Double‐diffusive convection in a rotating viscoelastic fluid layer,ZAMM - Journal of Applied Mathematics and Mechanics

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Double‐diffusive convection in a rotating viscoelastic fluid layer
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2021-01-08 , DOI: 10.1002/zamm.201900025
Kondethimmanahalli Rangadhamappa Raghunatha ₁ , Inapura Siddagangaiah Shivakumara ₂

Affiliation

The linear instability and a weakly nonlinear stability of a rotating double‐diffusive convection in a viscoelastic fluid layer are investigated. An Oldroyd‐B constitutive equation is used to describe the rheological behavior of the viscoelastic fluid. Several remarkable departures from those of single‐diffusive and double‐diffusive viscoelastic fluid systems are explored by performing the linear instability analysis. Under certain conditions, it is observed that (i) a non‐rotating double diffusive viscoelastic fluid layer becomes destabilized by rotation, (ii) a rotating viscoelastic fluid layer gets destabilized by the addition of heavy solute to the bottom of the layer, (iii) disconnected closed convex oscillatory neutral curve from the stationary neutral curve exists, and (iv) three critical thermal Rayleigh numbers are required to specify the linear instability criteria, as opposed to a single critical value. The nature of linear instability characteristics for Oldroyd‐B, Maxwell and Newtonian fluids is found to be contradictory for the identical values of governing parameters. By performing a weakly nonlinear stability analysis, a cubic Landau equation for the amplitude corresponding to stationary convection is derived and the stability of bifurcating equilibrium solution is discussed. The viscoelastic parameters influence the stability of stationary bifurcation despite their effect is not felt on the stationary onset. The influence of various parameters on heat and mass transfer is also elucidated.

中文翻译：

旋转粘弹性流体层中的双扩散对流

研究了粘弹性流体层中旋转双扩散对流的线性不稳定性和弱非线性稳定性。Oldroyd-B本构方程用于描述粘弹性流体的流变行为。通过进行线性不稳定性分析，探索了与单扩散和双扩散粘弹性流体系统的一些显着差异。在某些条件下，观察到（i）非旋转的双扩散粘弹性流体层因旋转而变得不稳定，（ii）旋转的粘弹性流体层因在层的底部添加重质溶质而变得不稳定，（iii ）存在与固定中性曲线断开的闭合凸凸振荡中性曲线，（iv）需要三个临界热瑞利数来指定线性不稳定性标准，而不是单个临界值。对于相同的控制参数值，发现Oldroyd-B，Maxwell和Newtonian流体的线性不稳定性特征是矛盾的。通过进行弱非线性稳定性分析，推导了对应于平稳对流的振幅的三次Landau方程，并讨论了分叉平衡解的稳定性。粘弹性参数影响固定分叉的稳定性，尽管在固定起步阶段并未感觉到它们的影响。还阐明了各种参数对传热和传质的影响。对于相同的控制参数值，发现Oldroyd-B，Maxwell和Newtonian流体的线性不稳定性特征是矛盾的。通过进行弱非线性稳定性分析，推导了对应于平稳对流的振幅的三次Landau方程，并讨论了分叉平衡解的稳定性。粘弹性参数影响固定分叉的稳定性，尽管在固定起步阶段并未感觉到它们的影响。还阐明了各种参数对传热和传质的影响。对于相同的控制参数值，发现Oldroyd-B，Maxwell和Newtonian流体的线性不稳定性特征是矛盾的。通过进行弱非线性稳定性分析，推导了对应于平稳对流的振幅的三次Landau方程，并讨论了分叉平衡解的稳定性。粘弹性参数影响固定分叉的稳定性，尽管在固定起步阶段并未感觉到它们的影响。还阐明了各种参数对传热和传质的影响。推导了对应于平稳对流的幅值的三次Landau方程，并讨论了分叉平衡解的稳定性。粘弹性参数影响固定分叉的稳定性，尽管在固定起步阶段并未感觉到它们的影响。还阐明了各种参数对传热和传质的影响。推导了对应于平稳对流的幅值的三次Landau方程，并讨论了分叉平衡解的稳定性。粘弹性参数影响固定分叉的稳定性，尽管在固定起步阶段并未感觉到它们的影响。还阐明了各种参数对传热和传质的影响。

更新日期：2021-01-08

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