Analyzing Slightly Inclined Cylindrical Binary Fluid Convection via Higher Order Dynamic Mode Decomposition

Abstract

An extended dynamical system is considered that shows some striking, very complex spatio-temporal patterns. Specifically, we consider superhighway patterns that appear in binary fluid convection in slightly inclined, shallow cylindrical containers. These patterns show a number of parallel thermal lanes, each containing aligned coherent structures that counterpropagate in adjacent lanes. Several types of superhighway convection states have been obtained by direct numerical simulation. The numerical outcomes are analyzed using a recent data processing tool, known as higher order dynamic mode decomposition, which efficiently identifies relevant spatio-temporal patterns in numerically computed data.

Delay-Embedding Spatio-Temporal Dynamic Mode Decomposition

“…The natural time units in (53) are days, so the long wave has a period of 45 days and the period of the short wave is approximately 14 days. These periods are comparable to the timescales observed in nature.…”

“…In (53), k 1 and k 2 are integer-valued wavenumbers set to k 1 = 2 and k 2 = 10, and ω 1 and ω 2 are time-dependent phases for the rationally independent frequencies ω 1 = 2π/45 and ω 2 = √ 10ω 1 . The color map of this pattern is depicted in Figure 1 (left).…”

“…Applications of spatiotemporal DMD span various fields, including fluid dynamics, neuroscience, climate science, and engineering, where understanding and predicting complex spatio-temporal behaviors is essential. Some recent publications related to the topic suggest applications in the fields of unsteady shear layer flow [48], wake of a circular cylinder [49], urban flow [50], aerodynamic modeling [51], turbulent flow [52] and binary fluid convection [53].…”

Stationary localized solutions in binary convection in slightly inclined rectangular cells

“…Other examples in which the snaking diagrams do not persist are discussed in the recent works of Lo Jacono et al [18] in doubly diffusive convection in a vertical slot when changing the boundary condition at one of the vertical walls, and of Azimi and Schneider [19] in plane Couette flow with wall-normal suction. The effect of adding a slight inclination in extended layers of binary mixtures heated from below has also been studied in a shallow cylinder filled with a positive Soret mixture [20,21]. The results on both tilted problems suggest that even very small inclinations produce substantial changes in the flow structure and result in new phenomena.…”