Dynamics of a two-layer flow with an interfacial heat source/sink: viscosity stratification

The temporal stability of a two-layer plane Couette flow with an interfacial heat source/sink is studied, in the presence viscosity stratification, predicting unstable streamwise and spanwise perturbations. Based on wavenumber at onset, perturbations are further classified as long-wave finite-wave, where mode investigated using asymptotic numerical analyses. finite-wave instability expected to be relevant for highly viscous fluids. Generally, source (sink) interface found have stabilising (destabilising) effect flow. However, if rate release exceeds certain threshold, new emerges, referred here ‘explosive’ instability, characterised by unbounded growth interaction between thermocapillarity inertia leads emergence another termed ‘interaction’ instability. possess higher rates than sink along when has influence, vice versa. thermocapillary generating negative temperature gradient across In contrast, increases interface, resulting positive fluids, leading suppression instabilities effect. If provides energy faster lost due Marangoni convection diffusion, then it accumulation energy, which presumably explosive