Approximate ship wake solution for fast computation

An approximate ship wake solution that accurately predicts both the wake patterns and the wake amplitudes in any water depth is proposed and validated. Derivation based on the small-amplitude wave theory is first revisited, treating a ship as a moving pressure field acting on the water surface. For ship shapes symmetric about the transverse (pitch) axis and away from the immediate vicinity of the ship, an approximate solution is sought. In contrast to the exact analytical solution consisting of a double integral, the approximate solution is simplified through analytical means to consist of a single integral. Singularities inside the integrand of the exact solution have also been removed. Hence, the computational effort is greatly reduced. Two extreme ship shape functions are considered to plot the solutions: a sharp rectangular shape and a smooth Gaussian shape. The newly derived approximate solution is validated using 37 satellite images of ship wakes, one towing tank experiment, and two field experiments. Then, water depth effects on wake patterns are discussed. Providing means to quickly relate the ship shape, weight, speed, and water depth to the wake characteristics, the new ship wake solution is a potentially powerful tool in the study of ship wake inversion. •A new approximate solution for ship wakes is derived and validated.•The new solution can be computed rapidly.•The new solution applies in both finite water depth and deep water.•Both continuous and discontinuous ship shapes can be considered.•Both the wake patterns and the wake amplitudes are captured.