DOI: https://doi.org/10.15587/1729-4061.2019.173909

### Determining the characteristics of diffracted sea waves of finite amplitude around a vessel in considerable shallow waters

Nina Efremova, Alexander Nilva, Nataliya Kotovskaya, Marina Dryha

#### Abstract

Vessels at shallow-water outer anchorage are exposed to a complex system of waves. This system results from the diffraction of sea-incident waves against a ship. When entering shallow waters, three-dimensional waves turn into two-dimensional ones. The wavelengths decrease while their periods are retained. Crests of the waves grow higher and become sharpened. A vessel at outer anchorage is surrounded by the emerging transformation zone where the waves become three-dimensional again. Defining characteristics for the sea waves, transformed by a vessel, is important for carrying out operations on eliminating oil spills. Tugboats, oil garbage collectors and boom crafts should work at any point around a vessel in emergency, in particular, from the side of incidence. That is why dimensions of the zone of waves’ transformation and the height of the waves in this zone define the safe operation of auxiliary ships. The available solution to the linear diffraction problem should be reworked to enable application of the nonlinear theory of waves.

The paper gives an equation of a wave profile at the preset points of observation around a stationary elongated vessel in considerable shallow waters. The equation was derived from the expression for the potential of velocities of the diffracted wave motion caused by the incidence of oblique regular waves with finite amplitude. The characteristics for incident waves were determined from the Stokes theory of fifth order. The non-linear problem has been transformed to a combination of five linear problems. It was solved using the method of matched asymptotic expansions (MAEM).

Based on the derived formulae, we calculated wave profiles at the assigned points around a vessel at the predefined time. There are variations in the depth of water area, the slope of waves, the course angle of waves. Examples have been provided for the profiles of nonlinear and linear waves in the plane of a vessel's cross section. We have demonstrated the similarities and differences between the linear and nonlinear waves around a vessel at shallow-water outer anchorage.

#### Keywords

diffraction of nonlinear waves against a vessel; method of matched asymptotic expansions; considerable shallow waters

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Copyright (c) 2019 Nina Efremova, Alexander Nilva, Nataliya Kotovskaya, Marina Dryha