Series Solutions and a Perturbation Formula for the Extended Rayleigh Problem of Hydrodynamic Stability

Proceedings Mathematical Sciences

M Subbiah²  V Ganesh¹ 

[1] Department of Mathematics, Sri Manakula Vinayagar Engineering College, Madagadipet, Pondicherry 0 0, India$$;Department of Mathematics, Pondicherry University, Kalapet, Pondicherry 0 0, India$$

关键词: Hydrodynamic stability;    extended Rayleigh problem;    shear instability.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

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 $k→ k_s$ − to the extended Rayleigh problem and subsequently, we use this formula to demonstrate the instability of a particular shear flow.

【 授权许可】

Unknown