| Abstract: |
| The stability of interfacial long waves in two-layer plane Couette flow is investigated
using a nonlinear, nonlocal asymptotic model derived from the Navier-Stokes equations and
valid for thin upper layers. Nonlocality enters through a coupling of the thin and main layers,
and crucial inertial effects are retained. The models generically support bistability phenomena
observed in experiments where two stable travelling waves, one unimodal and the other
bimodal, are recorded at the same lid velocity. In direct comparisons with experiments, the
models show remarkable agreement, both qualitatively and quantitatively. The two stable
travelling waves are identified, and their basins of attraction characterised via large-time
computations for different initial conditions. We also identify a new symmetry-breaking
travelling-wave branch bifurcating from the bimodal family, compute higher-wavenumber
travelling-wave branches, and present time-periodic orbits arising via Hopf bifurcations. |
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