Thermal instability-driven multiple solutions in a grooved channel

ABSTRACT

We present rich non-linear characteristics like multiple-stable states, bifurcation, and transition to chaos as a result of thermal instability-driven multiple solutions in a bottom-heated grooved channel undergoing natural convection with Rayleigh number varying from 1 × 10⁵ to 9 × 10⁵. From our analysis, we identify two different routes in which the solution of the system evolves along with the critical Rayleigh numbers associated with such transitions. In one route, the solution transforms from steady symmetric to chaotic solutions, while for the second route it first undergoes pitchfork bifurcation, where steady symmetric solution transforms to steady asymmetric, followed by Hopf bifurcation to periodic solutions. The two distinct solution routes clearly bring out the dependence of system solutions on initial conditions. The route to chaos in the grooved channel system has been successfully identified, which is supported by the results of time-series, power-spectra density and three-dimensional phase plots, apart from the positive values of largest Lyapunov exponent.