• M Subbiah

      Articles written in Proceedings – Mathematical Sciences

    • On Upper Bounds for the Growth Rate in the Extended Taylor–Goldstein Problem of Hydrodynamic Stability

      V Ganesh M Subbiah

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      For the extended Taylor–Goldstein problem of hydrodynamic stability governing the stability of shear flows of an inviscid, incompressible but density stratified fluid in sea straits of arbitrary cross-section a new estimate for the growth rate of an arbitrary unstable normal mode is given for a class of basic flows. Furthermore the Howard’s conjecture, namely, the growth rate $kc_i\to 0$ as the wave number $k\to\infty$ is proved for two classes of basic flows.

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

      M Subbiah V Ganesh

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      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 $0\leq z\leq D$.

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