|Budget Amount *help
¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 1997: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1996: ¥1,700,000 (Direct Cost: ¥1,700,000)
In recent reserches, it is pointed out that the coupled vibration equation (CVE) by Nochino is appicable for nonlinear water waves such as Solitary wave and for wave breaking. The goal of the project is to investigate the capability of CVE for nonlinear water waves on arbitarary configuration of depth, espesially the wave deformation on slope pf bottom and wave braking by the numerical calculation.
On first year of project (1996), the CVE for the orbitirary config ation of depth is derived by applying the Legendre polyniominals with both the even and odd oder series, in order to satisfy the baoundary condition at bottom. The numerical calculation are excuted with the new CVE.The results of the calculation show unstable at the wave bottom, which is clearly different from the unstablity of wave breaking.
On the second year (1997), the unstability of numerical calculation for nolinear water waves by the new CVE investigated by trying varius algorism of calculation. The problems of CFL number and the numerical instability of differenrial equations was carefully tested and ovewhlemed. the alculation results, however, sill show unstable. After careful research, it is found that the log wave at wave front stimulate the problem of CFL number. The numerical calculation is started from the water at still, and waves incident through the incident baoundary on the first year developed. The waves in the calculation region make up the wave front at the tip of waves progressing. Consiquently, waves in the region of its relative depth less than 1/20 are stable in the present calculation method. This region implies the shallow water waves and also is the same as one of the Boussinesq Equation is applicable.