## 1 Introduction  
The rising demand for oil and gas in society implies a greater need for transportation via pipelines, vessels, and other means, thereby escalating the frequency and scale of energy transportation activities. With the amplification of energy transport operations, the probability of oil spill incidents during transportation also increases. Factors contributing to this include natural environmental conditions during navigation, potential equipment and facility malfunctions, as well as human error [1; 2; 3]. On 26 July 2010, a crude oil pipeline rupture of the Canadian pipeline company Enbridge located in the territory of Michigan resulted in the flow of at least 4000 cubic meters of crude oil into the Kalamazoo River, which has become one of the largest crude oil spills in the history of the United States [4]. On 22 November 2013, an oil pipeline rupture occurred at the Qingdao Oil Transmission and Storage Company (QOTSC), with some of the crude oil entering the Jiaozhou Bay along a stormwater pipeline, resulting in the contamination of approximately 3000 square meters of sea surface in the Jiaozhou Bay. Subsequently, a huge explosion occurred, resulting in 63 deaths and 156 injuries [5]. On 5 July 2020, the Japanese cargo ship Wakashio spilled off the southeast coast of Mauritius, with more than 1000 tonnes of fuel oil leaking into the Indian Ocean, threatening many rare species [6]. Oil spills not only cause serious pollution to the environment but also cause serious damage to the flora and fauna in the watershed and even to human life [7; 8; 9]. The study on oil spills in waters began in the 1960s. With the long-term development of hydrodynamic modeling, oil spill modeling, and numerical methods, the observation of the physical behavior of oil spills in watersheds using numerical simulation has been widely applied [2; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19]. [PERSON] and [PERSON] et al. [20] established a two-dimensional hydrodynamic model of Daya Bay in the South China Sea and studied the behavior and fate of oil spills in both clockwise and anticlockwise currents. [PERSON] et al. [5] established a model of the oil spill in Jiaozhou Bay and verified the accuracy of the model with the \"11.22\" oil spill in Huangdao Island, and studied the effects of wind speed, tidal currents, and the location of leakage on the drifting and diffusion movements of oil spills. [PERSON] [21] established the Red Sea Lagrangian oil spill transport model to simulate the migration of oil spills in winter and summer seasons, different oil spill locations, and different current environments. [PERSON] [22] developed a trajectory modeling of the oil spill in the Bosphorus Strait, investigated the short-term spreading behavior of the oil spill under different wind directions, and made recommendations for the oil spill contingency plan in the basin. [PERSON] [18] developed a two-dimensional hydrodynamic and oil spill transport model for the Yangtze River estuary, which mainly investigated the effects of wind and wave current interactions on the drift and diffusion behavior of oil spills under strong wind conditions. [PERSON] and [PERSON] et al. [23] developed a hydrodynamic model and Lagrangian transport model for the Santana channel watershed in the lower Amazonian River flow, which simulated the spatial and temporal displacements of oil spills and the contaminated area of the oil sheer in the dry and rainy seasons and pointed out the critical contaminated zones and sensitive areas under the spill. [PERSON] and [PERSON] et al. [24] established an oil spill model for an inland waterway and calibrated and validated the model by using flume experiments. The model was applied to the Luoqi section of the Yangtze River, and the migration trajectories of the oil spill were simulated under two scenarios of high flow and low wind speed and low flow and high wind speed.