ANOTHER LOOK AT FRESHWATER LENSES

Rising seas threaten many coastal areas with seawater intrusion and/or a loss of floating freshwater lenses. Revisiting basic concepts can enhance understanding of the appropriate use of simple relationships and the limitations of various models. The Ghyben-Herzberg relation, in which the seawater/freshwater interface is found at a depth z 40 times the height h of the water table, is based on a 1-dimensional pressure balance and has long been used to model the position of the interface. Archimedes’ principle for buoyant objects, where the displaced weight must equal the weight of the floating object, is another relevant model that is less restrictive than the Ghyben-Herzberg relation. Some simple geometrical models of floating lenses, including 2-dimensional semi-circular and parabolic models and 3-dimensional semi-spherical and paraboloidal models are considered in the context of their adherence to the Ghyben-Herzberg relation. Numerical models of floating lenses are developed using both the USGS SEAWAT model and a 3 immiscible phase Lattice Boltzmann model and also examined in light of the Ghyben-Herzberg relation. Some of the simple geometrical models that satisfy Archimedes’ principle do not satisfy the Ghyben-Herzberg relation. The Lattice Boltzmann model underpredicts the Ghyben-Herzberg z/h = 40, possibly due to surface tension effects. Simulation of static floating lenses is complicated by the involvement of the dynamical processes of diffusion and recharge.