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Eigensolutions of the unsteady boundary-layer equations revisited (with extensions to three-dimensional modes)
| Content Provider | Scilit |
|---|---|
| Author | Duck, Peter W. Stephen, Sharon O. |
| Copyright Year | 2021 |
| Description | 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 decays 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 exhibits 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 length scales 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. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/2458FF225879807BF183B71123D6EBAC/S0022112021003153a.pdf/div-class-title-eigensolutions-of-the-unsteady-boundary-layer-equations-revisited-with-extensions-to-three-dimensional-modes-div.pdf |
| ISSN | 00221120 |
| e-ISSN | 14697645 |
| DOI | 10.1017/jfm.2021.315 |
| Journal | Journal of Fluid Mechanics |
| Volume Number | 917 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2021-06-25 |
| Access Restriction | Open |
| Subject Keyword | Journal of Fluid Mechanics Fluids and Plasmas Physics Boundary Layer Receptivity Boundary Layer Stability Transition To Turbulence |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Mechanics of Materials Condensed Matter Physics Mechanical Engineering |
