The two-dimensional, viscous boundary-value problem for fluctuations in boundary layers
Abstract
The spatial evolution of disturbances is described as an asymptotic solution of the forced Orr-Sommerfeld equation. The effects of vortical and irrotational freestream disturbances as well as stability waves are included. The velocity fluctuations and their derivatives are specified along the y-axis. A Fourier transform in time and a Laplace transform in the streamwise direction are used. Complementary and particular integrals are found. Possible fluctuations arising from the inverse Laplace transform include the discrete eigenmodes, integral contributions from two branch lines for downstream and upstream traveling vortical fluctuations, and contributions from poles for two exponentially-varying standing waves.
- Publication:
-
AIAA, Aerospace Sciences Meeting
- Pub Date:
- January 1983
- Bibcode:
- 1983aiaa.meetV....T
- Keywords:
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- Boundary Layer Stability;
- Computational Fluid Dynamics;
- Orr-Sommerfeld Equations;
- Oscillating Flow;
- Two Dimensional Boundary Layer;
- Viscous Flow;
- Asymptotic Methods;
- Boundary Value Problems;
- Flow Velocity;
- Fluctuation Theory;
- Free Flow;
- Integral Transformations;
- Parallel Flow;
- Standing Waves;
- Tollmien-Schlichting Waves;
- Vortices;
- Fluid Mechanics and Heat Transfer