Complex Transition of Double-Diffusive Convection in a Rectangular Enclosure with Height-to-Length Ratio Equal to 4: Part I (Communications in Computational Physics, 2018)
This is the first part of direct numerical simulation (DNS) of double-diffusiveconvection in a slim rectangular enclosure with horizontal temperature and concentrationgradients. We consider the case with the thermal Rayleigh number of 105, thePradtle number of 1, the Lewis number of 2, the buoyancy ratio of composition to temperaturebeing in the range of [0,1], and height-to-width aspect ration of 4. A new 7th-orderupwind compact scheme was developed for approximation of convective terms,and a three-stage third-order Runge-Kutta method was employed for time advancement.Our DNS suggests that with the buoyancy ratio increasing form 0 to 1, the flowof transition is a complex series changing from the steady to periodic, chaotic, periodic,quasi-periodic, and finally back to periodic. There are two types of periodic flow, oneis simple periodic flow with single fundamental frequency (FF), and the other is complexperiodic flow with multiple FFs. This process is illustrated by using time-velocityhistories, Fourier frequency spectrum analysis and the phase-space trajectories.