Tidal Cycles in Stratification and Shear and Their Relationship to Gradient Richardson Number and Eddy Viscosity Variations in Estuaries

Tidal cycles in stratification and shear lead to tidal variations in mixing in many estuaries. This study 1) defines readily observable dimensionless parameters for establishing the sense and magnitude of gradient Richardson number Ri and eddy viscosity K changes from maximum to minimum stratification during a tidal cycle and 2) calculates where representative estuaries fit in this parameter space. The dimensionless parameters are Ri calculated with tidal-averaged stratification and shear, scaled stratification amplitude, and a scaled shear parameter. The scaled stratification amplitude is approximately the tidal amplitude of stratification divided by the tidal-averaged stratification. The scaled shear parameter depends on the scaled tidal amplitude of shear and the phase difference between the tidal cycles of stratification and shear. Over most of the parameter space, Ri is larger at maximum stratification. If the scaled stratification amplitude falls below a threshold value defined in terms of the scaled shear parameter, shear effects dominate and cause Ri to be greater at minimum stratification. Two-thirds of the selected estuary locations have greater Ri at maximum stratification. The remaining locations are dominated by shear differences and have an atypical mixing cycle with greater Ri at minimum stratification. The Ri and K tidal variations and the position in the parameter space can drastically shift with the spring neap cycle and spatial variations within an estuary.