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

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    • Keywords


      Hydrodynamic stability; extended Rayleigh problem; shear instability.

    • Abstract


      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.

    • Author Affiliations


      V Ganesh1 M Subbiah2

      1. Department of Mathematics, Sri Manakula Vinayagar Engineering College, Madagadipet, Pondicherry 605 107, India
      2. Department of Mathematics, Pondicherry University, Kalapet, Pondicherry 605 014, India
    • Dates

  • Proceedings – Mathematical Sciences | News

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      Posted on July 25, 2019

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