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DOI: 10.23671/VNC.2016.4.5994

On the Problem of Shear Flow Stability with Respect to Long-Wave Perturbations

Revina S. V.
Vladikavkaz Mathematical Journal 2016. Vol. 18. Issue 4.
To find secondary flow branching to the steady flow it is necessary to consider linear spectral problem and linear adjoint problem. Long-wave asymptotics
of linear adjoint problem in two-dimensional case is under consideration. We assume the periodicity with spatial variables when one of the periods tends
to infinity.  Recurrence formulas are obtained for the $k$th term of the velocity and pressure asymptotics. If the deviation of the velocity from its period-average
value is an odd function of spatial variable, the velocity coefficients are odd for odd $k$ and even for even \(k\). The relations between coefficients of linear adjoint problem and linear spectral problem are obtained.
Keywords: stability of two-dimensional viscous flows, long-wave asymptotics, linear adjoint problem
Language: Russian Download the full text  
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