A Minimalist Turbulent Boundary Layer Model

TL;DR

This paper presents a simple vortex-based model of turbulent boundary layers that captures key flow features and offers insights into drag reduction phenomena, bridging theoretical modeling with experimental observations.

Contribution

It introduces a minimalist vortex model that reproduces essential turbulent boundary layer features and explores implications for drag reduction by polymers.

Findings

Reproduces viscous and logarithmic boundary sublayers.

Captures statistical moments of velocity fluctuations.

Provides heuristic insights into drag reduction mechanisms.

Abstract

We introduce an elementary model of a turbulent boundary layer over a flat surface, given as a vertical random distribution of spanwise Lamb-Oseen vortex configurations placed over a non-slip boundary condition line. We are able to reproduce several important features of realistic flows, such as the viscous and logarithmic boundary sublayers, and the general behavior of the first statistical moments (turbulent intensity, skewness and flatness) of the streamwise velocity fluctuations. As an application, we advance some heuristic considerations on the boundary layer underlying kinematics that could be associated with the phenomenon of drag reduction by polymers, finding a suggestive support from its experimental signatures.