A Nonlinear Stability Analysis of Rotating Navier-Stokes-Voigt Fluid Heated from Below

Sweta Sharma$^1$; Sunil$^1$; Poonam Sharma$^2$

Journal of Applied Nonlinear Dynamics

Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)

A Nonlinear Stability Analysis of Rotating Navier-Stokes-Voigt Fluid Heated from Below

Journal of Applied Nonlinear Dynamics 14(1) (2025) 19--29 | DOI:10.5890/JAND.2025.03.002

Sweta Sharma$^1$, Sunil$^1$, Poonam Sharma$^2$

$^1$ Department of Mathematics & Scientific Computing, National Institute of Technology Hamirpur, Hamirpur, H.P.- 177005, India

$^2$ Department of Mathematics, NSCBM Govt. College, Hamirpur, H.P.-177005, India

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Abstract

The nonlinear and linear approach, as well as a fully nonlinear energy argument, are used to thoroughly examine the thermal convection of simultaneously rotating Navier-Stokes-Voigt fluid for three distinct bounding surfaces. It is observed that the same critical Rayleigh number is obtained using both nonlinear and linear analyses, which ensures the absence of sub-critical instability. A nonlinear energy argument describes the important role of the Kelvin-Voigt parameter in energy decay, whereas the parameter doesn't affect the value of the Rayleigh number. The vertical fluid motion slows down due to rotation; thus, rotation postpones the onset of instability. Also, discussed the stability of Navier-Stokes-Voigt fluid contained in three different combinations of bounding surfaces.

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