Abstract
Navigating in two layers is a common case for ships. It's reported the rigid bed of shallow water areas, such as ports, navigation channels, harbors and river estuaries, is often covered by a mud layer which consists of a dense mixture of water and particles of sand, clay and etc1). Additionally, it's well known the density stratification occurs in Norwegian fiords and ice-rimmed seas. It's due to the variation in salinity and temperature with depth. When navigating at a low speed in such sites, a ship accidentally experiences the large drag mainly due to the wave-making on the interface. Understanding the ship hydrodynamics in two layers is a must for her safe navigation. However there apparently has been not so many experimental and theoretical works so far.This paper proposes a new method to solve the ship steady wave-making problem in two layers. A Green function which satisfies the linearized interface condition and the rigid bottom surface condition was newly derived and used for the expression of the velocity potentials. In this method, the hull shape and the interaction between the free surface and the interface can be considered more exactly so that the ship wave-making in two layers can be discussed more correctly. First, the wave patterns generated by a single source and the wave-making resistance of a submerged spheroid were calculated to prove the validity of the proposed method. Second, Wigley hull was used for calculations and it was numerically confirmed that the sharp increase of the wave-making resistance occurred when navigating close at the critical velocity of the internal waves. The proposed method succeeded to capture the waves both on the free surface and interface properly through a series of calulations.
