Intrinsic role of Lagrangian and Stokes drift owed to currents in a stratified three-layered channel with interfacial tensions

Abstract

The present study analyses the trajectories of the fluid particles, Stokes drift and Lagrangian drift mechanisms for three-layered internal flow having two interfaces with interfacial tensions. The three-fluid layers are of different densities. A uniform and two dimensional current is flowing in each fluid layer. The pathline equations with first-order solution analysis produces closed trajectories. The trajectories of the fluid particles in the middle layer shows non-monotonic trend as it is subjected to two interfaces and get shorten according to the strength of density stratification and interfacial tensions. The analytical expressions for Stokes drift are found in each layer using small-excursion principle. Based on these expressions, we found that the variation in density causes the Stokes drift displacement to increase more robustly after a critical density ratio for both interfaces. The underlying mechanism of this behaviour is the phase reversal phenomenon which is analysed via phase plane analysis. The trajectories in spatial phase plane are open implying that Stokes drift occurs in each fluid layer. Moreover, the change in density ratio alters the direction of these open trajectories in middle layer at both interfaces, which are shown by drawing their directional fields. The expressions for Lagrangian drift which are dependent on density variations and interfacial tensions are analysed by the ratio of Eulerian return flow to the depth averaged Stokes drift at both interfaces. It is found that weak stratification with higher tension at interface lead to dominance of Eulerian return flow over averaged Stokes drift for middle layer. Also, the effect of these parameters are predominant in the intermediate wave regimes. These observations are essential for understanding the wave characteristics, sediment movement, anticipating the dispersal of contaminants, and modelling climate-related processes like the spread of heat and carbon. Therefore, the study of multilayer systems with Stokes and Lagrangian drift has a considerable potential to further our understanding of marine processes, especially in areas where internal wave action and substantial stratification are present.