illustrating the suppression of extreme vortex-stretching events.
• Figure 3: Ratios $\zeta_p/p$ of longitudinal equal-time structure-function exponents as a function of order $p$ for different levels of homogeneous and fractal Fourier decimation (see legend). The undecimated case exhibits clear departures from the dimensional prediction $\zeta_p/p = 1/3$, while increasing decimation leads to a progressive collapse toward the dimensional value. (Inset) Hyperflatness of the PDFs of longitudinal velocity increments at inertial-range separations, approaching the Gaussian value 15 with increasing decimation.
• Figure 4: Singularity spectra $f(\alpha)$ obtained from a multifractal analysis of the dissipation field for different levels of decimation. The undecimated case exhibits a broad spectrum, whereas increasing decimation leads to a systematic narrowing, indicating a progressive loss of multifractality.
• Figure 5: Analyticity width $\delta$ as a function of the decimation parameter (either $D$ or $\rho$, see legend), extracted from the exponential decay of the statistically steady energy spectra. The monotonic increase of $\delta$ with decimation indicates a widening of the analyticity strip and a progressively smoother flow. (Inset) Kolmogorov constant as a function of decimation.