Analyzing Hydrothermal Wave Transitions through Rotational Field Application Based on Entropy Production

In this study, we evaluated the nonlinear dynamics of convection flow using the thermodynamic variational principle, focusing on scenarios where multiple external forces, such as a thermal gradient and rotational field, are applied to a shallow annular pool. We observed that with the increase in the thermal gradient, the flow changed from an axial flow to a rotational oscillatory flow with the wave amplitudes aligned. Further increasing the temperature difference led to a rotational oscillatory flow characterized by alternating wave generation and annihilation. Our analysis of the flow, considering heat fluxes orthogonal to the thermal gradient, allowed us to describe the flow state as a phase at equilibrium. The state transition of the flow was accompanied by a discontinuous jump in the heat flux, which occurred at the intersection of the entropy production curves. The first transition occurred at a temperature difference ΔT=12.4 K Marangoni number,Ma=1716 and the second at ΔT = 16.3 K Ma=2255. Analysis based on entropy production could accurately predict the observed transition points.