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- W4364387615 abstract "We delineate the complete structure of steady laminar anabatic flows within a stably stratified V-shaped valley through a dynamical systems methodology. Our approach is founded upon the identification of a quiescent conduction state, which then leads to the discovery of a distinctive asymmetric nested pitchfork bifurcation diagram. We characterize the flow via the stratification perturbation parameter, $Pi_s$, which is a measure of the surface heat flux relative to the strength of the background stable stratification, while keeping other dimensionless parameters fixed. At very low $Pi_s$ values, the pure conduction state remains stable. Beyond a threshold value of $Pi_s$, a bifurcation event transpires, giving rise to two discernible types of eigenmodes. One type is marked by a single dominant circulation positioned at the valley's center, while the other one exhibits dual circulations of equivalent strength within the same central valley region. Notably, the critical value associated with the central circulation mode is marginally lower than that of the dual circulation mode. Through three-dimensional Navier-Stokes simulations, we confirm that the central circulation mode generates a pair of asymmetric states, whereas the dual circulation mode leads to distinct upslope and downslope convection patterns. The dissimilarity between the two dual circulation patterns originates from the absence of a horizontal symmetry axis ($x$-axis) within the geometry. Linear modal analysis and numerical simulations jointly demonstrate the linear instability of the two dual circulation states, indicating that the slightest asymmetric perturbation will induce a transition towards the central circulation state." @default.
- W4364387615 created "2023-04-12" @default.
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- W4364387615 date "2023-04-10" @default.
- W4364387615 modified "2023-10-01" @default.
- W4364387615 title "Asymmetric nested pitchfork bifurcation in stratified anabatic flows in idealized valleys" @default.
- W4364387615 doi "https://doi.org/10.48550/arxiv.2304.04715" @default.
- W4364387615 hasPublicationYear "2023" @default.
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