Abstract
We present the kinematic model of the ship wake in the presence of horizontal subsurface current linearly varying with the depth of water. An extension of the Whitham–Lighthill theory for calm water is developed. It has been established that the structure of ship waves under the action of a shear flow can radically differ from the classical Kelvin ship wake model. Co propagating ship and shear current lead to increasing the total wedge angle up to full one 180° and decreases for the counter shear current. At relatively large unidirectional values of the shear current, cusp waves in the vicinity of the wedge boundary are represented by transverse waves and, conversely, by diverging waves directed almost perpendicular to the ship track for the opposite shear current. The presence of a shear flow crossing the direction of the ship’s movement gives a strong asymmetry of the wake. An increase in the perpendicular shear flow leads to an increase in the difference between the angles of the wake arms. The limiting value of the shear current corresponds to one or both arms angles equal to 90°. Transverse and divergent edge waves for this limiting case coincide.
Highlights
Our study aims to analyze the structure of stationary ship waves in the presence of a given shear current Uc
We extend the theory for the wave’s propagation in the presence of the shear current with constant vertical shear U 0
Collinear Propagation of the Ship and Shear Flow (U0X = 0, U0Y = 0) We start with the simplest case of collinear ship propagation and shear flow along the
Summary
The Kelvin solution’s main features were reproduced by Lighthill and Whitham [2,3], who suggested the kinematics of the ship wave’s model Comparison of these theoretical results with observations revealed that, there is generally acceptable qualitative agreement, there are essential differences between the predicted and measured geometry of the Kelvin diagram in the ship’s wake. The significant effects of finite water depth were included in consideration of this problem in [17] Another possibility of analyzing the influence of horizontal shear current on the ship’s wake is developing an extended kinematic model of the wake, originally proposed in [2,3]. This is the purpose of this study.
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