On investigation of space structure and variability of seiche oscillation in a basin of variable depth (Q2753406)

Influence of geometric characteristics of a rotating ring-shaped basin of variable thickness on the structure of axisymmetric and ring waves and also wave velocities is 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 of hydrodynamics equations 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. In the 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. Numeric experiments are performed and some conclusions concerning observations in nature are done.