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

Proceedings Mathematical Sciences

M Subbiah¹  V Ganesh² 

[1] Department of Mathematics, Pondicherry University, Kalapet, Pondicherry 0 0, India$$;Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham University, Ettimadai, Coimbatore 0, India$$

关键词: Hydrodynamic stability;    shear flows;    variable bottom;    sea straits.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

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 $0 < K(z)≤left(frac{𝜋^2}{D^2}+frac{T^2_0}{4}ight)$, where the flow domain is $0≤ z≤ D$.

【 授权许可】

Unknown