Non-linear long waves in problems with axial symmetry

✍ Scribed by A.M. Shermenev

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 485 KB
• Volume: 68
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/s0021-8928(04)90027-5

✦ Synopsis

Some classical types of waves on shallow water are investigated using the Boussinesq equation in polar coordinates. In these coordinate, normal perturbation theory methods lead to overdetermined systems of linear algebraic equations for unknown coefficients. It is shown that, the special cases examined, these equations are compatible, which makes it possible to construct solutions of Boussinesq equation with the same accuracy as that with which the equation was obtained. The velocity potential specified on the bottom and the function specifying the free surface of the water are expanded in a Fourier series in terms of time. The coefficients of their first two harmonics are expressed explicitly as polynomials in Bessel functions with coefficients in the form of elementary functions of the polar coordinates.