Unbounded stratified flow over a vertical barrier

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Abstract
The horizontal, linearly stratified, non-diffusive, high Reynolds number flow of an unbounded fluid over a two-dimensional vertical barrier is studied for a range of internal Froude numbers (Fi) under the Oseen and Boussinesq approximations. For F1 > 0·47 the most prominent feature of the flow is the system of large amplitude lee waves located downstream of the barrier with crests tilted in the upstream direction. For 0·47 < F1 < 0·6 the crests actually extend upstream of the barrier and appear as flows of alternating direction over the barrier. For 0·47 < Fi < 0·5 reversed flows due to these waves actually extend far upstream. For Fi < 0·47 a blocking column upstream of the obstacle, as well as large amplitude lee waves, is present. For even smaller 3. the amplitude of the lee-wave system diminishes but the blocking column remains. It is also shown that the steady-state solution obtained by Trustrum (1964, 1971) for the density and pressure field is drastically altered if a small viscosity is retained in the transient analysis.