One-dimensional turbulence modelling of incompressible temporally developing turbulent boundary layers with comparison to DNS

ABSTRACT

The incompressible temporally developing turbulent boundary layer (TBL) is analysed using the map-based stochastic one-dimensional turbulence (ODT) model. The TBL is a canonical flow problem, which is, in the present study, formed by a planar moving wall and a free stream at rest. An understanding of this idealised flow is of fundamental relevance for the numerical analysis of turbulent boundary-layer-type flows. In the present ODT simulations, the flow variables are resolved on all scales along a wall-normal, one-dimensional domain. These variables are evolved by a deterministic and a stochastic process. The latter models the effect of turbulent advection and pressure fluctuations, whereas the former represents molecular diffusion. The model is appropriate for high Reynolds numbers for which the turbulence field exhibits a broad range of scales and is notionally featureless. We show that ODT is able to capture salient features of the TBL by comparing the various statistics with available reference direct numerical simulation (DNS) results for different bulk Reynolds numbers in the range $250\le R{e}_b\le 2000$ using fixed model parameters. The influence of the model parameters is analysed for $R{e}_b=1000$ and optimal parameter values are provided. The results discussed in this paper suggest that ODT is an economical and reasonably accurate approach for the simulation of transient turbulent boundary-layer-type flows.

KEYWORDS:

• One-dimensional turbulence
• stochastic modelling
• turbulent boundary layers

Acknowledgements

We thank two anonymous reviewers for their constructive criticism and detailed discussions that have improved the quality of this work.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Rakhi http://orcid.org/0000-0002-0174-4680

Marten Klein http://orcid.org/0000-0003-0609-8961

Juan A. Medina M. http://orcid.org/0000-0002-1207-9604

Heiko Schmidt http://orcid.org/0000-0002-6475-6646

Additional information

Funding

R. and H.S. acknowledge financial support from the Graduate Research School (GRS) of the BTU Cottbus-Senftenberg, Cluster StochMethod SP7, ‘Stochastic Modelling of Turbulent Flow’.