Here are somes references related to the subject :

"Stability Analysis of Viscoelastic Flows "

Link :

https://pure.tue.nl/ws/files/3143656/200213682.pdf

http://shodhganga.inflibnet.ac.in/bitstream/10603/45320/5/05_chapter%201.pdf

Regards

Your question is interested. I think this may help you. See website here!

Link :

Article The stability of natural convection in a vertical layer of v...

https://www.ripublication.com/ijcam17/ijcamv12n1_13.pdf

Article Convective Stability of a General Viscoelastic Fluid Heated from Below

Article Thermoconvective Instability of a Rotating Viscoelastic Flui...

Hello,

Please can you show the equations, or give the model and hypothesis of your problem ?

If your layer is infinite, I advise you to use the Fourier normal modes. Be carefull with boundary conditions.

The different methods sometimes find different things. A normal mode analysis generally finds the linear stability criterion. An energy analysis generally finds the nonlinear stability criterion. If these yield identical results, then the bifurcation to convection is supercritical. If the results are different, then the bifurcation is subcritical. It is also possible to undertake a weakly nonlinear analysis which will confirm these results. Which method is more important? Well, if you don;t try both (or even all three) then you won't know what type of instability it is. Therefore both methods are essential.

To know the stability conditions, one needs to perform the linear stability using normal mode analysis. However, to know the type of instability or instability mechanism, one needs to perform the energy analysis.

The overview of the linear stability analysis provides only information about the development of the imposed infinitesimal disturbances. It cannot provide any information about the flow dynamics when a system is considered under a disturbance of finite amplitude. In such a situation, the nonlinear stability analysis can be used to determine the flow dynamics and the type of bifurcation at and beyond the linear stability boundary. There are different types of weakly nonlinear stability analyses, which are well established in the literature. For more information, you can go through the following article. In the mentioned article, we have analyzed the stability condition of Newtonian fluid flow as well as the instability mechanism via linear as well as nonlinear kinetic energy analysis.

Article Bifurcation and instability of annular Poiseuille flow in th...

Thank you