On Large-Scale Vortical Structures in (Incompressible) Fluids with Thermal Expansion

This paper extends the analysis of Ref. 1 to non-Boussinesq fluids whose thermal equation of state depends negligibly on pressure but non-negligibly on temperature. It is demonstrated that these fluids are more stable than the Boussinesq fluids under the same conditions. We study the effect of the helicity on the stability of the Bénard problem and demonstrate that there is no separatrix that divides the instability regimes into two classes. Here, the phenomenon of inverse energy cascade is present at all values of helicities.