Calculation of ship-wave height in inland waterways based on multi-factor coupling
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Abstract
As vessel-induced hydrodynamic effects intensify, the stability of inland waterway bank slopes is increasingly challenged, and ship-induced waves have emerged as a dominant dynamic driver. Beyond bank scour, these waves can trigger geotechnical damage in riparian zones, amplify the surging of moored vessels, and compromise navigational safety, often necessitating substantial investment in bank protection and slope rehabilitation. This challenge is particularly relevant to the Guangxi Pinglu Canal, where large cargo vessels operate in confined reaches and bank protection design depends on reliable estimates of ship-wave height. Existing prediction methods remain inadequate for modern canals. In particular, traditional semi-empirical approaches represented by the Delft Hydraulic Formula were largely calibrated using tugs, patrol boats, and empty barges operating in relatively open waters, and therefore do not fully capture the hydrodynamics of contemporary deep-draft bulk carriers and container ships in restricted cross-sections. Direct application of such legacy formulas can therefore produce large errors in inland settings. To address this gap, the present study investigates ship-wave height prediction in inland waterways through a combined program of large-scale indoor flume experiments and computational fluid dynamics (CFD) simulations. In the experimental component, high-precision 3D-printed scale models (1:108) of a standard KCS container ship and a 3,000-ton bulk carrier were tested in a large indoor flume. Wave elevation time series were recorded at multiple monitoring points to characterize maximum wave height and associated wake features. A total of 117 operating conditions were arranged by systematically varying three key variables: vessel speed, draft, and offshore distance. This dataset enabled two methodological advances. First, with explicit consideration of vessel scale, speed, and draft, the ship-type coefficient in the classic Delft Formula was recalibrated to better represent the hull characteristics of modern inland freight vessels. Second, a new, dimensionally consistent empirical wave-height formula was derived via multivariate linear regression. The model incorporates key nondimensional parameters—including the Froude number, blockage-related terms, and the depth-to-draft ratio—capturing coupled interactions between vessel motion and channel confinement. In parallel, a STAR-CCM+ CFD model was developed to simulate ship-wave evolution under the same operating conditions and to examine wave-generation mechanisms under multi-factor coupling. Comparison with laboratory measurements shows good agreement, supporting the reliability of the numerical framework. The integrated evidence indicates that channel backwater rise increases with draft and that the backwater influence zone expands as draft increases. In addition, the Kelvin wake angle and wave period decrease as vessel speed and draft increase. Under damping effects in confined waterways, the dominant wave trough shifts rearward and the wake pattern becomes increasingly complex. These changes influence wave height more strongly than wavelength, providing a practical reference for characterizing ship-wave dynamics in restricted inland channels. The principal conclusions are as follows. Vessel speed is the primary factor governing ship-induced waves. Wave height increases with speed and draft, whereas it decreases as channel water depth and offshore distance increase. Moreover, the hydrodynamic pressure exerted on the free surface increases with draft, contributing to the corresponding rise in wave height. The study verifies the feasibility and predictive accuracy of both the modified Delft Formula–based theoretical approach and the STAR-CCM+ CFD framework for inland ship-wave prediction, supporting their application in bank protection design and scour-mitigation planning. This research clarifies the generation mechanisms of ship-induced waves in inland waterways and provides a higher-accuracy method for predicting wave height under practical operating conditions. The findings offer direct engineering value for bank protection design and bank-slope erosion control and are particularly relevant to canal projects where ship-induced waves pose a persistent threat to bank stability, such as the Guangxi Pinglu Canal. The results also establish a basis for subsequent investigations of ship-wave impacts on bank-slope stability and provide guidance for the operation and maintenance of inland waterway infrastructure under dynamic loading.
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