Nonlinear Tollmien-Schlichting/vortex interaction in boundary layers

Philip Hall, F. T. Smith

Research output: Book/ReportOther ReportResearch

Abstract

The nonlinear interaction between two oblique three-dimensional Tollmien-Schlichting (TS) waves and their induced streamwise-vortex flow is considered theoretically for an incompressible boundary layer. The same theory applies to the de-stabilization of an incident vortex motion by sub-harmonic TS waves, followed by interaction. The scales and flow structure involved are addressed for high Reynolds numbers. The nonlinear interaction is powerful, starting at quite low amplitudes with a triple-deck structure for the TS waves but a large-scale structure for the induced vortex, after which strong nonlinear amplification occurs. This includes nonparallel-flow effects. The nonlinear interaction is governed by a partial-differential system for the vortex flow coupled with an ordinary differential one for the TS pressure. The solution properties found sometimes produce a break-up within a finite distance and sometimes further downstream, depending on the input amplitudes upstream and on the wave angles, and that then leads on to the second stages of interaction associated with higher amplitudes, the main second stages giving either long-scale phenomena significantly affected by nonparallelism or shorter quasiparallel ones governed by the full nonlinear triple-deck response. Qualitative comparisons with experiments are noted.
Original languageEnglish
Place of PublicationHampton VA USA
PublisherNASA Langley Research Center
Number of pages36
Publication statusPublished - Aug 1988
Externally publishedYes

Cite this

Hall, P., & Smith, F. T. (1988). Nonlinear Tollmien-Schlichting/vortex interaction in boundary layers. Hampton VA USA: NASA Langley Research Center.
Hall, Philip ; Smith, F. T. / Nonlinear Tollmien-Schlichting/vortex interaction in boundary layers. Hampton VA USA : NASA Langley Research Center, 1988. 36 p.
@book{94af5866544d4eeea795df6340bfd459,
title = "Nonlinear Tollmien-Schlichting/vortex interaction in boundary layers",
abstract = "The nonlinear interaction between two oblique three-dimensional Tollmien-Schlichting (TS) waves and their induced streamwise-vortex flow is considered theoretically for an incompressible boundary layer. The same theory applies to the de-stabilization of an incident vortex motion by sub-harmonic TS waves, followed by interaction. The scales and flow structure involved are addressed for high Reynolds numbers. The nonlinear interaction is powerful, starting at quite low amplitudes with a triple-deck structure for the TS waves but a large-scale structure for the induced vortex, after which strong nonlinear amplification occurs. This includes nonparallel-flow effects. The nonlinear interaction is governed by a partial-differential system for the vortex flow coupled with an ordinary differential one for the TS pressure. The solution properties found sometimes produce a break-up within a finite distance and sometimes further downstream, depending on the input amplitudes upstream and on the wave angles, and that then leads on to the second stages of interaction associated with higher amplitudes, the main second stages giving either long-scale phenomena significantly affected by nonparallelism or shorter quasiparallel ones governed by the full nonlinear triple-deck response. Qualitative comparisons with experiments are noted.",
author = "Philip Hall and Smith, {F. T.}",
year = "1988",
month = "8",
language = "English",
publisher = "NASA Langley Research Center",

}

Hall, P & Smith, FT 1988, Nonlinear Tollmien-Schlichting/vortex interaction in boundary layers. NASA Langley Research Center, Hampton VA USA.

Nonlinear Tollmien-Schlichting/vortex interaction in boundary layers. / Hall, Philip; Smith, F. T.

Hampton VA USA : NASA Langley Research Center, 1988. 36 p.

Research output: Book/ReportOther ReportResearch

TY - BOOK

T1 - Nonlinear Tollmien-Schlichting/vortex interaction in boundary layers

AU - Hall, Philip

AU - Smith, F. T.

PY - 1988/8

Y1 - 1988/8

N2 - The nonlinear interaction between two oblique three-dimensional Tollmien-Schlichting (TS) waves and their induced streamwise-vortex flow is considered theoretically for an incompressible boundary layer. The same theory applies to the de-stabilization of an incident vortex motion by sub-harmonic TS waves, followed by interaction. The scales and flow structure involved are addressed for high Reynolds numbers. The nonlinear interaction is powerful, starting at quite low amplitudes with a triple-deck structure for the TS waves but a large-scale structure for the induced vortex, after which strong nonlinear amplification occurs. This includes nonparallel-flow effects. The nonlinear interaction is governed by a partial-differential system for the vortex flow coupled with an ordinary differential one for the TS pressure. The solution properties found sometimes produce a break-up within a finite distance and sometimes further downstream, depending on the input amplitudes upstream and on the wave angles, and that then leads on to the second stages of interaction associated with higher amplitudes, the main second stages giving either long-scale phenomena significantly affected by nonparallelism or shorter quasiparallel ones governed by the full nonlinear triple-deck response. Qualitative comparisons with experiments are noted.

AB - The nonlinear interaction between two oblique three-dimensional Tollmien-Schlichting (TS) waves and their induced streamwise-vortex flow is considered theoretically for an incompressible boundary layer. The same theory applies to the de-stabilization of an incident vortex motion by sub-harmonic TS waves, followed by interaction. The scales and flow structure involved are addressed for high Reynolds numbers. The nonlinear interaction is powerful, starting at quite low amplitudes with a triple-deck structure for the TS waves but a large-scale structure for the induced vortex, after which strong nonlinear amplification occurs. This includes nonparallel-flow effects. The nonlinear interaction is governed by a partial-differential system for the vortex flow coupled with an ordinary differential one for the TS pressure. The solution properties found sometimes produce a break-up within a finite distance and sometimes further downstream, depending on the input amplitudes upstream and on the wave angles, and that then leads on to the second stages of interaction associated with higher amplitudes, the main second stages giving either long-scale phenomena significantly affected by nonparallelism or shorter quasiparallel ones governed by the full nonlinear triple-deck response. Qualitative comparisons with experiments are noted.

M3 - Other Report

BT - Nonlinear Tollmien-Schlichting/vortex interaction in boundary layers

PB - NASA Langley Research Center

CY - Hampton VA USA

ER -

Hall P, Smith FT. Nonlinear Tollmien-Schlichting/vortex interaction in boundary layers. Hampton VA USA: NASA Langley Research Center, 1988. 36 p.