Passive scalar cascade in the intermediate layer of turbulent channel flow for $Pr\leq 1$

TL;DR

This paper investigates the scale-by-scale behavior of passive scalar and velocity fields in turbulent channel flow at low Prandtl numbers, revealing asymptotic equilibria and Prandtl number-dependent scaling laws through simulations and asymptotic analysis.

Contribution

It introduces a novel analysis of scalar and velocity field equilibria in turbulence, highlighting Prandtl number effects and scale-dependent transfer and dissipation rates.

Findings

Scalar and velocity fields reach scale-by-scale equilibrium asymptotically.

The length scale of equilibrium and transfer ratios follow power laws of Prandtl number.

Differences in transfer contributions are evident when considering aligned/anti-aligned components.

Abstract

Similarities and differences between Kolmogorov scale-by-scale equilibria/non-equilibria for velocity and scalar fields are investigated in the intermediate layer of a fully developed turbulent channel flow with a passive scalar/temperature field driven by a uniform heat source. The analysis is based on intermediate asymptotics and direct numerical simulations at different Prandtl numbers lower than unity. Similarly to what happens to the velocity fluctuations, for the fluctuating scalar field Kolmogorov scale-by-scale equilibrium is achieved asymptotically around a length scale $r_{min}$, which is located below the inertial range. The lengthscale $r_{min}$ and the ratio between the inter-scale transfer and dissipation rates at $r_{min}$ vary following power laws of the Prandtl number, with exponents determined by matched asymptotics based on the hypothesis of homogeneous two-point physics in non-homogeneous turbulence. The interscale transfer rates of turbulent kinetic energy and passive scalar variance are globally similar but show evident differences when their aligned/anti-aligned contributions are considered.