A mathematical model for the drift and damage of drifting fish eggs incorporating multi-source damage factors

• The model incorporates the effects of multiple damage factors on fish eggs, including flow turbulence, bottom contact, and stranding. • The model differentiates between the transverse and longitudinal turbulent diffusion coefficients for egg drift and re-calibrates the proportionality constant β for the vertical turbulent diffusion coefficient. • The model summarizes the key principles for setting critical model parameters, such as the number of eggs, time step, and bottom contact damage rate. Against the strategic background of the Yangtze River Conservation and the construction of digital twin water conservancy projects, achieving high-precision, dynamic simulation of the entire process of early fish life resources, particularly for environmentally sensitive drifting eggs, has become an urgent need for river ecological management. However, existing egg drift models predominantly focus on trajectory simulation and lack quantitative, dynamic assessment of key damage factors such as flow turbulence and bottom contact, making it difficult to accurately predict egg damage risks. To address this, this study constructs a three-dimensional drift-damage mathematical model for drifting fish eggs that couples multiple damage factors. The core innovation lies in the model's systematic quantification of the damaging effects of flow turbulence, bottom contact, and stranding on eggs: it incorporates the impact of turbulent flow damage based on experimental results; determines a reasonable bottom contact damage rate through sensitivity analysis; and sets stranding water depth thresholds based on egg size. Furthermore, within the Lagrangian framework, the model innovatively differentiates between transverse and longitudinal turbulent diffusion coefficients, recalibrates the proportionality constant β for the vertical turbulent diffusion coefficient, and conducts sensitivity analyses on key model parameters, thereby enhancing the simulation accuracy for egg drift and damage. Finally, the model was deployed in both a generalized numerical flume and an actual river reach, shedding light on the fundamental patterns of egg drift and damage. This model provides a powerful simulation tool for scientifically evaluating the ecological regulation effects of river hydraulic projects, predicting the location and scale of fish spawning grounds, and precisely quantifying drifting egg risks, holding significant theoretical value and application potential for supporting river ecological protection and restoration.