On the Nonlinear Development of the Most Unstable Goertler Vortex Mode
INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA
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The nonlinear development of the most unstable Goertler vortex mode in boundary layer flows over curved walls is investigated. The most unstable Goertlermode is confined to a viscous wall layer of thickness OG to the 15th power and has spanwise wavelength OG to the 15th power it is, of course, most relevant to flow situations where the Gortler number G 1. The nonlinear equations governing the evolution of this mode over an OG to the 35th power streamwise lengthscale are derived and are found to be a fully nonparallel nature. The solution of these equations is achieved by making use of the numerical scheme used by Hall 1988 for the numerical solution of the nonlinear Goertler equations valid for O1 Goertler numbers. Thus, the spanwise dependence of the flow is described by a Fourier expansion whereas the streamwise and normal variations of the flow are dealt with by employing a suitable finite difference discretization of the governing equations. Our calculations demonstrate that, given a suitable initial disturbance, after a brief interval of decay, the energy in all the higher harmonics grows until a singularity is encountered at some downstream position. The structure of the flow field as this singularity is approached suggests that the singularity is responsible for the vortices, which are initially confined to the thin viscous wall layer, moving away from the wall and into the core of the boundary layer.
- Fluid Mechanics