# Energy Spectra and Fluxes in Dissipation Range of Turbulent and Laminar Flows

## TL;DR

This paper uses high-resolution simulations to analyze energy spectra and fluxes in turbulent and laminar flows, validating existing models for turbulence and proposing a new model for laminar flow energy spectra.

## Contribution

It provides a comprehensive numerical validation of turbulence models and introduces a novel spectral model for laminar flows.

## Key findings

- Numerical results agree with Pao and Pope models for turbulence.
- Proposed laminar flow model accurately predicts energy spectra and fluxes.
- Distinct energy transfer mechanisms identified: local in turbulence, nonlocal in laminar flows.

## Abstract

Two well-known turbulence models that describe the energy spectrum in the inertial and dissipative ranges simultaneously are by Pao~(1965) and Pope~(2000). In this paper, we compute the energy spectrum $E(k)$ and energy flux $\Pi(k)$ using direct numerical simulations on grids up to $4096^3$, and show consistency between the numerical results and the predictions by the aforementioned models. We also construct a model for laminar flows that predicts $E(k)\sim k^{-1} \exp(-k)$ and $\Pi(k)\sim k \exp(-k)$. Our model predictions match with the numerical results. We emphasize differences on the energy transfers in the two flows---they are {\em local} in the turbulent flows, and {\em nonlocal} in laminar flows.