Maximum power of saline and fresh water mixing in estuaries

According to Kleidon (2016), natural systems evolve towards a state of maximum power, leading to higher levels of entropy production by different mechanisms, including gravitational circulation in alluvial estuaries. Gravitational circulation is driven by the potential energy of fresh water. Due to the density difference between seawater and river water, the water level on the riverside is higher. The hydrostatic forces on both sides are equal but have different lines of action. This triggers an angular moment, providing rotational kinetic energy to the system, part of which drives mixing by gravitational circulation, lifting up heavier saline water from the bottom and pushing down relatively fresh water from the surface against gravity; the remainder is dissipated by friction while mixing.With a constant freshwater discharge over a tidal cycle, it is assumed that the gravitational circulation in the estuarine system performs work at maximum power. This rotational flow causes the spread of salinity inland, which is mathematically represented by the dispersion coefficient. In this paper, a new equation is derived for the dispersion coefficient related to density-driven mixing, also called gravitational circulation. Together with the steady-state advection-dispersion equation, this results in a new analytical model for densitydriven salinity intrusion. The simulated longitudinal salinity profiles have been confronted with observations in a myriad of estuaries worldwide. It shows that the performance is promising in 18 out of 23 estuaries that have relatively large convergence length. Finally, a predictive equation is presented to estimate the dispersion coefficient at the downstream boundary. Overall, the maximum power concept has provided a new physically based alternative for existing empirical descriptions of the dispersion coefficient for gravitational circulation in alluvial estuaries.