Pearl River Estuary：Nonlinearity of Subtidal Estuarine Circulation in the Pearl ...

The typical estuarine circulation has been characterized by a linear formula ever since a half-century ago when it was theorized that along-channel residual estuarine circulation is controlled by a balance between the horizontal pressure gradient and stress divergence (Pritchard, 1956[1]; Hansen and Rattray, 1965[2]; Chatwin, 1976[3]):

1ρ0⁢∂⁡p∂⁡x=Km⁢∂2⁡u∂2⁡z(1)

where, ρ0 is the water density, Km is the vertical eddy viscosity, and p and u are the tidally averaged pressure gradient and along-channel velocity, respectively. This classic theory was representative for the leading-order estuarine dynamics in the literature. Using this momentum balance and assumption of constant horizontal density gradient and vertical eddy viscosity, a linear analytical solution of the strength of residual estuarine circulation can be obtained from Eq. 1 as (Hansen and Rattray, 1965[4], namely HR65 hereafter):

uE=gρ0⁢∂⁡ρ∂⁡x⁢H348⁢Km≅...