An Alternative Scaling for Roughness Transitions in Turbulent Flows: The Role of the Internal Boundary Layer

TL;DR

This paper introduces a new scaling approach for roughness transitions in turbulent flows by analyzing the internal boundary layer (IBL), extending equilibrium theory to better model natural and industrial flow scenarios.

Contribution

It presents a novel extension of equilibrium theory to the nonequilibrium IBL, incorporating characteristic time-scales and velocity scales for improved modeling.

Findings

IBL height and edge velocity determine velocity profiles

The new scaling applies to various roughness transition types

Extended theory improves flow modeling accuracy

Abstract

When turbulent boundary layer flows encounter abrupt roughness changes, an Internal Boundary Layer (IBL) forms. Equilibrium theory breaks down in the nonequilibrium IBL, which may extend O(10) km for natural atmospheric flows. Here, we find that the IBL possesses a characteristic time-scale associated with the IBL height, ${\delta}_i$. We show that ${\delta}_i$ and the edge velocity set the scales of the mean and defect velocity profiles within the IBL, for simulation and experimental data covering a multitude of roughness transition types. We present a nontrivial extension of equilibrium theory to the dynamically adjusting IBL, which can be useful for modeling a range of environmental and industrial flows.