Status : Verified
| Personal Name | Mendoza, Adrian D. |
|---|---|
| Resource Title | Edge Tracking Method for Defining the Boundary Between Elevator Mode and Quiescent State in Constant Temperature Rayleigh-Bénard Convection |
| Date Issued | 8 September 2026 |
| Abstract | A wide range of natural phenomena involves thermally driven fluid flows, where temperature-induced density variations lead to organized flow patterns once stability in the system is achieved. This interaction, under a gravitational field, form what is known as the Rayleigh – Benard Convection (RBC). In RBC, emergence of convective cells is triggered by an instability called the elevator mode (EM), characterized by vertical columns of ascending hot fluid and descending cold fluid. Recently, a novel periodic solution distinct from EM has been identified at low Rayleigh Number (Ra), exhibiting quiescent energy behavior and indicating the existence of a new basin of attraction. Transition between these two flow states – EM and the periodic solution (PS) – are of particular interest in understanding flow regulation. To explore these transitions, this study employs an edge-tracking method to identify the edge state that delineates the basins of attraction. A set of new initial conditions is calculated through the use of the gradual descent within bisection, and the system’s evolution is analyzed via direct numerical simulation (DNS). The simulations use a spectral method for velocity and temperature fields, implemented in the FORTRAN programming language. Three key findings are reported: (1) identification of the edge state between EM and PS, (2) detection of both stable and unstable toroidal structures which emanates from a doubly periodic solution, and (3) observation of a bifurcation scenario occurring at a constant control parameter Ra – an instability hallmark in RBC. These results indicate that sensitivity to initial conditions can lead to distinct flow behaviors, i.e., solutions which also occur at other Ra values, even at fixed control parameters. Furthermore, the possibility of similar bifurcation phenomena across different Rayleigh numbers (Ra), as well as the potential presence of homoclinic tangency arising from the interaction of stable and unstable |
| Degree Course | Master of Science in Mechanical Engineering |
| Language | English |
| Keyword | Dynamical Systems; Rayleigh-Benard Convection |
| Material Type | Thesis/Dissertation |
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