On the stability and bifurcation of the non-rotating Boussinesq equation with the Kolmogorov forcing at a low Péclet number

Autor:	Yiqiu Mao, Quan Wang, Chanh Kieu, Zhimin Chen
Rok vydání:	2020
Předmět:	Physics Hopf bifurcation Numerical Analysis Convective heat transfer Applied Mathematics Mathematical analysis Reynolds number Péclet number Physics::Fluid Dynamics symbols.namesake Modeling and Simulation symbols Compressibility Stratified flow Shear flow Bifurcation
Zdroj:	Communications in Nonlinear Science and Numerical Simulation. 89:105322
ISSN:	1007-5704
DOI:	10.1016/j.cnsns.2020.105322
Popis:	This study examines the stability and potential bifurcations of a stratified shear flow governed by the non-rotating incompressible Boussinesq equation at a low Peclet number. For the ratio of the vertical scale to the horizontal scale of a stratified flow a ∈ [ 3 / 4 , 3 / 2 ) , it is shown that there exists a threshold for the Reynold number Re above which the steady stratified shear flow driven by the Kolmogorov forcing becomes linearly unstable. As a result, the Boussinesq equation exhibits a Hopf bifurcation. To further determine the type of the Hopf bifurcation, the model is reduced to a low-order system whose numerical analyses reveal that the Hopf bifurcation is supercritical. That is, a stable periodic solution emerges, which describes an oscillating thermal convection in a highly stratified shear flow arising in the atmosphere or interior of many stellar systems with low Peclet numbers.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::1ac341529c1863bad9698bad2e334cf0 https://doi.org/10.1016/j.cnsns.2020.105322 Zobrazit plný text záznamu Full Text from ScienceDirect