Investigation of baroclinic seiches in a basin with parabolic bottom profile (Q2754743)

A two-layered incompressible inviscid fluid fills a basin, which is infinite in \(y\) direction. Its width in \(x\) direction is equal to \(2l\), and its depth changes according to parabolic law \(h(x) = h_0(1-x^2/l^2)\), \(-l\leq x\leq l\). Interface between two fluids is assumed to be parabolic as well. Waves at the free surface and at the interface of fluids are studied. Both the weight force and Coriolis forces are taken into account. In the long-wave approximation, analytic expressions for frequencies of free oscillations, wave velocities and profiles of the free surface and the interface are found and analyzed for the first three modes. Numerical examples are considered.