The present paper treated the waves at the common boundary of tw superposed fluids of densities ρ, ρ', one above other, moving with velocities U, U', respectively, caused by the bottom configuration given by the next function,
|x|>a, y=0;|x|<a, y=-h+M(a2-x2)where
h the depth of lower fluid.
The profile of the boundary is of quite a different form according to
Δ+ξ+μ-ξμ>0 or<0,
where ξ=U
2/
gh, μ=U'
2/
gh', Δ=ρ'-ρ/ρ,
h', the depth of the upper fluid,
g the acceralation of gravity, and in the former case the boundary has a train of stationary waves behind the obstacle at the bottom, but in the latter only the forced deformation is caused, the maximum height of which lies just above the middle point of the obstacle. Moreover, in both cases the form of the disturbed boundary has the less resemblance to the bottom configuration, as the non-dimmensional quantity 2πμ√_??_becomes larger.
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