Hydrodynamic instabilities occur when a control parameter (vertical temperature difference in Rayleigh‒Bénard convection) exceeds a certain threshold. The generic Landau model of bifurcations may be applied to some instabilities. In the simplest case, the amplitude increases continuously and reversibly above threshold: in the Rayleigh‒Bénard case, it is determined by a balance between the driving forces due to the density gradient and the diffusive effects opposing it. This chapter then discusses instabilities governed by centrifugal forces (Taylor‒Couette) or surface-tension gradients (Bénard‒Marangoni). This last case leads to the concept of sub-critical instabilities. The Kelvin‒Helmholtz instability for parallel flows at different velocities is an example of open flows; the influence of the shape of the velocity profiles of these flows is described. Finally the stability of Couette and Poiseuille flows is discussed.
Sanjay Kumar Shailendra (Wed,) studied this question.