The influence of energy-containing scales on the distribution of spectral energy transfers

TL;DR

The paper addresses how energy-containing scales shape the distribution of spectral energy transfers in homogeneous isotropic turbulence by computing direct mode-to-mode transfers from DNS and introducing a mode-energy potential $Q(\bm{\kappa}, \bm{\kappa}')$ to predict intense transfer regions. It contrasts two locality concepts and leverages an EDQNM-based estimator $\hat{H}$ to benchmark detailed triad transfers, showing strong agreement in pattern and confirming a forward, scale-local cascade when shells are aggregated. A key finding is that the region of strongest transfers is governed by the spectral location of the energy-containing range rather than the intrinsic local/nonlocal nature of the triad, reframing nonlocal triads as catalyzed by energy-containing modes. The study further demonstrates how forcing at intermediate scales creates ring-like transfer structures around the sampling point and identifies residual nonlocal transfers near the ECR, offering refined insight into turbulence locality and potential improvements for spectral models.

Abstract

We present computations of individual mode-to-mode energy transfers from direct numerical simulations of homogeneous isotropic turbulence. Unlike previous approaches based on shell-filtered velocity fields, this method distinguishes between the energy exchanged by each pair of modes within a triad. We introduce a potential function based on the energy content of the modes involved and show that it predicts the distribution of intense energy transfers in the vicinity of the sampling mode considered. By performing simulations with forcing applied at intermediate wavenumbers, we demonstrate that the region of most intense transfers is determined by the spectral location of the energy-containing scales rather than by the local or nonlocal character of the triad. Direct energy exchanges with the energy-containing range are suppressed by geometric constraints from the divergence-free condition, but persist as residuals when the sampling mode is close to the energy-containing scales. The comparison with an estimator derived from EDQNM theory shows good agreement and recovers the forward, scale-local nature of energy transfer consistent with the cascade picture.

Figures (20)

• Figure 1: Scale-local energy transfer (ET) within a local interaction (a) and nonlocal interaction (b).
• Figure 2: Model kinetic spectrum with energy at largest scales (a), resulting mode-to-mode potential $\hat{Q}$ (b) and in log scale to show the decay of potential (c). Note that (c) is centered around $\kappa_{x}/2$ to highlight the symmetry of $\hat{Q}$.
• Figure 3: Distinction within a triad interaction with a mode in the energy containing range of the catalytic and reactingmode-to-mode energy transfers (ET)
• Figure 4: (a) Potential $\hat{Q}$ and (b) EDQNM estimator $\hat{H}$ computed from the model spectrum for $\bm{\kappa} = [200,0]$.
• Figure 5: Function $\hat{f}$ (a) and factor $b$ (b) from EDQNM estimator computed from the model spectrum for $\bm{\kappa} = [200,0]$.