Numerical analysis of the spectrum of the Orr–Sommerfeld problem
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 10, pp. 1672-1691
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A high-accuracy method for computing the eigenvalues $\lambda_n$ and the eigenfunctions of the Orr–Sommerfeld operator is developed. The solution is represented as a combination of power series expansions, and the latter are then matched. The convergence rate of the expansions is analyzed by applying the theory of recurrence equations. For the Couette and Poiseuille flows in a channel, the behavior of the spectrum as the Reynolds number $\mathrm R$ increases is studied in detail. For the Couette flow, it is shown that the eigenvalues $\lambda_n$ regarded as functions of $\mathrm R$ have a countable set of branch points $\mathrm R_k>0$ at which the eigenvalues have a multiplicity of 2. The first ten of these points are presented within ten decimals.
@article{ZVMMF_2007_47_10_a2,
author = {S. L. Skorokhodov},
title = {Numerical analysis of the spectrum of the {Orr{\textendash}Sommerfeld} problem},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {1672--1691},
publisher = {mathdoc},
volume = {47},
number = {10},
year = {2007},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_10_a2/}
}
TY - JOUR AU - S. L. Skorokhodov TI - Numerical analysis of the spectrum of the Orr–Sommerfeld problem JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2007 SP - 1672 EP - 1691 VL - 47 IS - 10 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_10_a2/ LA - ru ID - ZVMMF_2007_47_10_a2 ER -
S. L. Skorokhodov. Numerical analysis of the spectrum of the Orr–Sommerfeld problem. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 10, pp. 1672-1691. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_10_a2/