Circulation and Mixing in Steady-State Models: Well-Mixed Estuary
In this chapter, the analytic model of circulation and mixing in a well-mixed and laterally homogeneous estuary (Types 1 or D) will be presented.
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Circulation and Mixing in Steady-State Models: Well-Mixed Estuary
In this chapter, the analytic model of circulation and mixing in a well-mixed and laterally homogeneous estuary (Types 1 or D) will be presented. In contrast to that of the salt wedge estuary, the vertical salinity stratification of a well-mixed estuary is the complete opposite, being very weak. These conditions are characteristic of estuaries in regions of low river discharge, where the circulation and mixing processes are dominated by tidal forcing. As the vertical salinity (density) gradient is very low, it may be practically neglected, and in steady-state conditions, the fresh water discharge and tidal forcing remain constant during tidal cycles. In practice, these simplifying conditions are simulated by mean values during tidal cycles, resulting in a one-directional seaward circulation (Fig. 10.1). In the mixing zone (MZ), the longitudinal salinity (density) gradient is much less intense than that observed in partially mixed estuaries, as indicated in Chap. 8 (Fig. 8.1). However, the integrated influence of the baroclinic pressure gradient associated with the internal friction is one of the processes responsible for the occurrence of the small vertical velocity shear. Eventually, in relatively deep estuaries, this integrated influence may generate weak gravitational circulation and landward motions in bottom layers.
10.1
Hydrodynamic Formulation and Hypothesys
Let us consider a laterally homogeneous, well-mixed estuary with the objective of introduce an analytical model to calculate the vertical velocity profile, u = u(x, z), the free surface slope, ∂η/∂x, and the longitudinal salinity variation S = S(x, z), which are generated by the fresh water discharge, the gradient pressure force and the surface wind stress. The approach we will take to achieve this follows the articles of Arons and Stommel (1951), Maximon and Morgan (1955), Officer (1976, 1977) and Prandle (1985). By hypothesis, the estuary has a simple geometry with constant width (B) and depth (h), as schematically shown in Fig. 10.2. The Oxz © Springer Nature Singapore Pte Ltd. 2017 L. Bruner de Miranda et al., Fundamentals of Estuarine Physical Oceanography, Ocean Engineering & Oceanography 8, DOI 10.1007/978-981-10-3041-3_10
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10 Circulation and Mixing in Steady-State Models: Well-Mixed Estuary
Fig. 10.1 Steady-state vertical salinity and velocity distribution in a well-mixed estuary, with small vertical salinity gradients which may be found in nature. S0 is the salinity at the coastal ocean, which is a boundary condition to the salt conservation equation
Fig. 10.2 Diagram of a well-mixed estuary and the coordinate system used in the theoretical development. S = S(x, z) or q = q(x, z), η = η(x) and H0 indicate the longitudinal salinity or density distribution, the free surface slope and the depth at the estuary head, respectively
referential system will be used, with the vertical axis (Oz) originating at the free surface and oriented in the direction of the gravity accel
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