An analytical model for mass transport calculations in a viscous muddy layer

Abstract

This study aims to present analytical solutions to the interactions between waves, currents, and the muddy bed layer and compare the results for different constant, linear, and second-order current profiles. The effects of mean shear stress and its variations on wave dispersion relations as well as mud (particle and mass transport) velocities are investigated. It is found that the second-order profile presents the maximum effects on the wave field (wave dissipation and mud mass transport velocities) compared to the constant and linear current profiles. However, assuming the constant current profile, frequently applied in the literature models, results in the minimum effects. A local peak exists in the mud mean discharge over the current profile curvature. The mud velocity induced by the linear current profile presents the closest value to the particle velocity for the no-current case. Additionally, the second-order current profile provides slightly better results for the mud mass transport velocity rather than the constant current profile when comparing the results with the laboratory data.