Simulation of seiches in the Atlantic basin (Q2754721)

Free linear vibrations of fluid in a ring-shaped basin of variable thickness are studied. Coriolis forces are taken into account. It is assumed that waves are long, vibrations are small, fluid is homogeneous and inviscid, and the basin depth depends on the radial coordinate only. Solution for the components of velocity \(u\), \(v\) and the elevation of the free surface \(\zeta\) is sought in the form \(u(r, \theta, t)=\bar{u}(r)\cos\beta\), \(v(r, \theta, t)=\bar{v}(r)\sin\beta\), \(\zeta(r, \theta, t)=\bar{\zeta}(r)\sin\beta\), where \(\beta=s\theta+\sigma t\), \(\sigma\) is the frequency of vibrations, \(s\) is the wavenumber. As a result, a differential equation for amplitude of elevation \(\bar{\zeta}(r)\) and proper boundary conditions are derived. For solution of the obtained Cauchy problem, the fourth-order Runge-Kutta method is used. Numerical experiments are performed, and some conclusions concerning observations in nature are done.