• On Short Wave Stability and Sufficient Conditions for Stability in the Extended Rayleigh Problem of Hydrodynamic Stability

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      https://www.ias.ac.in/article/fulltext/pmsc/120/03/0387-0394

    • Keywords

       

      Hydrodynamic stability; shear flows; variable bottom; sea straits.

    • Abstract

       

      We consider the extended Rayleigh problem of hydrodynamic stability dealing with the stability of inviscid homogeneous shear flows in sea straits of arbitrary cross section. We prove a short wave stability result, namely, if $k>0$ is the wave number of a normal mode then $k>k_c$ (for some critical wave number $k_c$) implies the stability of the mode for a class of basic flows. Furthermore, if $K(z)=\frac{-({U''}_0-T_0{U'}_0)}{U_0-U_{0s}}$, where $U_0$ is the basic velocity, $T_0$ (a constant) the topography and prime denotes differentiation with respect to vertical coordinate 𝑧 then we prove that a sufficient condition for the stability of basic flow is $0 < K(z)\leq\left(\frac{\pi^2}{D^2}+\frac{T^2_0}{4}\right)$, where the flow domain is $0\leq z\leq D$.

    • Author Affiliations

       

      M Subbiah1 V Ganesh2

      1. Department of Mathematics, Pondicherry University, Kalapet, Pondicherry 605 014, India
      2. Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham University, Ettimadai, Coimbatore 641 105, India
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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