Calculation of Evanescent Wave Modes

Abstract

The numerical solution of the linear dispersion relation for water waves is considered for the case of the evanescent modes. A two-point Padeó approximation is constructed based upon correct asymptotic behavior at both high and low frequencies. This overcomes some difficulties experienced with a previous one-point Padeó approximation based on correct behavior at low frequencies. The two-point approximation is quite accurate but entails considerable preliminary work to obtain the coefficients. A completely different approach is also presented which only involves the solution of a quadratic equation. The results of this method are accurate to better than 0.35% for the first evanescent mode and are considerably better for the higher modes. They form reliable first estimates for use in the Newton iteration if very accurate results are required.