Nonlinear stability analysis of Rayleigh-Bard problem for a Navier-Stokes-Voigt fluid

Title

Nonlinear stability analysis of Rayleigh-Bard problem for a Navier-Stokes-Voigt fluid

Creator

Basavarajappa M.; Bhatta D.

Description

The linear and nonlinear stability analyses of thermosolutal convection in a non-Newtonian Navier-Stokes-Voigt fluid, considering Soret and Ekman damping effects, are conducted analytically. Instability thresholds are determined for thermosolutal convection within a viscoelastic fluid of the Kelvin-Voigt type, wherein a dissolved salt field exists. Two scenarios are examined: one where the fluid layer is heated from the bottom and concurrently salted from the bottom, and the other where the fluid layer is heated from the bottom and concurrently salted from the top. The governing partial differential equations system includes conservation laws of mass, momentum, energy, and salt concentration. Using the energy method, the disturbances to the fluid system are shown to decay exponentially. Analytical expressions are developed for the eigenvalue as a function of Soret, Lewis, Prandtl, Kelvin-Voigt, and Rayleigh friction numbers. The study illustrates the shift from a stationary mode of convection to an oscillatory mode and provides thresholds that indicate these transitions. It is found that the viscoelastic property of the fluid acts as a stabilizing agent for oscillatory mode convection. Rayleigh friction substantially controls the convection threshold. Upon comparing threshold values between linear and nonlinear theories, a subcritical instability region is observed in the heating bottom-salting bottom case (case-1), whereas such a region is absent in the heating bottom-salting top case (case-2). 2024 Elsevier Ltd

Source

International Journal of Non-Linear Mechanics, Vol-162

Date

2024-01-01

Publisher

Elsevier Ltd

Subject

Double diffusive convection; Ekman damping; Kelvin-Voigt; Navier-Stokes-Voigt fluid; Nonlinear stability analysis

Coverage

Basavarajappa M., School of Mathematical and Statistical Sciences, The University of Texas Rio Grande Valley, Edinburg, 78539, TX, United States, Center for Mathematical Needs, Department of Mathematics, CHRIST (Deemed to be University), Karnataka, Banglore, 560029, India; Bhatta D., School of Mathematical and Statistical Sciences, The University of Texas Rio Grande Valley, Edinburg, 78539, TX, United States

Rights

Restricted Access

Relation

ISSN: 207462; CODEN: IJNMA

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.1016/j.ijnonlinmec.2024.104712

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