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- W4386875124 abstract "We study by a combination of analytical and numerical methods multidimensional stability and transverse bifurcation of planar hydraulic shock and roll wave solutions of the inviscid Saint Venant equations for inclined shallow-water flow, both in the whole space and in a channel of finite width, obtaining complete stability diagrams across the full parameter range of existence. Technical advances include development of efficient multi-d Evans solvers, low- and high-frequency asymptotics, explicit/semi-explicit computation of stability boundaries, and rigorous treatment of channel flow with wall-type physical boundary. Notable behavioral phenomena are a novel essential transverse bifurcation of hydraulic shocks to invading planar periodic roll-wave or doubly-transverse periodic herringbone patterns, with associated metastable behavior driven by mixed roll- and herringbone-type waves initiating from localized perturbation of an unstable constant state; and Floquet-type transverse ``flapping'' bifurcation of roll wave patterns." @default.
- W4386875124 created "2023-09-20" @default.
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- W4386875124 date "2023-09-16" @default.
- W4386875124 modified "2023-09-27" @default.
- W4386875124 title "Multidimensional stability and transverse bifurcation of hydraulic shocks and roll waves in open channel flow" @default.
- W4386875124 doi "https://doi.org/10.48550/arxiv.2309.08870" @default.
- W4386875124 hasPublicationYear "2023" @default.
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