Nonlinear subcritical free-surface flow past topography: exponential-asymptotics solution

A theoretical study is made of steady, subcritical (Froude number $F \lt 1$ ) two-dimensional free-surface flow due to a uniform stream flowing over smooth, locally confined bottom topography of large horizontal extent ( $L \gg 1$ ) and finite peak height ( $\varepsilon = O(1)$ ). In earlier work, this flow was analysed based on the nonlinear shallow-water equations which neglect the effects of dispersion altogether. This so-called hydraulic theory predicts a steady disturbance confined in the v