Effects of Gravitational Settling and Riverbed‐Induced Mortality on the Transport of Drifting Fish Eggs in Rivers

Abstract Drifting fish eggs are a type of fish egg with a slightly higher density than water, requiring floating for successful hatching. While it is acknowledged that interaction with the riverbed surface can cause mortality of the eggs, the impact of this process on their downstream transport remains unclear. In this paper, we theoretically explore the transport of drifting fish eggs in turbulent open channel flows, taking into account both gravitational settling and riverbed mortality effects. This is done by incorporating a vertical drift term in the governing advection‐diffusion equation and an absorbing boundary condition for the riverbed surface, respectively. For the first time, we derive an analytical solution by the method of separation of variables for the vertical distribution of eggs during transport. Our analysis shows that in principle, settling can lead to egg accumulation near the riverbed, reducing the population's mean velocity, while conversely, riverbed mortality can decrease near‐bed accumulation and accelerate drifting to some extent. However, by estimating values of the mortality rate parameter in the real rivers, we conclude that while it can significantly affect the population size, it has a negligible effect on the vertical concentration distribution in practice, allowing for a considerable simplification of the analytical solution. Furthermore, we deduce an analytical solution for the mean velocity of the egg population, indicating variations of the deceleration rate compared to mean flow velocity, which is capable of assisting in the identification of spawning grounds. The obtained analytical solutions are validated by various numerical and experimental results.