Abstract
Abstract. 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 density-driven 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.
Highlights
Estuaries are water bodies in which rivers with fresh water meet the open sea
The dispersion derived with the maximum power method declines upstream from the inflection point in agreement with the total dispersion of the empirical Van der Burgh method, which corresponds to the theory that gravitational circulation is the dominant mixing mechanism in the landward part of these estuaries, especially in the center regime (e.g., Hansen and Rattray, 1965)
This study provides an approach to define the dispersion coefficient due to gravitational circulation, which is proportional to the product of the dispersive velocity of the gravitational circulation and the tidal excursion length
Summary
Estuaries are water bodies in which rivers with fresh water meet the open sea. The longitudinal salinity difference causes a water level gradient along the estuary. Since the hydrostatic forces at the seaside and the salinity limit are equal but opposed, this difference in the lines of action triggers an angular moment (a torque) that drives the gravitational circulation, whereby fresh water near the surface flows to the sea and saline water near the bottom moves upstream (Savenije, 2005) This density-driven gravitational circulation is one of the two most significant mixing mechanisms in alluvial estuaries; the other is the tide-driven mixing mechanism that can be dominant in the wider (downstream) part of estuaries (Fischer et al, 1979). The equation obtained appeared to have an analytical solution of a straight line for the longitudinal salinity distribution This is not correct, it can be seen as a first order approximation, which agrees with earlier theoretical work by Hansen and Rattray (1965), who developed their theory for the central region of the salt intrusion length at which the salinity gradient is at its maximum and dominated by density-driven mixing. This method has performed surprisingly well around the world and has been used in this paper as the benchmark model for comparison with the maximum power approach
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