Approximate ship wake solution for fast computation
Journal
Ocean Engineering
Journal Volume
235
Date Issued
2021
Author(s)
Lo P.H.-Y.
Abstract
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. ? 2021 Elsevier Ltd
Subjects
Analytical solution
Ship wake
Small-amplitude water wave theory
Sokhotski–Plemelji formula
Computation theory
Ships
Surface waters
Wakes
Approximate solution
Fast computation
Pressure-field
Ship wakes
Shipshapes
Small amplitude wave theory
Sokhotski–plemelji formula
Wake patterns
Water depth
Water waves
amplitude
analytical method
vessel
wake
water wave
Type
journal article