**1. Introduction**

Ships are getting larger and faster to meet the needs of world economic development. Engine power has been increased for bigger ships leading to the use of the twin-propeller system. Kim et al. [1] and PIANC [2] stated that the twin-propeller system improved the ship power system and its handling ability. A twin-propeller ship produces a complicated jet a ffecting the navigation safety in waterways and damaging the seabed condition. Seabed scour is widely discussed due to the direct impingement of a high-velocity jet to cause excessive sediment transport in harbour and waterways. Hamill [3] and Gaythwaite [4] stated that the impingement of the ship's propeller jet can damage the seabed.

Albertson et al. [5] firstly proposed the e fflux velocity within the plain water jet from orifice being predicted using axial momentum velocity. Blaauw and van de Kaa [6] and Verhey et al. [7] suggested the use of a theoretical foundation of a plain water jet in Albertson et al. to investigate the ship propeller jet induced seabed scour in the harbour without consideration of the berth structure. Hamill et al. [8], Lam et al. [9] and Hong et al. [10] continued the investigations in laboratories by using a physical single propeller model to observe the scouring condition. Hamill et al. [11] include the effects of the quay wall in the seabed scour prediction. The aforementioned researchers emphasised on the estimation of maximum scour depth induced by ship propeller wash. Wang et al. [12], Sun et al. [13] and Ma et al. [14] implemented the foundation of propeller jet induced scour to predict the wake of tidal turbine and the tidal turbine induced scour and Jiang et al. [15] proposed the theoretical structure of ship twin propeller jet.

The impingement of this rotating jet forms the scour pit with the scoured sediments being transported downstream to form dune deposited surrounding the scour pit on the seabed when the

watercraft or vessels entering a port. The accumulated sediment forms a dune reducing the water depth and increasing the risk of ship collision in shallow waterways. A ship propeller can be damaged when hitting the seabed. The understanding of both the scour pit and deposition dune are important to ensure navigation safety. Twin-propeller jet produces the scour profiles with deposited dune downstream, which is di fferent compared to the single-propeller. Yew et al. [16] and Hong et al. [10] stated that the deposition is an M-shaped distribution with the largest accumulated height on the longitudinal axis of both propellers. The height of deposited dunes decreased along the side of two propellers surrounding scour hole.

In this works, a purpose-built power train system was developed to rotate the physical propeller model at the desired rotational speeds in the laboratory in order to investigate the ship twin-propeller jet induced scour. Previous researchers used the maximum scour depth without available equations to predict the entire cross-section of the scour profile. The current experimental data were used to establish the 2D scour model by proposing the scour depth equation and Gaussian normal distribution to estimate the entire scour profile for both single-propeller and twin-propeller systems.
