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The nonlinear evolution of inviscid goertler vortices in three-dimensional boundary layers
| Content Provider | NASA Technical Reports Server (NTRS) |
|---|---|
| Author | Blackaby Sr., Nicholas Dando, Andrew Hall, Philip |
| Copyright Year | 1995 |
| Description | The nonlinear development of inviscid Gortler vortices in a three-dimensional boundary layer is considered. We do not follow the classical approach of weakly nonlinear stability problems and consider a mode which has just become unstable. Instead we extend the method of Blackaby, Dando, and Hall (1992), which considered the closely related nonlinear development of disturbances in stratified shear flows. The Gortler modes we consider are initially fast growing and we assume, following others, that boundary-layer spreading results in them evolving in a linear fashion until they reach a stage where their amplitudes are large enough and their growth rates have diminished sufficiently so that amplitude equations can be derived using weakly nonlinear and non-equilibrium critical-layer theories. From the work of Blackaby, Dando and Hall (1993) is apparent, given the range of parameters for the Gortler problem, that there are three possible nonlinear integro-differential evolution equations for the disturbance amplitude. These are a cubic due to viscous effects, a cubic which corresponds to the novel mechanism investigated in this previous paper, and a quintic. In this paper we shall concentrate on the two cubic integro-differential equations and in particular, on the one due to the novel mechanism as this will be the first to affect a disturbance. It is found that the consideration of a spatial evolution problem as opposed to temporal (as was considered in Blackaby, Dando, and Hall, 1992) causes a number of significant changes to the evolution equations. |
| File Size | 291954 |
| Page Count | 43 |
| File Format | |
| Alternate Webpage(s) | http://archive.org/details/NASA_NTRS_Archive_19960007446 |
| Archival Resource Key | ark:/13960/t6c29tm4w |
| Language | English |
| Publisher Date | 1995-09-01 |
| Access Restriction | Open |
| Subject Keyword | Fluid Mechanics And Heat Transfer Computational Fluid Dynamics Shear Flow Unsteady Flow Three Dimensional Boundary Layer Flow Stability Three Dimensional Flow Integral Equations Vortices Spreading Cubic Equations Nonlinear Evolution Equations Inviscid Flow Nonlinearity Boundary Layers Viscous Flow Ntrs Nasa Technical Reports Server (ntrs) Nasa Technical Reports Server Aerodynamics Aircraft Aerospace Engineering Aerospace Aeronautic Space Science |
| Content Type | Text |
| Resource Type | Article |
