Abstract
Several field studies in bays and estuaries have revealed pronounced subsurface maxima in the vertical profiles of the current amplitude of the principal tidal harmonic, or of its vertical shear, over the water column. To gain fundamental understanding about these phenomena, a semi-analytical model is designed and analysed, with focus on the sensitivity of the vertical structure of the tidal current amplitude to formulations of the vertical shape of the eddy viscosity. The new analytical solutions for the tidal current amplitude are used to explore their dependence on the degree of surface mixing, the vertical shape of eddy viscosity in the upper part of the water column and the density stratification. Sources of surface mixing are wind and whitecapping. Results show three types of current amplitude profiles of tidal harmonics, characterised by monotonically decreasing shear towards the surface, “surface jumps” (vertical shear of tidal current amplitude has a subsurface maximum) and “subsurface jets” (maximum tidal current amplitude below the surface), respectively. The “surface jumps” and “subsurface jets” both occur for low turbulence near the surface, whilst additionally the surface jumps only occur if the eddy viscosity in the upper part of the water column decreases faster than linearly to the surface. Furthermore, “surface jumps” take place for low density stratification, while and “subsurface jets” occur for high density stratification. The physics causing the presence of surface jumps and subsurface jets is also discussed.
Highlights
Tides are often a significant, if not dominant, constituent of the water motion in bays and estuaries
These results suggests that the SJ-I occurs if the eddy viscosity in the upper layer of water column decreases faster than linearly towards the surface (n > 1)
The key hypothesis was that these phenomena are related to site-specific conditions, in particular density stratification and sources of turbulence at the surface
Summary
Tides are often a significant, if not dominant, constituent of the water motion in bays and estuaries. Warner et al 2005; Burchard and Hetland 2010) These studies showed explicit results of tides obtained with models that apply second-order closure schemes for eddy viscosity. It appears that, in order to achieve good representations of the vertical structure of tidal currents, sophisticated formulations are required for vertical eddy viscosity, the latter representing the degree of vertical mixing. When the main interest is rather in gaining fundamental insight into tidal dynamics, i.e. to identify and analyse processes that cause a specific observed feature, such models are less suitable tools, owing to their complexity For such purposes, idealised models have been developed and analysed, which rely on simple formulations of eddy viscosity (Johns 1966; Ianniello 1977; Friedrichs and Hamrick 1996; Huijts et al 2006; Winant 2007; Zitman and Schuttelaars 2012)
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