Lagrangian model of a surface-advected river plume

A Lagrangian model of a surface-advected river plume is developed. The model combines the deterministic approach resulting from the momentum budget with a random-walk scheme. We validated and applied the model to the conditions of the region adjacent to the Mzymta River estuary in the Black Sea. Further, using the model, we investigated the dependencies between the spatial extent of the plume and the wind stress τ. The character of these dependencies proved to depend critically on the wind direction with respect to the geometry of the coast and the river mouth. With the offshore and “downwelling favorable” alongshore winds, the plume area initially grows with the increase of τ, and then starts to decrease when τ exceeds a certain critical value. With the onshore wind, the area decreases steadily (though not linearly) as τ increases. The most complex behavior is observed for the “upwelling favorable” alongshore wind: the plume area initially decreases until the wind stress exceeds a certain critical value, then starts to increase with τ and attains a maximum, and then eventually drops to zero as τ continues to increase. As expected, the increase of the inflow velocity, i.e., discharge rate, resulted in the growth of the plume area, while the patterns of the dependencies between the plume area and the wind stress configurations were robust in the broad range of intermediate discharge values. We also investigated the dependence of the plume area on the latitude, with all other conditions kept fixed. This dependence exhibited a distinct “M-shaped” pattern, with minima corresponding to the equatorial and polar regions, and maxima in the tropics. However, even moderate wind stress largely offsets the effect of the changing Coriolis parameter and strongly distorts the shape of the curve.