Lo P.H.-Y.HONG-YUEH LO2022-03-222022-03-22202100298018https://www.scopus.com/inward/record.uri?eid=2-s2.0-85109165176&doi=10.1016%2fj.oceaneng.2021.109405&partnerID=40&md5=0debb3824ace8854c0cd03af67d559f6https://scholars.lib.ntu.edu.tw/handle/123456789/598310An 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. ? 2021 Elsevier LtdAnalytical solutionShip wakeSmall-amplitude water wave theorySokhotski–Plemelji formulaComputation theoryShipsSurface watersWakesApproximate solutionFast computationPressure-fieldShip wakesShipshapesSmall amplitude wave theorySokhotski–plemelji formulaWake patternsWater depthWater wavesamplitudeanalytical methodvesselwakewater wave[SDGs]SDG7journal article10.1016/j.oceaneng.2021.1094052-s2.0-85109165176