Abstract
The stability of perfect-fluid capillary-gravity surface flows past a cylindrical obstacle is studied in the shallow water limit, using the two-dimensional compressible Euler equations, with leading-order dispersive corrections. Stationary solutions with different contact angles are obtained by Newton branch following, based on Fourier pseudospectral methods, using mapped Chebychev polynomials. Stable and unstable branches are found to meet, through a saddle-node bifurcation, at a critical speed beyond which no stationary solution exists. For large obstacles, the stable branch is compared with the stationary solutions of the compressible Euler equation without dispersion. Boundary layers are investigated. In this regime, the unstable dynamics are shown to lead to a finite-time dewetting singularity.
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