[M-IS21] Geophysical fluid dynamics-Transfield approach to geoscience

[MIS21-P03] Extraction of quasi-periodic features of thermal convection by data-driven analysis

*Takatoshi Yanagisawa^1,4, Masanori Kameyama^2,1, Daisuke Noto³, Yuji Tasaka^4,1 (1.Japan Agency for Marine-Earth Science and Technology, 2.Geodynamics Research Center, Ehime University, 3.University of Pennsylvania, 4.Faculty of Engineering, Hokkaido University)

Keywords:thermal convection, quasi-periodicity, mode decomposition

Convection in an enclosed volume is ubiquitous in nature, such as water flow in ice sheet, magma flow in dikes or sills, and various geothermal systems. As a simplified fundamental setting of these phenomena, we investigated thermal convection in three-dimensional enclosed rectangular geometries (xyz) driven by the temperature difference between the top and bottom boundaries, with all fixed velocity boundary conditions and adiabatic side walls. When the scale of one horizontal direction is extremely small, the setting is named as Hele-Shaw cell. It is known that convection in extremely narrow gaps like this, is comparable to the convection in porous medium described by the Darcy law. On the other hand, behaviors of convection in moderately narrow gaps are not fully understood yet, because of their complicated effect of two- and three- dimensionality. To make the complicated behaviors clear, we systematically searched convection patterns with various length scales of Lx and Ly, keeping Lz=1, by laboratory experiments and numerical simulations. With the increase of the Rayleigh number (Ra) under a fixed narrow geometry, we observed that the convective flow pattern changes from steady quasi-two-dimensional, time dependent quasi-two-dimensional, steady three-dimensional, and to time dependent three-dimensional one. In these various flow behaviors, time dependent quasi-two-dimensional pattern shows quasi-periodic oscillation at a certain range of Ra. We investigated the time-space features of the quasi-periodicity in more detail. As an example of data-driven analysis, we applied Proper Orthogonal Decomposition (POD), and Dynamic Mode Decomposition (DMD), for the convection with quasi-periodic behaviors. By either method, the flow behavior can be reconstructed by the sum of a small number of decomposed modes, and we succeeded in extracting time-space features of the behavior. In addition, we can identify specific frequencies of the oscillation and their fluctuations by DMD.