Eigensolutions of the unsteady boundary-layer equations revisited (with extensions to three-dimensional modes)Citation formats

Standard

Eigensolutions of the unsteady boundary-layer equations revisited (with extensions to three-dimensional modes). / Duck, Peter; Stephen, Sharon O.

In: Journal of Fluid Mechanics, 28.03.2021.

Research output: Contribution to journalArticlepeer-review

Harvard

APA

Vancouver

Author

Bibtex

@article{776f06191d8d4445bff7c43964993c8b,
title = "Eigensolutions of the unsteady boundary-layer equations revisited (with extensions to three-dimensional modes)",
abstract = "We consider the downstream development of small amplitude unsteady disturbances on a (Blasius) boundary layer. Two-dimensional disturbances have received much attention in the past, but herein lies an interesting conundrum, namely that two completely disparate families exist. The first, originally found by Lam & Rott and Ackerberg & Phillips, is located deep inside the boundary layer, and decay exponentially downstream with an increasingly short wavelength. The other family, originally found by Brown & Stewartson, is centred at the outer edge of the boundary layer, and exhibit slower decay than the former family. In this paper, we consider three-dimensional disturbances. Initially we mount a downstream {\textquoteleft}marching{\textquoteright} approach based on the {\textquoteleft}boundary-region{\textquoteright} equations, wherein spanwise scales are (notionally) comparable to the boundary-layer thickness. These calculations strongly suggest that disturbance growth is possible downstream, in contrast to two-dimensional disturbances that (on the streamwise lengthscales considered) all decay. We then mount a (heuristic) numerical investigation, performing a locally parallel eigenmode search at increasing downstream locations. This indicates that for two-dimensional disturbances, with increasingly downstream locations, progressively more eigenmodes evolve, that are clearly linked to the Lam & Rott and Ackerberg & Phillips family, being spawned from what appears to be the Brown & Stewartson variety. These results also clearly indicate three-dimensionality can have a profound effect on the two-dimensional modes, including the potential for downstream growth. This provides an explanation for the downstream growth witnessed in the downstream-developing calculations, and is then conclusively confirmed by (mathematically rigorous) asymptotic analyses, valid far downstream.",
author = "Peter Duck and Stephen, {Sharon O}",
year = "2021",
month = mar,
day = "28",
language = "English",
journal = "Journal of Fluid Mechanics",
issn = "0022-1120",
publisher = "Cambridge University Press",

}

RIS

TY - JOUR

T1 - Eigensolutions of the unsteady boundary-layer equations revisited (with extensions to three-dimensional modes)

AU - Duck, Peter

AU - Stephen, Sharon O

PY - 2021/3/28

Y1 - 2021/3/28

N2 - We consider the downstream development of small amplitude unsteady disturbances on a (Blasius) boundary layer. Two-dimensional disturbances have received much attention in the past, but herein lies an interesting conundrum, namely that two completely disparate families exist. The first, originally found by Lam & Rott and Ackerberg & Phillips, is located deep inside the boundary layer, and decay exponentially downstream with an increasingly short wavelength. The other family, originally found by Brown & Stewartson, is centred at the outer edge of the boundary layer, and exhibit slower decay than the former family. In this paper, we consider three-dimensional disturbances. Initially we mount a downstream ‘marching’ approach based on the ‘boundary-region’ equations, wherein spanwise scales are (notionally) comparable to the boundary-layer thickness. These calculations strongly suggest that disturbance growth is possible downstream, in contrast to two-dimensional disturbances that (on the streamwise lengthscales considered) all decay. We then mount a (heuristic) numerical investigation, performing a locally parallel eigenmode search at increasing downstream locations. This indicates that for two-dimensional disturbances, with increasingly downstream locations, progressively more eigenmodes evolve, that are clearly linked to the Lam & Rott and Ackerberg & Phillips family, being spawned from what appears to be the Brown & Stewartson variety. These results also clearly indicate three-dimensionality can have a profound effect on the two-dimensional modes, including the potential for downstream growth. This provides an explanation for the downstream growth witnessed in the downstream-developing calculations, and is then conclusively confirmed by (mathematically rigorous) asymptotic analyses, valid far downstream.

AB - We consider the downstream development of small amplitude unsteady disturbances on a (Blasius) boundary layer. Two-dimensional disturbances have received much attention in the past, but herein lies an interesting conundrum, namely that two completely disparate families exist. The first, originally found by Lam & Rott and Ackerberg & Phillips, is located deep inside the boundary layer, and decay exponentially downstream with an increasingly short wavelength. The other family, originally found by Brown & Stewartson, is centred at the outer edge of the boundary layer, and exhibit slower decay than the former family. In this paper, we consider three-dimensional disturbances. Initially we mount a downstream ‘marching’ approach based on the ‘boundary-region’ equations, wherein spanwise scales are (notionally) comparable to the boundary-layer thickness. These calculations strongly suggest that disturbance growth is possible downstream, in contrast to two-dimensional disturbances that (on the streamwise lengthscales considered) all decay. We then mount a (heuristic) numerical investigation, performing a locally parallel eigenmode search at increasing downstream locations. This indicates that for two-dimensional disturbances, with increasingly downstream locations, progressively more eigenmodes evolve, that are clearly linked to the Lam & Rott and Ackerberg & Phillips family, being spawned from what appears to be the Brown & Stewartson variety. These results also clearly indicate three-dimensionality can have a profound effect on the two-dimensional modes, including the potential for downstream growth. This provides an explanation for the downstream growth witnessed in the downstream-developing calculations, and is then conclusively confirmed by (mathematically rigorous) asymptotic analyses, valid far downstream.

M3 - Article

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -