Geodesic
Recurrence formulas for long wavelength asymptotics in the problem of shear flow stability
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 8, pp. 1387-1401

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Recurrence formulas are obtained for the kth term of the long wavelength asymptotics in the stability problem for two-dimensional viscous incompressible shear flows with a nonzero average. It is shown that the critical eigenvalues are odd functions of the wave number, while the critical values of the viscosity are even functions. If the deviation of the velocity from its period-average value is an odd function of spatial variable, the eigenvalues can be found exactly. 
@article{ZVMMF_2013_53_8_a13,
     author = {S. V. Revina},
     title = {Recurrence formulas for long wavelength asymptotics in the problem of shear flow stability},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1387--1401},
     publisher = {mathdoc},
     volume = {53},
     number = {8},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_8_a13/}
}
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S. V. Revina. Recurrence formulas for long wavelength asymptotics in the problem of shear flow stability. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 8, pp. 1387-1401. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_8_a13/