Combined Effects of Wind, Tide, and Horizontal Density Gradients on Stratification in Estuaries and Coastal Seas

Abstract

The aim of this one-dimensional water column study is to combine modified versions of three characteristic parameters for periodic tidal flow under the influence of a longitudinal buoyancy gradient?the horizontal Richardson number, the inverse Strouhal number, and the inverse Ekman number?into a parameter space study, including constant wind forcing from various directions. It is shown how the underlying dynamical equations can be cast into nondimensional form, depending mainly on these three nondimensional parameters plus the relative wind speed and the wind direction. Idealized model simulations are carried out for the whole realistic range of horizontal Richardson and inverse Strouhal numbers for various latitudes, showing the amplitude of the tidally induced stratification for a wide range of scenarios. It is found that classical threshold values for the horizontal Richardson number, indicating the switch from periodic stratification to permanent stratification, are valid only for special cases, and that this switch also strongly depends on the inverse Strouhal number, the inverse Ekman number, and the wind vector. The transverse residual flow is close to the thermal wind balance for a variety of parameters, and nondimensionalized longitudinal residual flow shows the classical estuarine exchange flow pattern with little variation in the near-bed onshore component. Wind straining is confirmed as an important estuarine and coastal process, enhancing estuarine circulation for offshore (down estuary) winds and vice versa. Agreement with field data from Liverpool Bay is good, including the explanation of a flood tide local maximum of the dissipation rate in the upper half of the water column. An equation for the second time derivative of the potential energy anomaly is derived for quantifying the dynamical processes leading to stratification due to the straining of the horizontal density gradient.