Analytical Model of the Time Developing Turbulent Boundary Layer

TL;DR

This paper introduces the first analytical model for the time-developing turbulent boundary layer over a flat plate, providing explicit formulas for key flow properties and validating them against DNS data.

Contribution

The paper presents a novel analytical model for TD-TBL that explicitly describes temporal and spatial flow profiles, filling a gap in turbulence modeling.

Findings

Profiles agree well with DNS data at Re_θ=1430 and 2900.

Provides explicit formulas for wall-shear stress and velocity distributions.

First analytical model for time-developing turbulent boundary layer.

Abstract

We present an analytical model for the time-developing turbulent boundary layer (TD-TBL) over a flat plate. The model provides explicit formulae for the temporal behavior of the wall-shear stress and both the temporal and spatial distributions of the mean streamwise velocity, the turbulence kinetic energy and Reynolds shear stress. The resulting profiles are in good agreement with the DNS results of spatially-developing turbulent boundary layers at momentum thickness Reynolds number equal to 1430 and 2900. Our analytical model is, to the best of our knowledge, the first of its kind for TD-TBL.