• R G Shandil

Articles written in Proceedings – Mathematical Sciences

• Bounds on the phase velocity in the linear instability of viscous shear flow problem in the β-plane

Results obtained by Joseph(J. Fluid Mech.33 (1968) 617) for the viscous parallel shear flow problem are extended to the problem of viscous parallel, shear flow problem in the beta plane and a sufficient condition for stability has also been derived.

• On Howard’s conjecture in heterogeneous shear flow problem

Howard’s conjecture, which states that in the linear instability problem of inviscid heterogeneous parallel shear flow growth rate of an arbitrary unstable wave must approach zero as the wave length decreases to zero, is established in a mathematically rigorous fashion for plane parallel heterogeneous shear flows with negligible buoyancy forcegΒ ≪ 1 (Miles J W,J. Fluid Mech.10 (1961) 496–508), where Β is the basic heterogeneity distribution function).

• On the Existence of Hydrodynamic Instability in Single Diffusive Bottom Heavy Systems with Permeable Boundaries

We utilize the reformulated equations of the classical theory, as derived by Banerjee et al.(J. Math. Anal. Appl. 175 (1993) 458), to establish mathematically, the existence of hydrodynamic instability in single diffusive bottom heavy systems, when considered in the more general framework of the boundary conditions of the type specified by Beavers and Joseph (J. Fluid Mech. 30 (1967) 197), in the parameter regime $T_0\alpha_2&gt;1$, where $T_0$ and $\alpha_2$ being some properly chosen mean temperature and coefficient of specific heat (at constant volume) variation due to temperature variation respectively.

• # Proceedings – Mathematical Sciences

Volume 131, 2021
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019