Quantifying the Contributions of Tidal Straining and Gravitational Circulation to Residual Circulation in Periodically Stratified Tidal Estuaries

Abstract

This numerical modeling study quantifies for the first time the contribution of various processes to estuarine circulation in periodically stratified tidal flow under the impact of a constant horizontal buoyancy gradient. The one-dimensional water column equations with periodic forcing are first cast into nondimensional form, resulting in a multidimensional parameter space spanned by the modified inverse Strouhal number and the modified horizontal Richardson number, as well as relative wind speed and wind direction and the residual runoff. The along-tide momentum equation is then solved for the tidal-mean velocity profile in such a way that it is equated to the sum of the contributions of tidal straining (resulting from the temporal correlation between eddy viscosity and vertical shear), gravitational circulation (resulting from the depth-varying forcing by a constant horizontal buoyancy gradient), wind straining, and depth-mean residual flow (resulting from net freshwater runoff). This definition of tidal straining does not only account for tidal asymmetries resulting from horizontal buoyancy gradients but also from wind straining and residual runoff. For constant eddy viscosity, the well-known estuarine circulation analytical solution with polynomial residual profiles is directly obtained. For vertically parabolic and constant-in-time eddy viscosity, a new analytic solution with logarithmic residual profiles is found, showing that the intensity of the gravitational circulation scales with the horizontal Richardson number. For scenarios with realistic spatially and temporally varying eddy viscosity, a numerical water column model equipped with a state-of-the-art two-equation turbulence closure model is applied to quantify the individual contributions of the various processes to estuarine circulation. The fundamental outcome of this study is that, for irrotational flow with periodic stratification and without wind forcing and residual runoff, the tidal straining is responsible for about two-thirds and gravitational circulation is responsible for about one-third of the estuarine circulation, proportionally dependent on the horizontal Richardson number, and weakly dependent on the Strouhal number. This new and robust result confirms earlier estimates by H. Burchard and H. Baumert, who suggested that tidal straining is the major generation mechanism for estuarine turbidity maxima. However, a sensitivity analysis of the model results to details of the turbulence closure model shows some uncertainty with respect to the parameterization of sheared convection during flood. Increasing down-estuary wind straining and residual runoff reduce the quantitative contribution of tidal straining. For relatively small horizontal Richardson numbers, the tidal straining contribution to estuarine circulation may even be reversed by down-estuary wind straining.

On the use of the Stokes number to explain frictional tidal dynamics and water column structure in shelf seas

“…By demonstrating that, apart from bottom and surface roughness lengths, Str is the only parameter defining the dynamics of the well-mixed irrotational pressure gradient driven tidal flow, they could show how the relative time lag of turbulent parameters with respect to the bed stress increases with Str, in a similar way to Simpson et al (2000) and Souza et al (2004). Burchard (2009), Burchard and Hetland (2010) and Souza et al (2013) have used this idea to define the behaviour of tidal and oscillatory flows in shelf seas using turbulent closure models. It needs to be mentioned that Prandle (1982), Baumert and Radach (1992), Burchard (2009) and Burchard and Hetland (2010) have defined the Strouhal wrongly as its inverse.…”

“…The results presented here also suggest that the rotational Stokes number should be used to describe shallow shelf seas or estuaries, where the effect of the earth's rotation is appreciable. This could be important in places like Liverpool Bay, where the frictional layer without considering rotation can be overestimated (cyclonic rotation) or underestimated (anticyclonic rotation) by more than 10 m. This should be considered when classifying estuaries and ROFIs (regions of freshwater influence), like those proposed by Burchard (2009) and Burchard and Hetland (2010). This is not unique to Liverpool Bay as there are other shelf seas that have shallow areas with strong cyclonic and anticyclonic currents, e.g.…”

“…Burchard (2009), Burchard and Hetland (2010) and Souza et al (2013) have used this idea to define the behaviour of tidal and oscillatory flows in shelf seas using turbulent closure models. It needs to be mentioned that Prandle (1982), Baumert and Radach (1992), Burchard (2009) and Burchard and Hetland (2010) have defined the Strouhal wrongly as its inverse.…”

Modelling-based assessment of suspended sediment dynamics in a hypertidal estuarine channel

“…From a physical process pointof-view, process-based modelling is extremely valuable towards isolating and assessing specific processes, either via the invasive numerical approach of switching on or off given processes, or via selective analysis of individual contributions from numerical simulations with high predictive skill (e.g. Burchard and Hetland, 2010). From a modelling point-of-view, even though three-dimensional baroclinic models are demanding both in terms of computational power and quantity of input data, they are necessary to fully represent estuarine dynamics.…”

“…Less complex approaches fundamentally rely on simplifying assumptions and may not be able to represent all required processes. For example, depth-averaged modelling cannot reproduce all baroclinic processes (e.g., Souza and Lane, 2013), and local one-dimensional vertical models commonly assume simple behaviour of horizontal (density) gradients (e.g., Simpson and Souza, 1995;Burchard and Hetland, 2010). …”