Uniform asymptotic approximations to solutions of the Orr-Sommerfeld equation for the asymptotic suction boundary layer profile
Abstract
It is shown that Reid's (1974) proposed uniform asymptotic approximations to solutions of the Orr-Sommerfeld equation are valid for the asymptotic suction boundary layer profile. The dominant-recessive solutions are found to be free of logarithmic terms at all orders of approximation, and the partly balanced solutions to involve the generalized Airy functions Bk (z, p, q) for q = 0 and 1 only. The analysis makes use of the theory of Chester et al. (1957).
- Publication:
-
Proceedings of the Royal Society of London Series A
- Pub Date:
- June 1985
- DOI:
- Bibcode:
- 1985RSPSA.399..321B
- Keywords:
-
- Asymptotic Methods;
- Boundary Layer Flow;
- Computational Fluid Dynamics;
- Couette Flow;
- Laminar Flow;
- Orr-Sommerfeld Equations;
- Airy Function;
- Hypergeometric Functions;
- Integral Equations;
- Polynomials;
- Fluid Mechanics and Heat Transfer