Articles written in Proceedings – Mathematical Sciences
Volume 123 Issue 2 May 2013 pp 293-302
We generalize Tollmien’s solutions of the Rayleigh problem of hydrodynamic stability to the case of arbitrary channel cross sections, known as the extended Rayleigh problem. We prove the existence of a neutrally stable eigensolution with wave number $k_s>0$; it is also shown that instability is possible only for $0 < k < k_s$ and not for $k>k_s$. Then we generalize the Tollmien–Lin perturbation formula for the behavior of $c_i$, the imaginary part of the phase velocity as the wave number $k\to k_s$ − to the extended Rayleigh problem and subsequently, we use this formula to demonstrate the instability of a particular shear flow.
Volume 131, 2021
Continuous Article Publishing mode
Click here for Editorial Note on CAP Mode