Recurrence formulas for long wavelength asymptotics in the problem of shear flow stability |
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| Authors: | S V Revina |
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| Institution: | 1. Southern Federal University, ul. B. Sadovaya 105/42, Rostov-on-Don, 344006, Russia
2. Southern Mathematical Institute, Vladikavkaz Research Center, Russian Academy of Sciences and the Government of the Republic of North Ossetia-Alania, ul. Markusa 22, Vladikavkaz, 362027, Republic of North Ossetia-Alania, Russia
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| Abstract: | 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. |
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