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Drivers of Residual Estuarine Circulation in Tidally Energetic Estuaries: Straight and Irrotational Channels with Parabolic Cross Section

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Drivers of Residual Estuarine Circulation in Tidally Energetic Estuaries: Straight and Irrotational Channels with Parabolic Cross Section 548 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 41 Drivers of Residual Estuarine Circulation in Tidally Energetic Estuaries: Straight and Irrotational Channels with Parabolic Cross Section HANS BURCHARD Leibniz Institute for Baltic Sea Research Warnemu¨nde, Rostock, Germany ROBERT D. HETLAND Department of Oceanography, Texas A&M University, College Station, Texas ELISABETH SCHULZ Leibniz Institute for Baltic Sea Research Warnemu¨nde, Rostock, Germany HENK M. SCHUTTELAARS Delft Institute of Applied Mathematics, Delft University of Technology, Delft, Netherlands (Manuscript received 19 February 2010, in final form 5 November 2010) ABSTRACT The generation of residual circulation in a tidally energetic estuary with constant longitudinal salinity gradient and parabolic cross section is examined by means of a two-dimensional cross-sectional numerical model, neglecting river runoff and Stokes drift. It is shown how the longitudinal and lateral residual circu- lation can be decomposed into contributions from various processes such as tidal straining circulation, gravitational circulation, advectively driven circulation, and horizontal mixing circulation. The sensitivity of the residual circulation and its components from various processes to changes in forcing is investigated by varying the Simpson number (nondimensional longitudinal buoyancy gradient) and the unsteadiness pa- rameter (nondimensional tidal frequency), as well as the bed roughness and the width of the estuary. For relatively weak salinity gradient forcing, the tidal straining circulation dominates the residual exchange cir- culation in support of classical estuarine circulation (up-estuary flow near the bed and down-estuary flow near the surface). The strength of the longitudinal estuarine circulation clearly increases with increased salinity gradient forcing. However, when the Simpson number exceeds 0.15, the relative contributions of both gravitational circulation and advectively driven circulation to estuarine circulation increase substantially. Lateral residual circulation is relatively weak for small Simpson numbers and becomes flood oriented (di- vergent flow near the bed and convergent flow near the surface) for larger Simpson numbers because of increasing contributions from gravitational and advectively driven circulation. Increasing the unsteadiness number leads to decreased longitudinal and lateral residual circulation. Although changes in bed roughness result in relatively small changes in residual circulation, results are sensitive to the width of the estuary, mainly because of changes in residual exchange circulation driven by tidal straining. 1. Introduction purpose, a two-dimensional cross-sectional numerical model is applied, with prescribed longitudinal salinity The aim of this study is to quantify the contributions gradients and barotropic pressure gradients induced by of major processes to longitudinal and lateral resid- semidiurnal tidal forcing, under the assumption that all ual circulation in tidally energetic estuaries. For this other longitudinal gradients are negligible. The residual circulation is decomposed into residual exchange and local runoff contributions from straining, gravitational Corresponding author address: Hans Burchard, Leibniz Institute for Baltic Sea Research Warnemu¨ nde, Seestraße 15, D-18119 circulation, lateral advection, and lateral mixing, both Rostock, Germany. in the longitudinal and lateral directions. Zero net river E-mail: [email protected] discharge and a rigid lid (neglect of Stokes drift) are DOI: 10.1175/2010JPO4453.1 Ó 2011 American Meteorological Society Unauthenticated | Downloaded 10/06/21 05:22 PM UTC MARCH 2011 B U R C H A R D E T A L . 549 assumed, and a symmetric, parabolic bathymetry is used. mixing during flood and suppression of vertical mixing Effects of the earth’s rotation, wind straining, bathymet- during ebb) contributes to estuarine circulation: during ric variations, residual river runoff, and Stokes drift will flood, considerably more momentum is mixed down to be investigated in follow-up studies. The major tool used the near-bottom region than during ebb, resulting in in the present study is the estuarine circulation analysis a near-bottom up-estuary excess velocity. In the present recently introduced by Burchard and Hetland (2010). study, this contribution to estuarine circulation is re- This analysis provides a semianalytical decomposition of ferred to as tidal straining circulation. Burchard and the residual flow profiles into contributions from all pro- Baumert (1998) showed in a (two-dimensional longitu- cesses included