On analytical solutions for transient water waves radiated by cylinders

Analytical solutions for transient water waves radiated by a circular cylinder in deep water are studied in this paper. Within the framework of the potential flow and linear water wave theory, time-domain solutions are analytically derived based on decomposition of the velocity potential consisting of an instantaneous term and a memory term. These two terms are solved by satisfying the governing equations and initial boundary conditions. Transient concentric water waves are further studied and evaluated for a pulsating circular cylinder which expands and contracts radially. Results are compared with those from other numerical models with a good agreement in terms of wave elevation on the free surface. Analytical solutions obtained in this work can be considered as a benchmark in time-domain analysis for linear hydrodynamic problems, and are of help to the theory and application of wavemakers and transient water waves.