in the momentum balance. These contri- dinal) numerical model study of a partially mixed estu- butions are solved numerically, because analytical solutions ary that this tidal straining circulation contributes more are available only for strongly simplified situations. This to the generation of estuarine circulation than gravita- analysis tool is extended here for two-dimensional cross- tional circulation. The importance of tidal straining sectional models, including longitudinal, lateral, and circulation has later been highlighted by Stacey et al. vertical velocity components. (2001, 2008). Recently, Burchard and Hetland (2010) This semianalytical method is based on the same prin- showed for periodically mixed estuaries that the tidal ciples as previous approaches that applied a vertically and straining amounts to typically two-thirds of the estuarine temporally constant eddy viscosity and calculated con- circulation (with a one-third contribution from gravita- tributions to residual currents by tidally averaging the tional circulation) for negligible wind stress, no river momentum equations and vertically integrating the discharge, and no effects from the earth’s rotation and resulting equations twice (Hansen and Rattray 1965; channel geometry. However, this dominance of the tidal Chatwin 1976; MacCready 2004; Huijts et al. 2006). Re- straining was shown to decrease with the stability of the cently, Huijts et al. (2009) demonstrated how analytical flow. solutions for the major contributions to residual currents Another important mechanism for creating estuarine can be obtained for longitudinal and lateral components, circulation has been proposed by Lerczak and Geyer assuming constant eddy viscosity (thus eliminating tidal (2004), who found in an idealized model study of a straining) and diagnostically prescribed lateral density straight channelized estuary that redistribution of lon- gradients (thus removing parts of the contributions from gitudinal momentum by lateral advection generates re- lateral advection driven by lateral density gradients). In sidual currents in support of estuarine circulation. The the present study, some simplifications made by Huijts underlying mechanism for generating the lateral circu- et al. (2009) due to the requirement for analytical solutions lation required for this advectively driven redistribution are removed by solving the resulting complex analytical has already been described by Nunes and Simpson expressions numerically. Apart from that, we follow the (1985) for weakly stratified estuaries: during flood, lat- approach of Huijts et al. (2009). eral differential advection builds up a salinity maximum Classically, estuarine circulation has been attributed in the center line of the estuary, which leads to lateral to gravitational circulation (see Pritchard 1952, 1954, salinity gradients toward both sides of the estuary, 1956; Hansen and Rattray 1965; Chatwin 1976). The generating in turn a lateral estuarine circulation with analytical solutions for gravitational circulation based near-bottom currents directed to the sides and converg- on constant eddy viscosity originally presented by ing near-surface currents, both associated with downw- Hansen and Rattray (1965) have been extended to in- elling in the center of the flow. With this, the advectively clude wind straining (Wong 1994; Ralston et al. 2008) driven contribution to estuarine circulation can be ex- and parabolic eddy viscosity (McGregor 1972; Ianniello plained as follows: During flood, the higher longitudinal 1977; Burchard and Hetland 2010). All these theories momentum is advected near the bottom toward the have in common that a tidal modulation of the estuarine sides (there increasing momentum). Furthermore, the circulation other than a modification of the tidal-mean downwelling advects faster near-surface currents down eddy viscosity is not considered. to the near-bottom region in the center of the flow. As Effects of ebb–flood asymmetries in vertical differ- a compensation, near the surface, slower velocities are ential advection have first been acknowledged by van advected toward the center of the flow, there de- Aken (1986) and Simpson et al. (1990) as processes creasing the flood momentum. Because the same hap- leading to a destabilization of the water column during pens during ebb, but with different signs of velocities flood (denser offshore waters sheared over less dense and their gradients (such that the advective terms have onshore waters) and vice versa during ebb. Jay and the same sign during ebb and flood), a residual current Musiak (1994) suggested a mechanism how the associ- with a near-bottom up-estuary component is forced. ated tidal mixing asymmetry (enhancement of vertical This mechanism has recently been confirmed for stratified Unauthenticated | Downloaded 10/06/21 05:22 PM UTC 550 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 41 estuaries by means of idealized (Cheng
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